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SUMMARY:Conference on Geometry and Statistics
DESCRIPTION:Conference on Geometry and Statistics \nDates: November 17–19\, 2025 \nLocation: CMSA G10\, 20 Garden Street\, Cambridge MA & via Zoom \n  \nSpeakers \n\nCharles Fefferman\, Princeton University\nStephan Huckemann\, Georg-August Universität Göttingen\nSungkyu Jung\, Seoul National University\nKei Kobayashi\, Keio University\nClément Levrard\, Université de Rennes\nKer-Chau Li\, University of California\, Los Angeles\nRong Ma\, Harvard University\nSteve Marron\, University of North Carolina\nEzra Miller\, Duke University\nHans-Georg Müller\, University of California\, Davis\nWilderich Tuschmann\, Karlsruhe Institute of Technology\nMelanie Weber\, Harvard University\nAndrew Wood\, Australian National University\nHorng-Tzer Yau\, Harvard University\n\nOrganizer: Zhigang Yao\, National University of Singapore \n  \nYoutube Playlist \n  \nSCHEDULE \ndownload pdf \nMonday\, Nov. 17\, 2025 \n9:00–9:25 am\nMorning refreshments \n9:25–9:30 am\nIntroductions \n9:30–10:30 am\nSpeaker: Stephan Huckemann\, Georg-August Universität Göttingen\nTitle: The Probability of the Cut Locus of a Fréchet Mean\nAbstract: We show that the cut locus of a Fréchet mean of a random variable on a connected and complete Riemanian manifold has zero probability\, a result known previously in special cases (Le and Barden\, 2014) and conjectured in general. The proof is based on first order and second order considerations\, where the latter are based on a recent result by Générau (2020) on “Laplacians in the barrier sense”. This generalizes to Fréchet p-means for p > 2. The former allow also to rule out stickiness on Riemannian manifolds\, and for generalization to 1 <= p < 2\, with a conjecture. We close with discussing and conjecturing extensions to noncomplete manifolds and more general metric spaces. This is joint work with Alexander Lytchak. \n\nGénérau\, F. (2020). Laplacian of the distance function on the cut locus on a Riemannian manifold. Nonlinearity 33(8)\, 3928.\nLe\, H. and D. Barden (2014).  On the measure of the cut locus of a Fréchet mean. Bulletin of the London Mathematical Society 46(4)\, 698–708.\nLytchak\, A. and S. F. Huckemann (2025). Zero mass at the cut locus of a Fréchet mean on a Riemannian manifold. arXiv preprint arXiv:2508.00747.\n\n10:30–10:45 am\nbreak \n10:45 am–11:45 am\nSpeaker: Hans-Georg Müller\, University of California\, Davis\nTitle: Conformal Inference for Random Objects\nAbstract: The underlying probability measure of random objects\, i.e.\, metric-space-valued random variables\, can be probed by distance profiles. These are one-dimensional distributions of probability mass falling into balls of increasing radius. In a regression setting with Euclidean covariates X and responses Y that are random objects\, one can consider conditional Fréchet means that can be implemented with Fréchet regression and also conditional distance profiles\, conditioning on X. Conditional distance profiles can then be leveraged to obtain conditional average transport costs\, the expected cost for transporting a fixed conditional distance profile to a randomly selected conditional distance profile. The conditional average transport costs can then be utilized to obtain conditional conformity scores. In conjunction with the split conformal algorithm these scores lead to conditional prediction sets located in the object space with asymptotic conditional validity and attractive finite sample behavior. Based on joint work Hang Zhou (UNC). \n11:45 am–1:15 pm\nLunch (Catered) \n1:15–2:15 pm\nSpeaker: Horng-Tzer Yau\, Harvard\nTitle: Ramanujan property of random regular graphs and delocalization of random band matrices\nAbstract: In this lecture\, we review recent works on random matrices. The first result is about the normalized adjacency matrix of a random $d$-regular graph on $N$ vertices with any fixed degree $d\geq 3$ and denote its eigenvalues as $\lambda_1=d/\sqrt{d-1}\geq \lambda_2\geq\lambda_3\cdots\geq \lambda_N$. We establish the edge universality for random $d$-regular graphs\, namely\, the distributions of $\lambda_2$ and $-\lambda_N$ converge to the Tracy-Widom$_1$ distribution associated with the Gaussian Orthogonal Ensemble. As a consequence\, for sufficiently large $N$\, approximately $69\%$ of $d$-regular graphs on $N$ vertices.\nare Ramanujan\, meaning $\max\{\lambda_2\,|\lambda_N|\}\leq 2$. This resolves a conjecture by Sarnak and Miller-Novikoff-Sabelli\nThe second result concerns $ N \times N$ Hermitian $d$-dimensional random band matrices with band width $W$. In the bulk of the spectrum and in the large $ N $ limit\, we prove that all $ L^2 $- normalized eigenvectors are delocalized in all dimensions under suitable conditions on $W$ and $N$. In addition\, we proved that the eigenvalue statistics are given by those of the Gaussian unitary ensemble. \n2:15–2:45 pm\nbreak with refreshments \n2:45–3:45 pm\nSpeaker: Clément Levrard\, Université de Rennes\nTitle: Optimal reach estimation\nAbstract: The reach of an embedded submanifold\, a notion that dates back to the famous work Curvature measures of H. Federer\, may be understood as a scale under which the submanifold is flat enough so that traditional Euclidean techniques in statistics locally apply\, up to some approximation. I will expose several ways to estimate the reach from sample (on the submanifold)\, some of them being optimal from the point of view of minimax estimation theory. Along the way\, intermediate estimation problems of local and global quantities will arise (curvature estimation\, weak feature size estimation\, distance estimation\, etc.)\, for which various phenomenons can occur from a statistical point of view (different convergence rates\, inconsistency). This will be an opportunity to provide a selective overview of the state of the art on these issues. \n4:30–5:30 pm\nCMSA Colloquium\nSpeaker: Zhigang Yao (National University of Singapore)\nTitle: Interaction of Statistics and Geometry: A New Landscape for Data Science\nAbstract:  Classical statistics views data as real numbers or vectors in Euclidean space\, but modern challenges increasingly involve data with intrinsic geometric structures. A central problem in this direction is manifold fitting\, with origins in H. Whitney’s work of the 1930s. The Geometric Whitney Problems ask: given a set\, when can we construct a smooth 𝑑-dimensional manifold that approximates it\, and how accurately can we estimate it?\nIn this talk\, I will discuss recent progress on manifold fitting and its role in bridging geometry and data science. While many existing methods rely on restrictive assumptions\, the manifold hypothesis—that data often lie near non-Euclidean structures—remains fundamental in modern statistical learning. I will highlight both theoretical insights and algorithmic challenges\, drawing on recent works with\, as well as ongoing research. \nYoutube video \n  \nTuesday\, Nov. 18\, 2025 \n9:00–9:30 am\nMorning refreshments \n9:30–10:30 am\nSpeaker: Charles Fefferman\, Princeton University (via Zoom)\nTitle: Extrinsic and intrinsic manifold learning\, old and new\nAbstract: The talk will include an exposition of the old paper “Testing the manifold hypothesis”\, joint work with S. Mitter and H. Narayanan\, on extrinsic manifold learning (the manifold to be learned is assumed to be embedded in a high-dimensional Euclidean space). The talk will also include a new result on intrinsic manifold learning (the manifold to be learned is not assumed to be embedded\, and the data consist of intrinsic distances corrupted by noise)\, provided the result is proven by the time of the conference. \n10:30–10:45 am\nbreak \n10:45 am–11:45 am\nSpeaker: Steve Marron\, University of North Carolina\nTitle: Data Integration Via Analysis of Manifolds (DIVAM)\nAbstract: A major challenge in the age of Big Data is the integration of disparate data types into a single data analysis. That was tackled by Data Integration Via Analysis of Subspaces (DIVAS) in the context of data blocks measured on a common set of experimental cases. Joint variation was defined in terms of modes of variation having identical scores across data blocks. DIVAS allowed mathematically rigorous formulation of individual variation within each data block in terms of individual modes. The goal of DIVAM is to intrinsically extend the DIVAS approach to data objects lying in manifolds\, such as shape data. \n11:45 am–1:15 pm\nLunch Break \n1:15–2:15 pm\nSpeaker: Ker-Chau Li\, University of California\, Los Angeles\nTitle: Investigation of Data clouds: From Galton’s Ellipses to Explainable AI (XAI)\, modeling or molding?\nAbstract: Francis Galton’s seminal 1886 visualization of regression toward the mean in trait inheritance is arguably the first and most influential example of geometric thinking applied to statistical modeling. The pioneering geometric insight driving Galton’s use of elliptical contours to discover the bivariate normal distribution laid down the foundation for classic multivariate analysis (e.g.\, PCA\, canonical correlation) and profoundly impacts modern methods like diffusion models.\nStatistical models\, particularly those based on parsimony\, are effective for characterizing data distribution and facilitating scientific rule induction. However\, the rise of unstructured big data (like images) has challenged these parsimonious approaches\, necessitating the use of deep learning models. These models\, containing billions of parameters\, sacrifice transparency to excel in prediction. Seeking solutions to this “black-box” dilemma is now the heart of Explainable AI (XAI).\nLeveraging the simplicity of elementary geometric concepts\, this talk will present a new path toward interpretable and parsimonious XAI. Unstructured big data is highly plastic. Our approach moves beyond the standard data modeling perspective—which answers what the data is—and introduces a novel data molding perspective. This shift is key to unlocking the full potential of data’s plasticity\, allowing us to effectively answer the crucial question: what the data can be used for.\nI will first discuss a connection between manifold learning and my earlier works\, helical confounding and liquid association. I will then turn to the data molding perspective and present two novel notions: mold-compliance and artificial-trait configurative-generation (ATCG). These notions guide our recent efforts in formulating novel algorithms for image data investigation\, addressing issues like prediction validity and within-class heterogeneity. Data molding entails a dramatically different feature space extraction\, which consequently shifts the subsequent investigation on the data clouds from out-of-distribution (OOD) to mold-violation\, and from UMAP clustering to ATCG-induced hierarchical clustering. \n2:15–2:45 pm\nbreak with refreshments \n2:45–3:45 pm\nSpeaker: Andrew Wood\, Australian National University\nTitle: Empirical likelihood methods for Fréchet means on open books\nAbstract: The open book is a simple example of a stratified space that captures some (but not all) of the properties of stratified spaces. Central limit theory for open books plus relevant background is given by Hotz et al. (2013\, Annals of Applied Probability). In this talk I will describe some basic inference procedures for Fréchet means in open books based on empirical likelihood (Owen\, book\, 2001). Empirical likelihood (EL) is a type of nonparametric likelihood that can be useful for many types of data\, including manifold-valued data and data from stratified spaces. An EL approach to basic inference for Fréchet means will be described. In particular\, it will be shown how the non-regularity in the geometry of open books can result in non-regular behaviour in Wilks’s theorem (i.e. the large sample likelihood ratio test). The talk will also discuss difficulties in extending the EL inference theory from open books to more general stratified spaces\, where the difference in dimension of adjacent strata can be 2 or more. For discussion of more general stratified spaces than open books\, see the orthant spaces discussed in Barden and Le (2018\, Proc of London Math Society) and the general stratified space setting considered by Mattingly et al. (2023\, arxiv). \n3:45–4:00 pm\nbreak \n4:00–5:00 pm\nSpeaker: Wilderich Tuschmann\, Karlsruhe Institute of Technology\nTitle: A Spectator’s Perspective on the Manifold Hypothesis\nAbstract: At its core\, the Manifold Hypothesis asserts that real-world\, high-dimensional data is not uniformly or randomly distributed throughout its high-dimensional “ambient” space\, but concentrated on or near a low-dimensional manifold (or a collection of manifolds) embedded within that high-dimensional ambient space.\nIn my talk\, I will discuss reasons and facts that speak for as well as against this hypothesis and also address geometric alternatives. \n  \nWednesday\, Nov. 19\, 2025 \n9:00–9:30 am\nMorning refreshments \n9:30–10:30 am\nSpeaker: Melanie Weber\, Harvard University\nTitle: Ricci Curvature\, Ricci Flow\, and the Geometry of Learning\nAbstract: Geometric structure in data plays a crucial role in machine learning. In this talk\, we study this observation through the lens of Ricci curvature and its associated Ricci flow. We start by reviewing a discrete notion of Ricci curvature introduced by Ollivier and the geometric flow that it induces. We further discuss the relationship between discrete Ricci curvature and its continuous counterpart via discrete-to-continuum consistency results\, which imply that discrete Ricci curvature can provably characterize the geometry of a data manifold based on a finite sample. This provides a theoretical foundation for several applications of discrete Ricci curvature in machine learning\, two of which we discuss in the remainder of this talk. First\, we analyze learned feature representations in deep neural networks and show that they transform during training in ways that closely resemble a discrete Ricci flow. Our analysis reveals that nonlinear activations shape class separability and suggests geometry-informed training principles such as early stopping and depth selection. Second\, we turn to deep learning on graphs\, where we address representational limitations of state of the art graph neural networks through curvature-based data augmentations. We show that augmenting input graphs with geometric information provably increases the representational power of such models and yields performance gains in practice. \n10:30–10:45 am\nbreak \n10:45 am–11:45 am\nSpeaker: Ezra Miller\, Duke University\nTitle: Extracting bar lengths from multiparameter persistent homology\nAbstract: Persistent homology in one parameter can be summarized using bar codes or persistence diagrams\, which are elementary gadgets with many features amenable to vectorization and hence statistical analysis. For example\, early work with Bendich\, Marron\, Pieloch\, and Skwerer showed how to extract meaningful statistics from the top 100 bar lengths in persistent homology summaries of brain arteries. The story for persistent homology with multiple parameters\, on the other hand\, is still developing. Although it has the potential to be much more flexible and informative\, multipersistence has structural issues that present fundamental mathematical challenges. There is no consensus on what might be meant by a “bar”\, let alone “the top 100 bar lengths”. This talk recalls the basics of single and multiparameter persistent homology and discusses some of the mathematical issues\, including obstacles and potential routes forward. \n11:45 am–1:15 pm\nLunch Break \n1:15–2:15 pm\nSpeaker: Kei Kobayashi\, Keio University\nTitle: Metric Transformations of Data Spaces: Curvature Control and Related Developments\nAbstract: We present our proposed method of increasing the accuracy of data analysis by means of two transformations of the metric of the data space. The first transformation is based on the curve length defined by the integral of the power of the density function\, which can be computed approximately using an empirical graph; the second transformation can be interpreted as the extrinsic distance when the data space is embedded in a metric cone. The advantage of both distance transformations is that the hyperparameters allow the curvature to be monotonically transformed in a specific sense. Some statistical applications of these transformations and theoretical justifications are presented. Detailed analyses of the geodesics obtained by this method for several simple probability distributions will also be presented. The main part of this work is based on joint works with Henry P. Wynn. \n2:15–2:45 pm\nbreak with refreshments \n2:45–3:45 pm\nSpeaker: Sungkyu Jung\, Seoul National University\nTitle: Generalized Frechet means with random minimizing domains and its strong consistency\nAbstract: In this talk\, I will discuss a novel extension of Frechet means\, referred to as generalized  Frechet  means\, as a comprehensive framework for describing the characteristics of random elements. The generalized Frechet mean is defined as the minimizer of a cost function\, and the framework encompasses various extensions of Frechet means that have appeared in the literature. The most distinctive feature of the proposed framework is that it allows the domain of minimization for the empirical generalized Frechet means to be random and different from that of its population counterpart. This flexibility broadens the applicability of the Frechet mean framework to various statistical scenarios\, including sequential dimension reduction for non-Euclidean data. We establish a strong consistency theorem for generalized Frechet means. Applications such as verifying the consistency of principal geodesic analysis on the hypersphere\, compositional principal component analysis on the composition space\, and k-medoids clustering for data on a metric space will be discussed. \n3:45–4:00 pm\nbreak \n4:00–5:00 pm\nSpeaker: Rong Ma\, Harvard University\nTitle: Modern Nonlinear Embedding Methods Unpacked\nAbstract: Learning and representing low-dimensional structures from noisy\, high-dimensional data is a cornerstone of modern data science. Stochastic neighbor embedding algorithms\, a family of nonlinear dimensionality reduction and data visualization methods\, with t-SNE and UMAP as two leading examples\, have become very popular in recent years. Yet despite their wide applications\, these methods remain subject to points of debate\, including limited theoretical understanding\, ambiguous interpretations\, and sensitivity to tuning parameters. In this talk\, I will present our recent efforts to decipher and improve these nonlinear embedding approaches. Our key results include a rigorous theoretical framework that uncovers the intrinsic mechanisms\, large-sample limits\, and fundamental principles underlying these algorithms; a set of theory-informed practical guidelines for their principled use in trustworthy biological discovery; and a collection of new algorithms that address current limitations and improve performance in areas such as bias reduction and stability. Throughout the talk\, I will highlight how these advances not only deepen our theoretical understanding but also open new avenues for scientific discovery.
URL:https://cmsa.fas.harvard.edu/event/geostat_2025/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Conference
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251112T090000
DTEND;TZID=America/New_York:20251114T170000
DTSTAMP:20260504T060537
CREATED:20250502T181545Z
LAST-MODIFIED:20251113T214753Z
UID:10003745-1762938000-1763139600@cmsa.fas.harvard.edu
SUMMARY:Geometry Meets Physics: Finiteness\, Tameness\, and Complexity
DESCRIPTION:Geometry Meets Physics: Finiteness\, Tameness\, and Complexity \nDates: November 12–14\, 2025 \nLocation: CMSA G10\, 20 Garden Street\, Cambridge MA 02138 \n(note: this event is in-person only) \nFiniteness is a fundamental property in consistent physical theories. From the earliest days of quantum field theory and string theory\, the drive to eliminate unphysical infinities has been a guiding principle. More recently\, finiteness has emerged as a key criterion for constraining effective theories that can be embedded in quantum gravity.  Formulating and testing these constraints remains a central challenge in current research. \nIn parallel\, mathematics has made remarkable advanced in addressing finiteness questions using tame geometry. Built on the framework of o-minimal structures\, tame geometry offers a precise language for describing objects of finite geometric complexity. Recent developments\, such as sharp o-minimality\, go further by introducing a quantitative notion of complexity\, opening new directions for analyzing finiteness in mathematics and physics alike. \nThis workshop brings together mathematicians and physicists to exchange ideas\, explore new perspectives\, and spark collaborations at the interface of geometry\, logic\, and fundamental physics. \nInvited Speakers \n\nVijay Balasubramanian (UPenn)\nGregorio Baldi (CNRS\, IMJ-PRG & IAS)\nGal Binyamini (Weizmann Institute & IAS)\nRaf Cluckers (Lille\, France)\nMatilda Delgado (Max Planck Institute Munich)\nBruno Klingler (Humboldt University\, Berlin & IAS)\nAdele Padgett (Vienna)\nDavid Prieto (Utrecht)\nWashington Taylor (MIT)\nDavid Urbanik (IHES\, France & IAS)\nCumrun Vafa (Harvard)\nMick van Vliet (Utrecht)\nBenny Zak (Weizmann Institute & IAS)\n\nOrganizers: Thomas Grimm\, Harvard CMSA & Utrecht University | Gal Binyamini\, Weizmann Institute & IAS | Bruno Klingler\, Humboldt University\, Berlin & IAS \n  \nSchedule \n(download pdf) \nWednesday Nov. 12\, 2025 \n8:30–8:55 am\nMorning refreshments (Common Room) \n8:55–9:00 am\nIntroductions \n9:00–10:30 am\nLecture\nSpeaker: Gal Binyamini\, Weizmann Institute & IAS\nTitle: O-minimality: finiteness and complexity\nAbstract: O-minimality is a mathematical formalism of “tame geometry”: a geometry where every set has finite geometric complexity. I will give an introduction to o-minimality in general\, and to quantitative variants where one measures the complexity of sets in terms of some natural parameters. I’ll try to focus on the main examples that potentially come up in the interaction with physics\, and describe the state of the art and some conjectures. \n10:30–11:00 am\nBreak \n11:00 am–12:00 pm\nSpeaker: Benny Zak\, Weizmann Institute & IAS\nTitle: Analytic tameness – complex cells\nAbstract: Complex cells are a complex anayltic version of cells from o-minimality\, invented by Binyamini and Novikov. We aim to introduce complex cells\, and demonstrate their usefullness in quantifying the analytic information present in a complex set. If time permits\, we will discuss applications of this theory. \n12:00–1:00 pm\nCatered Lunch (Common Room) \n1:00–2:30 pm\nLecture\nSpeakers: David Prieto and Mick van Vliet\, Utrecht\nTitle: Tameness and Complexity in Physical Theories\nAbstract: We give an introductory overview of recent applications of o-minimality to physics\, focusing on quantum field theories and quantum gravity. In the first part of the lecture we explain how o-minimality makes a first appearance in physical theories when considering amplitudes in quantum field theory. In the second part\, we concentrate on a class of theories where finiteness principles seem to be essential\, namely the quantum field theories which are consistent with quantum gravity. We review some of these finiteness principles and interpret them through the lens of the o-minimal framework. Along the way\, we highlight recent progress in this direction\, as well as open questions to explore in the future. \n2:30–3:00 pm\nBreak with refreshments (Common Room) \n3:00–4:00 pm\nSpeaker: Matilda Delgado\, Max Planck Institute Munich\nTitle: Dualities and the Compactifiability of Moduli Space\nAbstract:  After introducing (self-)dualities in string theory and their action on the field content & spectrum of the theory\, I will present the notion of compactifiability for the moduli space of massless fields as the condition that its volume is finite or grows no faster than Euclidean space. I will argue that compactifiability generically implies the existence of non-trivial dualities by providing evidence from string theory. Moreover\, I will explain how one can connect compactifiability to the condition that the spectrum of objects charged under the duality group transform in a semisimple representation. Finally\, I will provide a bottom-up argument for compactifiability\, and argue that it (at least in supersymmetric cases) can be explained by the finiteness of the number of massless states upon compactification to 1D. Based on arXiv:2412.03640. \n5:00 PM\nMillennium Lecture and Reception: Pierre Deligne (IAS) (Science Center Hall D)\nTitle: What is the Hodge conjecture? \n  \nThursday\, Nov. 13\, 2025 \n8:30–9:00 am\nMorning refreshments (Common Room) \n9:00–10:30 am\nLecture\nSpeaker: Bruno Klingler\, Humboldt University\, Berlin & IAS\nTitle: Tame geometry and Hodge theory\nAbstract: I will give an introduction to applications of o-minimality in complex geometry\, in particular in Hodge theory. \n10:30–11:00 am\nBreak \n11:00 am–12:00 pm\nSpeaker: Cumrun Vafa\, Harvard\nTitle: The Swampland Program \n12:00–1:30 pm\nCatered Lunch (Common Room) \n1:30–2:30 pm\nSpeaker: Gregorio Baldi\, CNRS\, IMJ-PRG & IAS\nTitle: The Hodge locus\nAbstract: We will survey various recent results around the distribution of the Hodge locus of a (mixed) variation of Hodge structures. Various concrete applications to moduli spaces will also be presented. \n2:30–3:00 pm\nBreak with refreshments (Common Room) \n3:00–4:00 pm\nSpeaker: Vijay Balasubramanian\, U Penn\nTitle: Chaos and complexity in quantum dynamics \n4:30–5:30\nDiscussion/Q&A session \n6:30 PM\nDinner: Changsho Restaurant\, 1712 Massachusetts Ave.\, Cambridge\, MA 02138 \n  \nFriday Nov. 14\, 2025 \n8:30–9:00 am\nMorning refreshments (Common Room) \n9:00–10:00 am\nSpeaker: Washington Taylor\, MIT\nTitle: Finiteness\, connectivity\, and the power of fibrations in the Calabi-Yau landscape \n10:00–10:30am\nBreak \n10:30–11:30 am\nSpeaker: Adele Padgett\, Vienna\nTitle: Tameness of multisummable series\nAbstract: There are sophisticated theories of summability that map divergent series solutions of differential or functional equations to solutions that are holomorphic in sector-like domains. Van den Dries and Speissegger proved that functions obtained from real multisummable power series have tame geometric behavior when restricted to the real numbers. It would be desirable to know that these functions are also tame on their whole sector-like domains\, but recently Speissegger and I proved that these functions are in general only tame on part of their domains. I will present this result and discuss the domains on which some examples are tame\, including the Stirling series which appears in the asymptotic expansion of the Gamma function. In this talk\, “tame” means definable in an o-minimal structure. \n11:30 am–1:00 pm\nCatered Lunch (Common Room) \n1:00–2:00 pm\nSpeaker: Raf Cluckers\, Lille\, France\nTitle:  Finiteness and tameness in (non-archimedean) geometry\nAbstract: Non-archimedean geometry work with orders of magnitude rather than with precise measurements. The former works for example with orders of vanishing of functions\, and the latter typically works with real or complex numbers. I will discuss recent progress on non-archimedean tame geometry. I will present analogues of o-minimality\, of Pila-Wilkie’s o-minimal counting results\, and of other finiteness results\, in non-archimedean settings. \n2:00–2:30 pm\nBreak with refreshments (Common Room) \n2:30–3:30 pm\nSpeaker: David Urbanik\, IHES\, France & IAS\nTitle: Degrees of Hodge Loci \n\n    \n  \n 
URL:https://cmsa.fas.harvard.edu/event/geophys/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Conference,Event,Workshop
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END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250915T090000
DTEND;TZID=America/New_York:20250918T170000
DTSTAMP:20260504T060537
CREATED:20250710T134311Z
LAST-MODIFIED:20250930T154307Z
UID:10003755-1757926800-1758214800@cmsa.fas.harvard.edu
SUMMARY:The Geometry of Machine Learning
DESCRIPTION:The Geometry of Machine Learning \nDates: September 15–18\, 2025 \nLocation: Harvard CMSA\, Room G10\, 20 Garden Street\, Cambridge MA 02138 \nDespite the extraordinary progress in large language models\, mathematicians suspect that other dimensions of intelligence must be defined and simulated to complete the picture. Geometric and symbolic reasoning are among these. In fact\, there seems to be much to learn about existing ML by considering it from a geometric perspective\, e.g. what is happening to the data manifold as it moves through a NN?  How can geometric and symbolic tools be interfaced with LLMs? A more distant goal\, one that seems only approachable through AIs\, would be to gain some insight into the large-scale structure of mathematics as a whole: the geometry of math\, rather than geometry as a subject within math. This conference is intended to begin a discussion on these topics. \nSpeakers \n\nMaissam Barkeshli\, University of Maryland\nEve Bodnia\, Logical Intelligence\nAdam Brown\, Stanford\nBennett Chow\, USCD & IAS\nMichael Freedman\, Harvard CMSA\nElliot Glazer\, Epoch AI\nJames Halverson\, Northeastern\nJesse Han\, Math Inc.\nJunehyuk Jung\, Brown University\nAlex Kontorovich\, Rutgers University\nYann Lecun\, New York University & META*\nJared Duker Lichtman\, Stanford  & Math Inc.\nBrice Ménard\, Johns Hopkins\nMichael Mulligan\, UCR & Logical Intelligence\nPatrick Shafto\, DARPA & Rutgers University\n\nOrganizers: Michael R. Douglas (CMSA) and Mike Freedman (CMSA) \n  \nGeometry of Machine Learning Youtube Playlist \n  \nSchedule \nMonday\, Sep. 15\, 2025 \n\n\n\n8:30–9:00 am\nMorning refreshments\n\n\n9:00–10:00 am\nJames Halverson\, Northeastern \nTitle: Sparsity and Symbols with Kolmogorov-Arnold Networks \nAbstract: In this talk I’ll review Kolmogorov-Arnold nets\, as well as new theory and applications related to sparsity and symbolic regression\, respectively.  I’ll review essential results regarding KANs\, show how sparsity masks relate deep nets and KANs\, and how KANs can be utilized alongside multimodal language models for symbolic regression. Empirical results will necessitate a few slides\, but the bulk will be chalk.\n\n\n10:00–10:30 am\nBreak\n\n\n10:30–11:30 am\nMaissam Barkeshli\, University of Maryland \nTitle: Transformers and random walks: from language to random graphs \nAbstract: The stunning capabilities of large language models give rise to many questions about how they work and how much more capable they can possibly get. One way to gain additional insight is via synthetic models of data with tunable complexity\, which can capture the basic relevant structures of real data. In recent work we have focused on sequences obtained from random walks on graphs\, hypergraphs\, and hierarchical graphical structures. I will present some recent empirical results for work in progress regarding how transformers learn sequences arising from random walks on graphs. The focus will be on neural scaling laws\, unexpected temperature-dependent effects\, and sample complexity.\n\n\n11:30 am–12:00 pm\nBreak\n\n\n12:00–1:00 pm\nAdam Brown\, Stanford \nTitle: LLMs\, Reasoning\, and the Future of Mathematical Sciences \nAbstract: Over the last half decade\, the mathematical capabilities of large language models (LLMs) have leapt from preschooler to undergraduate and now beyond. This talk reviews recent progress\, and speculates as to what it will mean for the future of mathematical sciences if these trends continue.\n\n\n\n  \nTuesday\, Sep. 16\, 2025 \n\n\n\n8:30–9:00 am\nMorning refreshments\n\n\n9:00–10:00 am\nJunehyuk Jung\, Brown University \nTitle: AlphaGeometry: a step toward automated math reasoning \nAbstract: Last summer\, Google DeepMind’s AI systems made headlines by achieving Silver Medal level performance on the notoriously challenging International Mathematical Olympiad (IMO) problems. For instance\, AlphaGeometry 2\, one of these remarkable systems\, solved the geometry problem in a mere 19 seconds! \nIn this talk\, we will delve into the inner workings of AlphaGeometry\, exploring the innovative techniques that enable it to tackle intricate geometric puzzles. We will uncover how this AI system combines the power of neural networks with symbolic reasoning to discover elegant solutions.\n\n\n10:00–10:30 am\nBreak\n\n\n10:30–11:30 am\nBennett Chow\, USCD and IAS \nTitle: Ricci flow as a test for AI\n\n\n11:30 am–12:00 pm\nBreak\n\n\n12:00–1:00 pm\nJared Duker Lichtman\, Stanford & Math Inc. and Jesse Han\, Math Inc. \nTitle: Gauss – towards autoformalization for the working mathematician \nAbstract: In this talk we’ll highlight some recent formalization progress using a new agent – Gauss. We’ll outline a recent Lean proof of the Prime Number Theorem in strong form\, completing a challenge set in January 2024 by Alex Kontorovich and Terry Tao. We hope Gauss will help assist working mathematicians\, especially those who do not write formal code themselves.\n\n\n5:00–6:00 pm\nSpecial Lecture: Yann LeCun\, Science Center Hall C\n\n\n\n  \nWednesday\, Sep. 17\, 2025 \n\n\n\n8:30–9:00 am\nRefreshments\n\n\n9:00–10:00 am\nMichael Mulligan\, UCR and Logical Intelligence \nTitle: Spontaneous Kolmogorov-Arnold Geometry in Vanilla Fully-Connected Neural Networks \nAbstract: The Kolmogorov-Arnold (KA) representation theorem constructs universal\, but highly non-smooth inner functions (the first layer map) in a single (non-linear) hidden layer neural network. Such universal functions have a distinctive local geometry\, a “texture\,” which can be characterized by the inner function’s Jacobian\, $J(\mathbf{x})$\, as $\mathbf{x}$ varies over the data. It is natural to ask if this distinctive KA geometry emerges through conventional neural network optimization. We find that indeed KA geometry often does emerge through the process of training vanilla single hidden layer fully-connected neural networks (MLPs). We quantify KA geometry through the statistical properties of the exterior powers of $J(\mathbf{x})$: number of zero rows and various observables for the minor statistics of $J(\mathbf{x})$\, which measure the scale and axis alignment of $J(\mathbf{x})$. This leads to a rough phase diagram in the space of function complexity and model hyperparameters where KA geometry occurs. The motivation is first to understand how neural networks organically learn to prepare input data for later downstream processing and\, second\, to learn enough about the emergence of KA geometry to accelerate learning through a timely intervention in network hyperparameters. This research is the “flip side” of KA-Networks (KANs). We do not engineer KA into the neural network\, but rather watch KA emerge in shallow MLPs.\n\n\n10:00–10:30 am\nBreak\n\n\n10:30–11:30 am\nEve Bodnia\, Logical Intelligence \nTitle: \nAbstract: We introduce a method of topological analysis on spiking correlation networks in neurological systems. This method explores the neural manifold as in the manifold hypothesis\, which posits that information is often represented by a lower-dimensional manifold embedded in a higher-dimensional space. After collecting neuron activity from human and mouse organoids using a micro-electrode array\, we extract connectivity using pairwise spike-timing time correlations\, which are optimized for time delays introduced by synaptic delays. We then look at network topology to identify emergent structures and compare the results to two randomized models – constrained randomization and bootstrapping across datasets. In histograms of the persistence of topological features\, we see that the features from the original dataset consistently exceed the variability of the null distributions\, suggesting that the observed topological features reflect significant correlation patterns in the data rather than random fluctuations. In a study of network resiliency\, we found that random removal of 10 % of nodes still yielded a network with a lesser but still significant number of topological features in the homology group H1 (counts 2-dimensional voids in the dataset) above the variability of our constrained randomization model; however\, targeted removal of nodes in H1 features resulted in rapid topological collapse\, indicating that the H1 cycles in these brain organoid networks are fragile and highly sensitive to perturbations. By applying topological analysis to neural data\, we offer a new complementary framework to standard methods for understanding information processing across a variety of complex neural systems.\n\n\n11:30 am–12:00 pm\nBreak\n\n\n12:00–1:00 pm\nAlex Kontorovich\, Rutgers University \nTitle: The Shape of Math to Come \nAbstract: We will discuss some ongoing experiments that may have meaningful impact on what working in research mathematics might look like in a decade (if not sooner).\n\n\n5:00–6:00 pm\nMike Freedman Millennium Lecture: The Poincaré Conjecture and Mathematical Discovery (Science Center Hall D)\n\n\n\n  \nThursday\, Sep. 18\, 2025 \n\n\n\n8:30–9:00 am\nMorning refreshments\n\n\n9:00–10:00 am\nElliott Glazer\, Epoch AI \nTitle: FrontierMath to Infinity \nAbstract: I will discuss FrontierMath\, a mathematical problem solving benchmark I developed over the past year\, including its design philosophy and what we’ve learned about AI’s trajectory from it. I will then look much further out\, speculate about what a “perfectly efficient” mathematical intelligence should be capable of\, and discuss how high-ceiling math capability metrics can illuminate the path towards that ideal.\n\n\n10:00–10:30 am\nBreak\n\n\n10:30–11:30 am\nBrice Ménard\, Johns Hopkins \nTitle:Demystifying the over-parametrization of neural networks \nAbstract: I will show how to estimate the dimensionality of neural encodings (learned weight structures) to assess how many parameters are effectively used by a neural network. I will then show how their scaling properties provide us with fundamental exponents on the learning process of a given task. I will comment on connections to thermodynamics.\n\n\n11:30 am–12:00 pm\nBreak\n\n\n12:00–12:30 pm\nPatrick Shafto\, Rutgers \nTitle: Math for AI and AI for Math \nAbstract: I will briefly discuss two DARPA programs aiming to deepen connections between mathematics and AI\, specifically through geometric and symbolic perspectives. The first aims for mathematical foundations for understanding the behavior and performance of modern AI systems such as Large Language Models and Diffusion models. The second aims to develop AI for pure mathematics through an understanding of abstraction\, decomposition\, and formalization. I will close with some thoughts on the coming convergence between AI and math.\n\n\n12:30–12:45 pm\nBreak\n\n\n12:45–2:00 pm\nMike Freedman\, Harvard CMSA \nTitle: How to think about the shape of mathematics \nFollowed by group discussion \n \n\n\n\n  \n  \n  \nSupport provided by Logical Intelligence. \n \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mlgeometry/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Conference,Event
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250911T090000
DTEND;TZID=America/New_York:20250912T170000
DTSTAMP:20260504T060537
CREATED:20250502T175902Z
LAST-MODIFIED:20251026T044243Z
UID:10003743-1757581200-1757696400@cmsa.fas.harvard.edu
SUMMARY:Big Data Conference 2025
DESCRIPTION:Big Data Conference 2025 \nDates: Sep. 11–12\, 2025 \nLocation: Harvard University CMSA\, 20 Garden Street\, Cambridge & via Zoom \nThe Big Data Conference features speakers from the Harvard community as well as scholars from across the globe\, with talks focusing on computer science\, statistics\, math and physics\, and economics. \nInvited Speakers \n\nMarkus J. Buehler\, MIT\nYiling Chen\, Harvard\nJordan Ellenberg\, UW Madison\nYue M. Lu\, Harvard\nPankaj Mehta\, BU\nNick Patterson\, Harvard\nGautam Reddy\, Princeton\nTrevor David Rhone\, Rensselaer Polytechnic Institute\nTess Smidt\, MIT\n\nOrganizers: \nMichael M. Desai\, Harvard OEB |  Michael R. Douglas\, Harvard CMSA | Yannai A. Gonczarowski\, Harvard Economics | Efthimios Kaxiras\, Harvard Physics | Melanie Weber\, Harvard SEAS \n  \nBig Data Youtube Playlist \n  \nSchedule \nThursday\, Sep. 11\, 2025 \n  \n\n\n\n9:00 am\nRefreshments\n\n\n9:30 am\nIntroductions\n\n\n9:45–10:45 am\nGautam Reddy\, Princeton \nTitle: Global epistasis in genotype-phenotype maps\n\n\n10:45–11:00 am\nBreak\n\n\n11:00 am –12:00 pm\nNick Patterson\, Harvard \nTitle: The Origin of the Indo-Europeans \nAbstract: Indo-European is the largest family of human languages\, with very wide geographical distribution and more than 3 billion native speakers. How did this family arise and spread? This question has been discussed for nearly 250 years but with the advent of the availability of DNA from ancient fossils is now largely understood\, at least in broad outlines. We will describe what we now know about the origins.\n\n\n12:00–1:30 pm\nLunch break\n\n\n1:30–2:30 pm\nMarkus Buehler\, MIT \nTitle: Superintelligence for scientific discovery \nAbstract: AI is moving beyond prediction to become a partner in invention. While today’s models excel at interpolating within known data\, true discovery requires stepping outside existing truths. This talk introduces superintelligent discovery engines built on multi-agent swarms: diverse AI agents that interact\, compete\, and cooperate to generate structured novelty. Guided by Gödel’s insight that no closed system is complete\, these swarms create gradients of difference – much like temperature gradients in thermodynamics – that sustain flow\, invention\, and surprise. Case studies in protein design and music composition show how swarms escape data biases\, invent novel structures\, and weave long-range coherence\, producing creativity that rivals human processes. By moving from “big data” to “big insight”\, these systems point toward a new era of AI that composes knowledge across science\, engineering\, and the arts.\n\n\n2:30–2:45 pm\nBreak\n\n\n2:45–3:45 pm\nJordan Ellenberg\, UW Madison \nTitle: What does machine learning have to offer mathematics?\n\n\n3:45–4:00 pm\nBreak\n\n\n4:00–5:00 pm\nPankaj Mehta\, Boston University \nTitle: Thinking about high-dimensional biological data in the age of AI \nAbstract: The molecular biology revolution has transformed our view of living systems. Scientific explanations of biological phenomena are now synonymous with the identification of the genes and proteins. The preeminence of the molecular paradigm has only become more pronounced as new technologies allow us to make measurements at scale. Combining this wealth of data with new artificial intelligence (AI) techniques is widely viewed as the future of biology. Here\, I will discuss the promise and perils of this approach. I will focus on our unpublished work with collaborators on two fronts: (i) transformer-based models for understanding genotype-to-phenotype maps\, and (ii) LLM-based ‘foundational models’ for cellular identity\, such as TranscriptFormer\, which is trained on single-cell RNA sequencing (scRNAseq) data. While LLMs excel at capturing complex evolutionary and demographic structure in DNA sequence data\, they are much less adept at elucidating the biology of cellular identity. We show that simple parameter-free models based on linear-algebra outperform TranscriptFormer on downstream tasks related to cellular identity\, even though TranscriptFormer has nearly a billion parameters. If time permits\, I will conclude by showing how we can combine ideas from linear algebra\, bifurcation theory\, and statistical physics to classify cell fate transitions using scRNAseq data.\n\n\n\n  \nFriday\, Sep. 12\, 2025  \n\n\n\n9:00-9:45 am\nRefreshments\n\n\n9:45–10:45 am\nYiling Chen\, Harvard \nTitle: Data Reliability Scoring \nAbstract: Imagine you are trying to make a data-driven decision\, but the data at hand may be noisy\, biased\, or even strategically manipulated. Can you assess whether such a dataset is reliable—without access to ground truth?\nWe initiate the study of reliability scoring for datasets reported by potentially strategic data sources. While the true data remain unobservable\, we assume access to auxiliary observations generated by an unknown statistical process that depends on the truth. We introduce the Gram Determinant Score\, a reliability measure that evaluates how well the reported data align with the unobserved truth\, using only the reported data and the auxiliary observations. The score comes with provable guarantees: it preserves several natural reliability orderings. Experimentally\, it effectively captures data quality in settings with synthetic noise and contrastive learning embeddings.\nThis talk is based on joint work with Shi Feng\, Fang-Yi Yu\, and Paul Kattuman.\n\n\n10:45–11:00 am\nBreak\n\n\n11:00 am –12:00 pm\nYue M. Lu\, Harvard \nTitle: Nonlinear Random Matrices in High-Dimensional Estimation and Learning \nAbstract: In recent years\, new classes of structured random matrices have emerged in statistical estimation and machine learning. Understanding their spectral properties has become increasingly important\, as these matrices are closely linked to key quantities such as the training and generalization performance of large neural networks and the fundamental limits of high-dimensional signal recovery. Unlike classical random matrix ensembles\, these new matrices often involve nonlinear transformations\, introducing additional structural dependencies that pose challenges for traditional analysis techniques. \nIn this talk\, I will present a set of equivalence principles that establish asymptotic connections between various nonlinear random matrix ensembles and simpler linear models that are more tractable for analysis. I will then demonstrate how these principles can be applied to characterize the performance of kernel methods and random feature models across different scaling regimes and to provide insights into the in-context learning capabilities of attention-based Transformer networks.\n\n\n12:00–1:30 pm\nLunch break\n\n\n1:30–2:30 pm\nTrevor David Rhone\, Rensselaer Polytechnic Institute \nTitle: Accelerating the discovery of van der Waals quantum materials using AI \nAbstract: van der Waals (vdW) materials are exciting platforms for studying emergent quantum phenomena\, ranging from long-range magnetic order to topological order. A conservative estimate for the number of candidate vdW materials exceeds ~106 for monolayers and ~1012 for heterostructures. How can we accelerate the exploration of this entire space of materials? Can we design quantum materials with desirable properties\, thereby advancing innovation in science and technology? A recent study showed that artificial intelligence (AI) can be harnessed to discover new vdW Heisenberg ferromagnets based on Cr2Ge2Te6 [1]\, [2] and magnetic vdW topological insulators based on MnBi2Te4 [3]. In this talk\, we will harness AI to efficiently explore the large chemical space of vdW materials and to guide the discovery of vdW materials with desirable spin and charge properties. We will focus on crystal structures based on monolayer Cr2I6 of the form A2X6\, which are studied using density functional theory (DFT) calculations and AI. Magnetic properties\, such as the magnetic moment are determined. The formation energy is also calculated and used as a proxy for the chemical stability. We also investigate monolayers based on MnBi2Te4 of the form AB2X4 to identify novel topological materials. Further to this\, we study heterostructures based on MnBi2Te4/Sb2Te3 stacks. We show that AI\, combined with DFT\, can provide a computationally efficient means to predict the thermodynamic and magnetic properties of vdW materials [4]\,[5]. This study paves the way for the rapid discovery of chemically stable vdW quantum materials with applications in spintronics\, magnetic memory and novel quantum computing architectures.\n[1]        T. D. Rhone et al.\, “Data-driven studies of magnetic two-dimensional materials\,” Sci. Rep.\, vol. 10\, no. 1\, p. 15795\, 2020.\n[2]        Y. Xie\, G. Tritsaris\, O. Granas\, and T. Rhone\, “Data-Driven Studies of the Magnetic Anisotropy of Two-Dimensional Magnetic Materials\,” J. Phys. Chem. Lett.\, vol. 12\, no. 50\, pp. 12048–12054.\n[3]        R. Bhattarai\, P. Minch\, and T. D. Rhone\, “Investigating magnetic van der Waals materials using data-driven approaches\,” J. Mater. Chem. C\, vol. 11\, p. 5601\, 2023.\n[4]        T. D. Rhone et al.\, “Artificial Intelligence Guided Studies of van der Waals Magnets\,” Adv. Theory Simulations\, vol. 6\, no. 6\, p. 2300019\, 2023.\n[5]        P. Minch\, R. Bhattarai\, K. Choudhary\, and T. D. Rhone\, “Predicting magnetic properties of van der Waals magnets using graph neural networks\,” Phys. Rev. Mater.\, vol. 8\, no. 11\, p. 114002\, Nov. 2024.\nThis work used the Extreme Science and Engineering Discovery Environment (XSEDE)\, which is supported by National Science Foundation Grant No. ACI-1548562. This research used resources of the Argonne Leadership Computing Facility\, which is a DOE Office of Science User Facility supported under Contract No. DE-AC02-06CH11357. This material is based on work supported by the National Science Foundation CAREER award under Grant No. 2044842.\n\n\n2:30–2:45 pm\nBreak\n\n\n2:45–3:45 pm\nTess Smidt\, MIT \nTitle: Applications of Euclidean neural networks to understand and design atomistic systems \nAbstract: Atomic systems (molecules\, crystals\, proteins\, etc.) are naturally represented by a set of coordinates in 3D space labeled by atom type. This poses a challenge for machine learning due to the sensitivity of coordinates to 3D rotations\, translations\, and inversions (the symmetries of 3D Euclidean space). Euclidean symmetry-equivariant Neural Networks (E(3)NNs) are specifically designed to address this issue. They faithfully capture the symmetries of physical systems\, handle 3D geometry\, and operate on the scalar\, vector\, and tensor fields that characterize these systems. \nE(3)NNs have achieved state-of-the-art results across atomistic benchmarks\, including small-molecule property prediction\, protein-ligand binding\, force prediciton for crystals\, molecules\, and heterogeneous catalysis. By merging neural network design with group representation theory\, they provide a principled way to embed physical symmetries directly into learning. In this talk\, I will survey recent applications of E(3)NNs to materials design and highlight ongoing debates in the AI for atomistic sciences community: how to balance the incorporation of physical knowledge with the drive for engineering efficiency.\n\n\n\n 
URL:https://cmsa.fas.harvard.edu/event/bigdata_2025/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Big Data Conference,Conference,Event
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DTSTART;TZID=America/New_York:20250404T090000
DTEND;TZID=America/New_York:20250405T170000
DTSTAMP:20260504T060537
CREATED:20241213T155434Z
LAST-MODIFIED:20250415T134135Z
UID:10003651-1743757200-1743872400@cmsa.fas.harvard.edu
SUMMARY:Current Developments in Mathematics 2025
DESCRIPTION:When: April 4\, 2025 – April 5\, 2025\n\n\nWhere: Science Center Hall C \nAddress: 1 Oxford Street\, Cambridge\, MA 02138\, United States\n\nSpeaker: Michael Chapman – NYU | Pazit Haim-Kislev – Institute for Advanced Study | Jianfeng Lin – Tsinghua University | Laura Monk – University of Bristol | Ramon van Handel – Princeton University\n\nIN-PERSON REGISTRATION\nLimited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support\, please register and send a letter to cdm@math.harvard.edu. \nA letter indicating your name\, address\, current status\, university affiliation\, citizenship\, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student\, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research. \nDetailed schedule of lectures and events coming soon. \nOrganizers: David Jerison\, Paul Seidel\, Nike Sun (MIT); Denis Auroux\, Mark Kisin\, Lauren Williams\, Horng-Tzer Yau\, Shing-Tung Yau (Harvard).  \nSponsored by the National Science Foundation (pending)\, Harvard University Mathematics\, and the Massachusetts Institute of Technology. \nHarvard University is committed to maintaining a safe and healthy educational and work environment in which no member of the University community is\, on the basis of sex\, sexual orientation\, or gender identity\, excluded from participation in\, denied the benefits of\, or subjected to discrimination in any University program or activity. More information can be found here. \n\n\nCurrent Developments in Mathematics 2025 \n \n 
URL:https://cmsa.fas.harvard.edu/event/cdm2025/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Conference,Event
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240906T090000
DTEND;TZID=America/New_York:20240907T170000
DTSTAMP:20260504T060537
CREATED:20240325T141950Z
LAST-MODIFIED:20250415T154033Z
UID:10003287-1725613200-1725728400@cmsa.fas.harvard.edu
SUMMARY:Big Data Conference 2024
DESCRIPTION:  \n \nYoutube Playlist \nOn September 6-7\, 2024\, the CMSA hosted the tenth annual Conference on Big Data. The Big Data Conference features speakers from the Harvard community as well as scholars from across the globe\, with talks focusing on computer science\, statistics\, math and physics\, and economics. \nLocation: Harvard University CMSA\, 20 Garden Street\, Cambridge & via Zoom \n  \nSpeakers: \n\nTianxi Cai\, Harvard Chan School\nRaj Chetty\, Harvard\nBianca Dumitrascu\, Columbia\nBoris Hanin\, Princeton\nPeter Hull\, Brown\nJamie Morgenstern\, U Washington\nKavita Ramanan\, Brown\nNeil Thompson\, MIT\nMelanie Weber\, Harvard\nKun-Hsing Yu\, Harvard Medical School\n\nOrganizers: \n\nRediet Abebe\, Harvard Society of Fellows\nMorgane Austern\, Harvard University Statistics\nMichael R. Douglas\, Harvard CMSA\nYannai Gonczarowski\, Harvard University Economics and Computer Science\nSam Kou\, Harvard University Statistics\n\nSCHEDULE (downloadable pdf) \nFriday\, Sep. 6\, 2024 \n9:00 am: Breakfast \n9:30 am: Introductions \n9:45–10:45 am\nSpeaker: Peter Hull\, Brown University\nTitle: Measuring Discrimination in Multi-Phase Systems\, with an Application to Child Protection\nAbstract: Large racial disparities have been documented in many high-stakes settings—such as employment\, health care\, housing\, and criminal justice—raising concerns of discrimination by individual decision-makers. At the same time\, there is growing understanding that a focus on individual decisions can yield an incomplete view of discrimination; an extensive theoretical literature shows how discrimination can arise and compound across multiple decision-makers in interconnected systems. We develop new empirical tools for studying discrimination in such multi-phase systems and apply them to the setting of foster care placement by child protective services. Leveraging the quasi-random assignment of two sets of decision-makers—initial hotline call screeners and subsequent investigators—we study how unwarranted racial disparities arise and propagate through this system. Using a sample of over 200\,000 maltreatment allegations\, we find that calls involving Black children are 55% more likely to result in foster care placement than calls involving white children with the same potential for future maltreatment in the home. Call screeners account for up to 19% of this unwarranted disparity\, with the remainder due to investigators. Unwarranted disparity is concentrated in cases with potential for future maltreatment\, suggesting that white children may be harmed by “underplacement” in high-risk situations. \n10:45–11:00 am: Break \n11:00 am –12:00 pm\nSpeaker: Jamie Morgenstern\, U Washington\nTitle: What governs predictive disparity in modern machine learning applications?\nAbstract: The deployment of statistical models in impactful environments is far from new—simple correlations have been used to guide decisions throughout the sciences\, health care\, political campaigns\, and in pricing financial instruments and other products for decades. Many such models\, and the decisions they supported\, were known to have different degrees of predictive power for different demographic groups. These differences had numerous sources\, including: limited expressiveness of the statistical models; limited availability of data from marginalized populations; noisier measurements of both features and targets from certain populations; and features with less mutual information about the prediction target for some populations than others.\nModern decision systems which use machine learning are more ubiquitous than ever\, as are their differences in performance for different populations of people. In this talk\, I will discuss some similarities and differences in the sources of differing performance in contemporary ML systems including facial recognition systems and those incorporating generative AI. \n12:00–1:30 pm: Lunch Break \n1:30–2:30 pm\nSpeaker: Kavita Ramanan\, Brown University\nTitle: Understanding High-dimensional Stochastic Dynamics on Realistic Networks\nAbstract: Large collections of randomly evolving particles that interact locally with respect to an underlying network model a variety of phenomena ranging from magnetism\, the spread of diseases\, neural and neuronal networks\, opinion dynamics and load balancing on computer networks. Due to their high-dimensional nature\, these systems are typically intractable to analyze exactly. Classical work\, falling under the rubric of mean-field approximations\, has mostly focused on the case when this interaction graph is dense.  However\, most real-world networks are sparse and often random. We describe a new approach to develop principled approximations for dynamics on realistic networks that beats the curse of dimensionality\, and illustrate its efficacy on a class of epidemiological models. This is based on joint works with Michel Davydov\, Ankan Ganguly and Juniper Cocomello. \n2:30–2:45 pm: Break \n2:45–3:45 pm\nSpeaker: Raj Chetty\, Harvard University\nTitle: The Science of Economic Opportunity: New Insights from Big Data\nAbstract: How can we improve economic opportunities for children growing up in low-income families? This talk will present findings from a recent set of studies that use various sources of big data — ranging from anonymized tax records to social network data — to understand the science of economic opportunity. Among other topics\, the talk will discuss how and why children’s chances of climbing the income ladder vary across neighborhoods\, the drivers of racial disparities in economic mobility\, how highly selective colleges may amplify the persistence of privilege\, and the role of social capital as a driver of upward mobility. The talk will conclude by giving examples of how academic research using big data is informing policy decisions from the local to federal level to expand opportunities for all. \n3:45–4:00 pm: Break \n4:00–5:00 pm\nSpeaker: Neil Thompson\nTitle: How Algorithmic Progress is driving progress in Big Data and AI\nAbstract: Algorithm improvement is one of the purest forms of innovation: it allows the same computational task to be achieved with far fewer resources by proposing clever new ways to do that computation. In this talk\, I will discuss the work that my lab has done tracking and quantifying progress across decades of algorithm research and practice. As I will show\, this algorithmic progress has often outpaced hardware improvement as the most important driver of progress in Big Data and AI. \n  \nSaturday\, Sep. 7\, 2024 \n9:00 am: Breakfast \n9:30 am: Introductions \n9:45–10:45 am\nSpeaker: Tianxi Cai\, Harvard Chan School\nTitle: Crowdsourcing with Multi-institutional EHR to Improve Reliability of Real World Evidence – Opportunities and Challenges\nAbstract: The wide adoption of electronic health records (EHR) systems has led to the availability of large clinical datasets available for discovery research. EHR data\, linked with bio- repository\, is a valuable new source for deriving real-word\, data-driven prediction models of disease risk and progression. Yet\, they also bring analytical difficulties especially when aiming to leverage multi-institutional EHR data. Synthesizing information across healthcare systems is challenging due to heterogeneity and privacy. Statistical challenges also arise due to high dimensionality in the feature space. In this talk\, I’ll discuss analytical approaches for mining EHR data to improve the reliability and generalizability of real world evidence generated from the analyses. These methods will be illustrated using EHR data from Mass General Brigham and Veteran Health Administration. \n10:45–11:00 am: Break \n11:00 am–12:00 pm\nSpeaker: Bianca Dumitrascu\, Columbia Data Science Institute\nTitle: Statistical machine learning for learning representations of embryonic development\nAbstract: During embryonic development\, single cells read in local information from their environments and use this information to move\, divide and specialize. As a result\, the environments themselves change.  However\, it remains unclear how gene expression programs interact with cell morphology and mechanical forces to orchestrate organogenesis in early embryos. Recent advances in single cell techniques and in toto imaging enable unique venues in exploring this link between genomics and biophysics\, which dynamically maps cells to organisms.\nIn this talk\, I will describe statistical machine learning frameworks aimed at understanding how tissue level mechanical and morphometric information impact gene expression patterns in spatio-temporal contexts. We use these tools to understand boundary formation in the early development of mouse embryos and to align data from light sheet recordings of pre-gastrulation development. \n12:00–1:30 pm: Lunch Break \n1:30–2:30 pm\nSpeaker: Melanie Weber\, Harvard Mathematics\nTitle: Data and Model Geometry in Deep Learning\nAbstract: Data with geometric structure is ubiquitous in machine learning. Often such structure arises from fundamental symmetries in the domain\, such as permutation-invariance in graphs and sets\, and translation-invariance in images. In this talk we discuss implications of this structure on the design and complexity of neural networks. Equivariant architectures\, which encode symmetries as inductive bias\, have shown great success in applications with geometric data\, but can suffer from instabilities as their depths increases. We propose a new architecture based on unitary group convolutions\, which allows for deeper networks with less instability. In the second part of the talk we discuss the impact of data and model geometry on the learnability of neural networks. We discuss learnability in several geometric settings\, including equivariant neural networks\, as well as learnability with respect to the geometry of the input data manifold. \n2:30–2:45 pm: Break \n2:45–3:45 pm\nSpeaker: Boris Hanin\, Princeton University\nTitle: Scaling Limits of Neural Networks\nAbstract: Neural networks are often studied analytically through scaling limits: regimes in which taking some structural network parameters (e.g. depth\, width\, number of training datapoints\, and so on) to infinity results in simplified models of learning. I will motivative and discuss recent results using several such approaches. I will emphasize both new theoretical insights into how model\, training data\, and optimizer impact learning and their practical implications for hyperparameter transfer. \n3:45–4:00 pm: Break \n4:00–5:00 pm\nSpeaker: Kun-Hsing Yu\, Harvard Medical School\nTitle: Foundation Models for Real-Time Cancer Diagnosis\nAbstract: Artificial intelligence (AI) is transforming the landscape of medical research and practice. Recent advances in microscopic image digitization\, foundation models\, and scalable computing infrastructure have opened new avenues for AI-enhanced cancer diagnosis. In this talk\, I will highlight recent breakthroughs in multi-modal AI systems for cancer pathology evaluation\, discuss integrative biomedical informatics methods that link cell morphology with molecular profiles\, and outline critical challenges in developing robust medical AI systems. \n  \n\nInformation about the 2023 Big Data Conference can be found here.
URL:https://cmsa.fas.harvard.edu/event/bigdata_2024/
LOCATION:20 Garden Street\, Cambridge\, MA 02138\, MA\, MA\, 02138\, United States
CATEGORIES:Big Data Conference,Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Big-Data-2024_8.5x11-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240826T090000
DTEND;TZID=America/New_York:20240828T170000
DTSTAMP:20260504T060537
CREATED:20240209T180835Z
LAST-MODIFIED:20241212T152847Z
UID:10001874-1724662800-1724864400@cmsa.fas.harvard.edu
SUMMARY:Advances in Probability Theory and Interacting Particle Systems
DESCRIPTION:Advances in Probability Theory and Interacting Particle Systems\n\nA conference in honor of S. R. Srinivasa Varadhan.\n\nAugust 26 – August 28\, 2024\n\nHarvard Geological Lecture Hall\n\n\nConference Website: www.math.harvard.edu/event/math-conference-honoring-srinivasa-varadhan\n\nSpeakers\n\n\nInes Armendariz\, Universidad de Buenos Aires\nYuri Bakhtin\, Courant Institute\nGérard Ben Arous\, Courant Institute\nSourav Chatterjee\, Stanford University\nAmir Dembo\, Stanford University\nPeter K. Friz\, TU-Berlin\nNina Holden\, Courant Institute\nJiaoyang Huang\, University of Pennsylvania\nElena Kosygina\, City University of New York\nClaudio Landim\, IMPA\nEyal Lubetzky\, Courant Institute\nChiranjib Mukherjee\, Uni Münster\nStefano Olla\, Université Paris Dauphine\nJeremy Quastel\, University of Toronto\nKavita Ramanan\, Brown University\nAlejandro Ramirez\, NYU Shanghai\nFraydoun Rezakhanlou\, Berkeley\nSunder Sethuraman\, University of Arizona\nScott Sheffield\, MIT\nOfer Zeitouni\, Weizmann Institute\n\nOrganizers: Paul Bourgade (New York University\, Courant Institute) and Horng-Tzer Yau (Harvard University).\n\n\nSponsored by Harvard University Department of Mathematics and the Center of Mathematical Studies and Applications (CMSA).\n\nHarvard University is committed to maintaining a safe and healthy educational and work environment in which no member of the University community is\, on the basis of sex\, sexual orientation\, or gender identity\, excluded from participation in\, denied the benefits of\, or subjected to discrimination in any University program or activity. More information can be found here.
URL:https://cmsa.fas.harvard.edu/event/advances-in-probability-theory-and-interacting-particle-systems/
LOCATION:Harvard Geological Lecture Hall\, 24 Oxford St\, Cambridge\, 02138\, United States
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=application/pdf:https://cmsa.fas.harvard.edu/media/Varadhan-Poster.pdf
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240529T090000
DTEND;TZID=America/New_York:20240531T170000
DTSTAMP:20260504T060537
CREATED:20240105T071351Z
LAST-MODIFIED:20240624T164905Z
UID:10001120-1716973200-1717174800@cmsa.fas.harvard.edu
SUMMARY:Amplituhedra\, Cluster Algebras\, and Positive Geometry
DESCRIPTION:Amplituhedra\, Cluster Algebras\, and Positive Geometry \nDates: May 29-31\, 2024 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge MA 02138 & via Zoom \nIn recent years\, a remarkable paradigm shift has occurred in understanding quantum observables in particle physics and cosmology\, revealing their emergence from underlying novel mathematical objects known as positive geometries. The conference will center on the amplituhedron—the first and major example of a positive geometry. Building on the work of Lusztig and Postnikov on the positive Grassmannian\, the physicists Arkani-Hamed and Trnka introduced the amplituhedron in 2013 as a geometric object that “explains” the so-called BCFW recurrence for scattering amplitudes in N = 4 super Yang Mills theory (SYM). Simultaneously\, cluster algebras\, originally introduced by Fomin and Zelevinsky to study total positivity\, have been revealed to have a crucial role in describing singularities of N = 4 SYM scattering amplitudes. Thus\, one can use ideas from quantum field theory (QFT) to connect cluster algebras to positive geometries\, and in particular to the amplituhedron. Additionally\, QFT can also be used to discover new examples of positive geometries. The conference will bring together a wide range of mathematicians and physicists both to draw new connections within algebraic combinatorics and geometry and to advance our physical understanding of scattering amplitudes and QFT. \nThe conference features: Introductory Lectures\, an Open Problems Forum\, Emerging Scholars Talks\, and talks by experts in the fields. \n  \nConference Videos (Youtube Playlist) \n  \nConfirmed Speakers: \n\nEvgeniya Akhmedova\, Weizmann Institute of Science\nNima Arkani-Hamed\, IAS\nPaolo Benincasa\, MPI\nNick Early\, Weizmann Institute of Science\nCarolina Figueiredo\, Princeton University\nYu-tin Huang\, National Taiwan University\nDani Kaufman\, University of Copenhagen\nChia-Kai Kuo\, National Taiwan University\nThomas Lam\, University of Michigan\nYelena Mandelshtam\, UC Berkeley\nShruti Paranjape\, UC Davis\nLizzie Pratt\, UC Berkeley\nLecheng Ren\, Brown University\nSebastian Seemann\, KU Leuven\nKhrystyna Serhiyenko\, University of Kentucky\nMelissa Sherman-Bennett\, MIT & UC Davis\nMarcus Spradlin\, Brown University\nRan Tessler\, Weizmann Institute of Science\nHugh Thomas\, Université du Québec à Montréal\nJaroslav Trnka\, UC Davis\nAnastasia Volovich\, Brown University\n\nOrganizers: \n\nMatteo Parisi\, Harvard CMSA\nLauren Williams\, Harvard Mathematics\n\nParticipants (PDF) \nThis event is co-funded by the National Science Foundation. \nLimited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support\, please register above and send an email to amplituhedra@cmsa.fas.harvard.edu no later than Friday\, April 19\, 2024. \nPlease include your name\, address\, current status\, university affiliation\, citizenship\, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student\, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research. If you are a postdoc\, please include a copy of your CV. \n\nSCHEDULE (pdf download) \nWednesday\, May 29\, 2024\n8:30 – 9:00 am\nRegistration and Breakfast \n9:00 – 10:00 am\nJaroslav Trnka\, UC Davis\nTitle: Amplituhedron\nAbstract: I will review basics of the Amplituhedron\, connection to the positive Grassmannian on the mathematical side\, and the scattering amplitudes on the physics side. \n10:00 – 10:15 am\nCoffee Break \n10:15 – 11:15 am\nvia Zoom\nKhrystyna Serhiyenko\, University of Kentucky\nTitle: Introduction to Cluster Algebras\nAbstract: Cluster algebras is a class of commutative rings with an intricate combinatorial structure. They were introduced by Fomin and Zelevinsky in 2002 to study total positivity and canonical basis in Lie Theory\, but quickly evolved into a highly active research area with surprising connections to numerous other areas of mathematics and physics.\nIn this course we will introduce cluster algebras and discuss their basic properties including positivity and Laurent phenomenon. We will also review cluster structures coming from coordinate rings of Grassmannians and the combinatorics of plabic graphs. \n11:15 – 11:30 am\nCoffee Break \n11:30 – 12:30 pm\nThomas Lam\, University of Michigan\nTitle: Introductory Lecture on Positive Geometries\nAbstract: Positive geometries are semialgebraic spaces that appear in the study of scattering amplitudes. Examples include polytopes\, totally nonnegative parts of flag varieties\, and conjecturally\, the amplituhedron. We will give a broad introduction to positive geometries\, and to their canonical forms. \n12:30 – 2:00 pm\nLunch Break \n2:00 – 2:50 pm\nAnastasia Volovich\, Brown University\nTitle: Scattering Amplitudes and Cluster Algebras\nAbstract: I will review some of the deep connections between cluster algebras and the (loop level) scattering amplitudes in N=4 super Yang-Mills theory\, focusing on the cases of n=6 and 7 particles where the corresponding Grassmannian cluster algebras Gr(4\,n) are finite and certain features of the amplitudes are known or believed to be true to all loop order. \n2:50 – 3:00 pm\nCoffee Break \n3:00 – 3:50 pm\nMarcus Spradlin\, Brown University\nTitle: Scattering Amplitudes\, Positive Geometry and the Amplituhedron\nAbstract: I will review the status of (loop level) scattering amplitudes in N=4 super Yang-Mills theory for n>7\, where the corresponding Grassmannian cluster algebras Gr(4\,n) are infinite and novel features emerge\, notably the appearance of certain “marginally positive” algebraic functions of cluster variables. \n3:50 – 4:00 pm\nCoffee Break \n4:00 – 4:30 pm\nCarolina Figueiredo\, Princeton University\nTitle: All-order splits and multi-soft limits for particle and string amplitude\nAbstract: The most important aspects of scattering amplitudes have long been thought to be associated with their poles. Recently a very different sort of “split” factorizations for a wide range of particle and string tree amplitudes have been discovered away from poles. In this talk\, I will explain how natural properties of the binary geometry of the curve integral formulation for scattering amplitudes for Tr$(\Phi^3)$ theory give a simple\, conceptual origin for these splits\, that generalizes them to all orders in the topological expansion. I will also explain how the splits allow us to access and compute loop-integrated multi-soft limits for particle and string amplitudes in Tr$(\Phi^3)$ theory\, the non-linear sigma model and Yang-Mills theory. \n4:30 – 5:15 pm\nYelena Mandelshtam\, UC Berkeley\nTitle: Combinatorics of m=1 Grasstopes\nAbstract: A Grasstope is a linear projection of the totally nonnegative Grassmannian to a smaller Grassmannian. This is a generalization of the amplituhedron\, a geometric object of great importance to calculating scattering amplitudes in physics. The amplituhedron is a Grasstope arising from a totally positive linear map. While amplituhedra are relatively well-studied\, much less is known about general Grasstopes. In this talk\, I will discuss combinatorics and geometry of Grasstopes in the m=1 case. In particular\, I will show that they can be characterized as unions of cells of a hyperplane arrangement satisfying a certain sign variation condition and argue that amplituhedra are (in a certain sense) minimal Grasstopes. This is based on joint work with Dmitrii Pavlov and Lizzie Pratt. \n5:30 – 6:30 pm\nWelcome Reception \n  \nThursday\, May 30\, 2024 \n8:30 – 9:00 am\nBreakfast \n9:00 – 10:00 am\nNima Arkani-Hamed\, IAS\nTitle: Surface Kinematics and THE all-loop integrand for gluon amplitudes \n10:00 – 10:30 am\nCoffee Break \n10:30 – 11:20 am\nHugh Thomas\, Université du Québec à Montréal\nTitle: u-equations from finite dimensional algebras\nAbstract: In this talk\, I will explain how to write down and solve a system of u-equations associated to any finite dimensional algebra with finitely many indecomposable representations. These vastly generalize the system of equations written down by Koba and Nielsen in 1969\, which from our point of view are associated to the representation theory of a Dynkin type A quiver. I will discuss features of the resulting solution spaces\, including connections to tau-tilting theory\, and the relationships that exist among different spaces of solutions. I will also say something about how different choices of finite-dimensional algebra put us in (i) the setting of cluster algebras\, (ii) the Grassmannian combinatorics of non-kissing complexes\, or (iii) the curves-on-surfaces model directly relevant to amplitudes. This talk reports on joint work with Nima Arkani-Hamed\, Hadleigh Frost\, Pierre-Guy Plamondon\, and Giulio Salvatori. \n11:20 – 11:30 am\nCoffee Break \n11:30 – 12:20 pm\nDani Kaufman\, University of Copenhagen\nTitle: Affine Cluster Algebras\nAbstract: Affine cluster algebras form the simplest examples of non-finite type cluster algebras. While they have infinitely many clusters\, they are still mutation finite and have essentially one mutation sequence which produces infinitely many clusters. I will give an introduction to these cluster algebras by comparing them with finite cluster algebras. I will also show how some structures similar to finite type cluster algebras appear “in the limit” along this infinite mutation sequence. If time I will also mention how the “infinite cluster variables” which live in the limit are related to the algebraic letters appearing in the symbol alphabet for 8 particle N=4 SYM amplitudes. \n12:30-12:45 pm\nGroup Photo\, 20 Garden Street\, front entrance stairs outside building \n12:45 – 2:00 pm\nLunch Break \n2:00 – 2:50 pm\nvia Zoom\nRan Tessler\, Weizmann Institute of Science\nTitle: The magic number for the m=2 amplituhedron\nAbstract: We will start by reviewing the amplituhedron and its tilings.\nWe will then show that all tilings of the m=2 amplituhedron have the same cardinality (“the magic number”)\, proving the m=2 case of a conjecture that the same holds for all even-m amplituhedra. If time permits we will discuss related results and consequences.\nBased on a joint work with Parisi\, Sherman-Bennett and Williams. \n2:50 – 3:00 pm\nCoffee Break \n3:00 – 3:50 pm\nMelissa Sherman-Bennett\, MIT & UC Davis\nTitle: Cluster algebras and tilings of amplituhedra\nAbstract: Physicists Arkani-Hamed and Trnka introduced the amplituhedron to better understand scattering amplitudes in N=4 super Yang-Mills theory. The amplituhedron is the image of the totally nonnegative Grassmannian under the “amplituhedron map”. Examples of amplituhedra include cyclic polytopes\, the totally nonnegative Grassmannian itself\, and cyclic hyperplane arrangements. Of primary interest to physics are tilings of amplituhedra\, which are roughly analogous to subdivisions of polytopes. I will discuss joint work with Even-Zohar\, Lakrec\, Parisi\, Tessler and Williams on BCFW tilings of m=4 amplituhedra and the surprising connection between these tilings and the cluster algebra structure of the Grassmannian. \n3:50 – 4:00 pm\nCoffee Break \n4:00 – 5:30 pm\nOpen Problems Forum \n6:00 – 8:00 pm\nConference Dinner (by invitation) \n  \nFriday\, May 31\, 2024 \n8:30 – 9:00 am\nBreakfast \n9:00 – 10:00 am\nYu-tin Huang\, National Taiwan University\nTitle: Chambers and all loop geometry for four-point correlators\nAbstract: The all loop amplituhedron for N=4 SYM (and ABJM theory) can be recast into the notion of loop fibration over tree geometry. This leads to a further dissection of the tree geometry into “chambers”\, whose boundaries represents when the associated loop-form changes. In this talk I will present a new geometry associated with the all loop four-point correlator of N=4 SYM\, where similar description is present. Interestingly\, at four-loops\, this gives a first example where the chamber form is rational even though it’s loop form contains elliptic integrals. \n10:00 – 10:15 am\nCoffee Break \n10:15 – 12:30 am\nEmerging Scholar Talks \n10:15 – 10:40 am\nEvgeniya Akhmedova\, Weizmann Institute of Science\nTitle: The tropical amplituhedron\nAbstract: The Amplituhedron is a geometric object discovered recently by Arkani-Hamed and Trnka\, that provides a completely new direction for calculating scattering amplitudes in quantum field theory. We define a tropical analogue of this object\, the tropicial amplituhedron and study its structure and boundaries. It can be considered as both the tropical limit of the amplituhedron and a generalization of the tropical positive Grassmannian. \n10:40 – 11:10 am\nLizzie Pratt\, UC Berkeley\nTitle: The Chow-Lam Form\nAbstract: The classical Chow form encodes any projective variety by one equation. We introduce the Chow-Lam form for subvarieties of a Grassmannian. By evaluating the Chow-Lam form at twistor coordinates\, we obtain universal projection formulas\, which were pioneered by Thomas Lam for positroid varieties in the study of amplituhedra. This is joint work with Bernd Sturmfels. \n11:10– 11:30 am\nSebastian Seemann\, KU Leuven\nTitle: Vandermonde cells as positive geometries\nAbstract: Vandermonde cells represent semialgebraic subsets of R^n\, characterized as the image of a simplex under the Vandermonde map. However\, within the realm of positive geometry\, several challenges arise in establishing canonical forms for these cells. These include issues such as non-normal boundaries\, non-transversal intersections\, and singularities of boundary curves. Even more difficulties appear when considing the limiting Vandermonde cell\, which is not semi-algebraic and thus doesn’t fit within the standard framework of positive geometries. In this presentation\, I will first review the notion of Polypols and their canonical forms\, examining the complexities encountered when dealing with Vandermonde cells. In particular\, I will explain what goes wrong in the case of Vandermonde cells and which obstructions we can deal with. \n11:30 – 11:40 am\nCoffee break \n11:40 – 12:10 pm\nChia-Kai Kuo\, National Taiwan University\nTitle: Geometric transition from maximal SYM to ABJM\nAbstract: Recently\, the ABJM amplituhedron has been proposed\, encoding all-loop and all-multiplicity ABJM amplitudes. It is constructed by slightly modifying the original definition. In this talk\, I will explore the significance of these modifications in transitioning theoretical models from super Yang-Mills theory to ABJM theory. A key focus will be on how symplectic reduction and the overall sign change in the positivity conditions ensure the consistency of ABJM amplitudes. Additionally\, I will discuss some distinct features of this geometry. \n12:10– 12:30 pm\nLecheng Ren\, Brown University\nTitle: Symbol alphabets from tensor diagrams\nAbstract: We propose to use tensor diagrams and the Fomin-Pylyavskyy conjectures to explore the connection between symbol alphabets of n-particle amplitudes in planar N= 4 Yang-Mills theory and certain polytopes associated to the Grassmannian Gr(4\, n). We show how to assign a web (a planar tensor diagram) to each facet of these polytopes. Webs with no inner loops are associated to cluster variables (rational symbol letters). For webs with a single inner loop we propose and explicitly evaluate an associated web series that contains information about algebraic symbol letters. In this manner we reproduce the results of previous analyses of n ≤ 8\, and find that the polytope C(4\,9) encodes all rational letters\, and all square roots of the algebraic letters\, of known nine-particle amplitudes. \n12:30 – 2:00 pm\nLunch Break \n2:00 – 2:50 pm\nvia Zoom\nPaolo Benincasa\,  MPI\nTitle: Cosmological Polytopes & Beyond\nAbstract: Together with being the source of the most profound questions in fundamental physics\, cosmology turns out to be an arena from where novel combinatorial structures emerge. In this talk\, I will give a gentle introduction to the cosmological polytopes\, describing the so-called Bunch-Davies wavefunction for a large class of scalar theories\, and how it can be used to define and characterize less conventional objects\, named optical polytopes and weighted cosmological polytopes\, which provide examples of non-convex and weighted geometries respectively. \n2:50 – 3:00 pm\nCoffee Break \n3:00 – 3:45 pm\nShruti Paranjape\, UC Davis\nTitle: Loops in a loop expansion\nAbstract: In a paper by Arkani-Hamed\, Henn and Trnka\, it was shown that the amplituhedron construction of N=4 SYM can be recast in terms of negative geometries with a certain hierarchy of loops (closed cycles) in the space of loop momentum twistors. Furthermore\, using differential equation methods\, it was possible to calculate and resum integrated expressions and obtain strong coupling results. In this talk\, we provide a more general framework for the loops of loops expansion and outline a powerful method for the determination of differential forms for higher-order geometries. In particular\, we will focus on the case of 1 closed cycle in loop space and select integrated results. \n3:45 – 4:30 pm\nNick Early\, Weizmann Institute of Science\nTitle: Minimal Kinematics on $\mathcal{M}_{0\,n}$\, and beyond\nAbstract: Minimal Kinematics (MK) identifies kinematic degenerations of the CHY scattering potential where the critical points are given by rational formulas. These rest on the Horn uniformization of Kapranov-Huh; they are specified combinatorially by 2-trees. On the other hand\, Planar Kinematics (PK) identifies the locus in $M_{0\,n}$ which is fixed by cyclic permutation.  Combining MK and PK realizes a maximally thin relative of the associahedron known as the PK polytope; it is a reflexive polytope\, and its polar dual\, the root polytope\, has volume a Catalan number. In this talk\, we start by exploring MK and PK on the moduli space $M_{0\,n}$.  We explain how this story generalizes to moduli spaces $X(k\,n)$ of points in projective space $\mathbb{P}^{k-1}$\, to CEGM amplitudes and beyond. \n4:30 – 5:00 pm\nCoffee and Farewell \n  \n \n  \nAbout the image: \n\nLeft: the 3-dimensional associahedron\, Fomin and Zelevinsky\n\nCenter: artistic depiction of the amplituhedron\, Gilmore\nRight: Schlegel diagram of a hypersimplex\, Ziegler
URL:https://cmsa.fas.harvard.edu/event/amplituhedra2024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Conference
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/amplituhedron_cluster-algebras_posgeometry.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240405T140000
DTEND;TZID=America/New_York:20240406T170000
DTSTAMP:20260504T060537
CREATED:20240105T070812Z
LAST-MODIFIED:20250305T204914Z
UID:10001118-1712325600-1712422800@cmsa.fas.harvard.edu
SUMMARY:Current Developments in Mathematics Conference 2024
DESCRIPTION:CURRENT DEVELOPMENTS IN MATHEMATICS 2024\nAPRIL 5-6\, 2024\nHARVARD UNIVERSITY SCIENCE CENTER\nLECTURE HALL C\nhttps://www.math.harvard.edu/event/current-developments-in-mathematics-2024/\n  \n\nSpeakers:\nDaniel Cristofaro-Gardiner – University of Maryland\nSamit Dasgupta – Duke University\nJiaoyang Huang – University of Pennsylvania\nDaniel Litt – University of Toronto\nLisa Piccirillo – MIT/University of Texas\n\n\n\n\nDownload PDF for a detailed schedule of lectures and events. \n  \n\n\n\n\n\n\n\n\nFriday\, April 5 \n\n\n\n\n\n\n\n\n\n\nSaturday\, April 6 \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n1:30 p.m. – 2:20 p.m. Part 1\n2:20 p.m. – 2:30 p.m. Break\n2:30 p.m. – 3:20 p.m. Part 2\n\nJiaoyang Huang \nRandom Matrix Statistics and Airy Line Ensembles \n\n\n\n\n\n\n\n\n\n\n\n9:05 a.m. – 9:55 a.m. Part 1\n9:55 a.m. – 10:05 a.m. Break\n10:05 a.m. – 10:55 a.m. Part 2\n\nDaniel Litt \nMotives\, mapping class groups\, and monodromy \n\n\n\n\n\n\n\n\n\n\n\n\n3:20 p.m. – 3:35 p.m. \nBreak \n\n\n\n\n\n\n\n\n\n\n10:55 a.m. – 11:10 a.m. \nBreak \n\n\n\n\n\n\n\n\n\n\n\n\n\n3:35 p.m. – 4:25 p.m. Part 1\n4:25 p.m. – 4:35 p.m. Break\n4:35 p.m. – 5:25 p.m. Part 2\n\nLisa Piccirillo \nExotic phenomena in dimension 4 \n\n\n\n\n\n\n\n\n\n\n\n11:10 a.m. – 12 p.m. Part 1\n12 p.m. – 1:30 p.m. Lunch\n1:30 p.m. – 2:20 p.m. Part 2\n\nSamit Dasgupta \nStark’s conjectures and explicit class field theory \n\n\n\n\n\n\n\n\n\n\n\n\n\n2:20 p.m. – 2:35 p.m. \nBreak \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n2:35 p.m. – 3:25 p.m. Part 1\n3:25 p.m. – 3:35 p.m. Break\n3:35 p.m. – 4:25 p.m. Part 2\n\nDan Cristofaro-Gardiner \nLow-dimensional topology and dynamics \n\n\n\n\n\n\n\n\n  \n  \nOrganizers: David Jerison\, Paul Seidel\, Nike Sun (MIT); Denis Auroux\, Mark Kisin\, Lauren Williams\, Horng-Tzer Yau\, Shing-Tung Yau (Harvard). \nSponsored by the National Science Foundation\, Harvard University Mathematics\, and the Massachusetts Institute of Technology. \nHarvard University is committed to maintaining a safe and healthy educational and work environment in which no member of the University community is\, on the basis of sex\, sexual orientation\, or gender identity\, excluded from participation in\, denied the benefits of\, or subjected to discrimination in any University program or activity. More information can be found here.
URL:https://cmsa.fas.harvard.edu/event/cdm-2024/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Conference
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Updated-2024-CDM-Poster-scaled.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240325T090000
DTEND;TZID=America/New_York:20240329T170000
DTSTAMP:20260504T060537
CREATED:20240105T034700Z
LAST-MODIFIED:20240624T182211Z
UID:10001114-1711357200-1711731600@cmsa.fas.harvard.edu
SUMMARY:Arithmetic Quantum Field Theory Conference
DESCRIPTION:Arithmetic Quantum Field Theory Conference \nDates: March 25-29\, 2024 \nLocation: Room G10\, Harvard CMSA\, 20 Garden Street\, Cambridge MA 02138 \nArithmetic Quantum Field Theory Conference Youtube Playlist \nOrganizers: \n\nDavid Ben-Zvi (University of Texas Austin)\nSolomon Friedberg (Boston College)\nNatalie Paquette (University of Washington Seattle)\nBrian Williams (Boston University)\n\nScientific Goals: On one hand\, there has been tremendous progress in the past decade in our understanding of the algebraic structures underlying quantum field theory as expressed in terms of the geometry and topology of low-dimensional manifolds\, both on the level of states (via the formalism of extended\, functorial field theory) and on the level of observables (via the formalism of factorization algebras). On the other hand\, the arithmetic topology (or “knots and primes”) dictionary provides a sturdy bridge between the topology of 2- and 3-manifolds and the arithmetic of number fields. Thus\, one can now port over quantum field theoretic ideas to number theory\, as first proposed by Minhyong Kim with his arithmetic counterpart of Chern-Simons theory. Moreover\, automorphic objects appear in string theory where they play a role in the study of graviton scattering. Most recently\, the work of Kapustin-Witten has been extended towards an understanding of the Langlands program as an arithmetic avatar of electric-magnetic duality in four-dimensional gauge theory to reveal a hidden quantum mechanical nature of the theory of L-functions. \nThe conference will bring together a wide range of mathematicians and physicists working on adjacent areas to explore the emerging notion of arithmetic quantum field theory as a tool to bring quantum physics to bear on questions of interest for the theory of automorphic forms\, representation theory\, harmonic analysis and L-functions. Conversely\, we will explore potential geometric and physical consequences of arithmetic ideas. Our program will also build on the significant interactions between number theorists and physicists arising from the frequent appearance of modular and automorphic forms in partition functions\, scattering amplitudes\, and other quantities of interest in quantum field theory and quantum gravity. \nMonday\, March 25: Connections for Women in Mathematics and Physics\nSpeakers \n\nCharlotte Chan (U Michigan)\nKim Klinger-Logan (Kansas State)\nSarah Harrison (Northeastern)\nMelanie Matchett Wood (Harvard)\nFei Yan (Brookhaven National Lab)\n\nTuesday\, March 26–Friday\, March 29: Arithmetic Quantum Field Theory\nSpeakers \n\nAnne-Marie Aubert (IMJ-PRG)\nRoman Bezrukavnikov (MIT)\nSasha Braverman (Toronto / Perimeter)\nAlejandra Castro (Cambridge)\nYoungJu Choie (POSTECH)\nPavel Etingof (MIT)\nDavide Gaiotto (Perimeter)\nAxel Kleinschmidt (Max Planck Institute for Gravitational Physics)\nKobi Kremnitzer (Oxford)\nSpencer Leslie (Boston College)\nDavid Nadler (Berkeley)\nBảo Châu Ngô (U Chicago)\nGeorge Pappas (Michigan State)\nSam Raskin (Yale)\nPeng Shan (Tsinghua)\nZhiwei Yun (MIT)\n\n\nConference Schedule \nArithmetic Quantum Field Theory Conference \nMarch 25–29\, 2024 \nDownload Program (pdf) \n\nMonday\, March 25\, 2024 – Women in Math and Physics \n\n\n\n\n\n8:30 – 9:00 am \n\n\nBreakfast \n\n\n\n\n9:00 – 10:00 am \n\n\nMelanie Matchett Wood (Harvard) \nTitle: Statistics of Number fields\, function fields\, and 3-manifolds \nAbstract: Motivated by conjectures of Cohen\, Lenstra\, and Martinet on the distribution of class groups of number fields\, we describe the analogous questions of understanding distributions of class groups and fundamental groups of curves over finite fields\, and the distribution of fundamental groups of 3-manifolds. We describe results on these distributions in the cases of curves over finite fields and 3-manifolds\, joint with Liu\, Zureick-Brown\, and Sawin\, and discuss how ideas have passed back and forth between the number field\, curves over finite fields\, and 3-manifold settings. \n\n\n\n\n10:00 – 10:20 am \n\n\nCoffee break \n\n\n\n\n10:20 – 11:20 am \n\n\nCharlotte Chan (U Michigan) \nTitle: Generic character sheaves on parahoric subgroups \nAbstract: Lusztig’s theory of character sheaves for connected reductive groups is one of the most important developments in representation theory in the last few decades. I will give an overview of this theory and explain the need\, from the perspective of the representation theory of p-adic groups\, of a theory of character sheaves on jet schemes. Recently\, R. Bezrukavnikov and I have developed the “generic” part of this desired theory. In the simplest nontrivial case\, this resolves a conjecture of Lusztig and produces perverse sheaves on jet schemes compatible with parahoric Deligne–Lusztig induction. This talk is intended to describe in broad strokes what we know about these generic character sheaves\, especially within the context of the Langlands program. \n\n\n\n\n11:30 – 12:30 pm \n\n\nKim Klinger–Logan (Kansas State) \nTitle: Connections between special values of L-functions and scattering amplitudes \nAbstract: In this talk we will attempt make a connection between zeros and special values of L-functions and scattering amplitudes. The connection is best seen through solutions to differential equations of the form $(\Delta-\lambda)f = S$ on $X=SL(2\,\Z)\SL(2\,\R)/SO(2\,\R)$ for $\Delta=y^2(\partial_x^2+\partial_y^2)$ and $H^{-\infty}(X)\cup M$ where $M$ is the space of moderate growth functions. Recently\, Bombieri and Garrett (following work of Hass\, Hejhal\, and Colin de Verdiere) laid out the possibly connection with eigenvalue solutions to equations of this form with zeros of L-functions. On the other hand\, physicists such as Green\, Russo\, Vanhove found that eigenfunction solutions to equations of this form give coefficients of the 4-graviton scattering amplitude. We will elaborate on these connections and discuss some recent work on finding solutions for such equations. This work is in collaboration with Ksenia Fedosova\, Stephen D. Miller\, Danylo Radchenko and Don Zagier. \nSlides (pdf) \n\n\n\n\n12:30 – 2:15 pm \n\n\nLunch  \n\n\n\n\n2:15 – 3:15 pm \n\n\nFei Yan (Brookhaven National Lab) \nTitle: Topological defects on the lattice \nAbstract: Topological defects\, endowed with a rich mathematical structure\, play important roles in condensed matter physics\, high energy theory and quantum information science. Realization of such defects on the lattice not only has interesting theoretical consequences\, but also opens the pathway to quantum simulation of physical systems. In this talk\, I will discuss lattice realizations of topological defects in simple (1+1)-d systems\, taking the transverse field Ising model and the three-state Potts model as examples. Time permitting\, I will also briefly comment on topological defects in non-equilibrium systems\, such as periodically-driven Floquet systems. \n\n\n\n\n3:15 – 3:30 pm \n\n\nCoffee break \n\n\n\n\n3:30 – 4:30 pm \n\n\nSarah Harrison (Northeastern) \nTitle: Liouville Theory and Weil-Petersson Geometry \nAbstract: Two-dimensional conformal field theory is a powerful tool to understand the geometry of surfaces. Liouville conformal field theory in the classical (large central charge) limit encodes the geometry of the moduli space of Riemann surfaces. I describe an efficient algorithm to compute the Weil–Petersson metric to arbitrary accuracy using Zamolodchikov’s recursion relation for conformal blocks\, focusing on examples of a sphere with four punctures and generalizations to other one-complex-dimensional moduli spaces. Comparison with analytic results for volumes and geodesic lengths finds excellent agreement. In the case of M_{0\,4}\, I discuss numerical results for eigenvalues of the Weil-Petersson Laplacian and connections with random matrix theory. Based on work with K. Coleville\, A. Maloney\, K. Namjou\, and T. Numasawa. \nSlides (pdf) \n\n\n\n\n  \nTuesday\, March 26\, 2024 \n\n\n\n\n9:00 – 9:30 am \n\n\nBreakfast \n\n\n\n\n9:30 – 10:30 am \n  \n\n\nRoman Bezrukavnikov (MIT) \nTitle: From affine Hecke category to invariant distributions \nAbstract: By a result of Ben-Zvi\, Nadler and Preygel the cocenter of the affine Hecke category can be identified with coherent sheaves on the appropriate stack of commuting pairs in the Langlands dual group. In a joint work (in progress) with Ciubotaru\, Kazhdan and Varshavsky we recover the space of unipotent invariant distributions on the p-adic group from that category and develop applications to harmonic analysis\, including endoscopic property of unipotent L-packets. Time permitting\, I will explain how a part of this result can be recovered from a geometric realization of Lusztig’s asymptotic affine Hecke algebra J (joint with Karpov and Krylov)\, and present a conjecture generalizing the story to other depth zero representations; another special case of this generalization appears in a joint work with Varshavsky. \n  \n\n\n\n\n10:30 – 11:00am \n\n\nCoffee break \n\n\n\n\n11:00 – 12:00 pm \n\n\nSasha Braverman (Toronto/Perimeter) \nTitle: Hecke operators for algebraic curves over local non-archimedian fields: a survey of some recent results \nAbstract: The main goal of this talk is to discuss Hecke operators and Hecke eigen-functions for the moduli space of G-bundles on a smooth projective algebraic curve X defined over a local non-archimedian field K (possibly with level structures at finitely many points). The plan is to discuss the following subjects: 1) Definition of Hecke operators and the space on which they act 2) Relation to “classical story” – i.e. eigen-functions of Hecke operators for curves over a finite field. 3) Detailed discussion of the examples when X has genus zero and we consider bundles with trivialization at two points. In this case we’ll discuss the relation to classical representation theory of p-adic groups and two representation theory of Cherednik algebras. Based on joint works with P. Etingof\, D.Kazhdan\, and A. Polishchuk. \n\n\n\n\n12:00 – 12:15 pm \n\n\nGroup photo.  \n\n\n\n\n12:15 – 1:30 pm \n\n\nLunch  \n\n\n\n\n1:30 – 2:30 pm \n\n\nPeng Shan (Tsinghua) \nTitle: Modularity for W-algebras\, affine Springer fibres and associated variety \nAbstract: I will explain a bijection between admissible representations of affine Kac-Moody algebras and fixed points in affine Springer fibres. I will also explain how to match the modular group action on the characters of representations with the one defined by Cherednik in terms of double affine Hecke algebras\, and extensions of these relations to representations of W-algebras. If time permits\, I will discuss some extension of these results to non-admissible levels and some conjectures about their associated varieties. This is based on joint work with Dan Xie\, Wenbin Yan\, and Qixian Zhao. \n\n\n\n\n2:30 – 3:00 pm \n\n\nCoffee break \n\n\n\n\n3:00 – 4:00 pm \n\n\nBảo Châu Ngô (U Chicago) \nTitle: On the nonabelian Fourier kernel and the Lafforgue transform \nAbstract: In the case of SL2\, we present an analytic formula for the nonabelian Fourier kernel responsible for the functional equation of automorphic L-functions. We use the Gelfand-Graev formula for Langlands’ stable transfer factor and a linear map between the Bernstein center and the cocenter that we call the Lafforgue transform. This is a joint work with Zhilin Luo. \n\n\n\n\n  \nWednesday\, March 27\, 2024 \n  \n\n\n\n\n9:00 – 9:30 am \n\n\nBreakfast \n\n\n\n\n9:30 – 10:30 am \n\n\nYoungJu Choie (POSTECH) \nTitle: Schubert Eisenstein series and Poisson summation for Schubert varieties \nAbstract: Schubert Eisenstein series by restricting the summation in a degenerate Eisenstein series to a particular Schubert variety has been studied. In the case of GL3 over Q it was proved that these Schubert Eisenstein series have meromorphic continuations in all parameters and conjectured the same is true in general. We revisit the conjecture and relate it to the program of Braverman\, Kazhdan\, Lafforgue\, Ngˆo\, and Sakellaridis aimed at establishing generalizations of the Poisson summation formula. This is a joint work with Jayce Getz. \nSlides (pdf) \n\n\n\n\n10:30 – 11:00 am \n\n\nCoffee break \n\n\n\n\n11:00 – 12:00 pm \n\n\nAxel Kleinschmidt (MPI) \nTitle: Automorphic representations in string amplitudes \nAbstract: I will review how automorphic representations arise in the low-energy expansion of string scattering amplitudes\, highlighting the connection found by Green/Miller/Vanhove between wavefront sets and BPS conditions. To study the wavefront sets I will present reduction principles for the calculation of Fourier coefficients. String theory also predicts new types of automorphic objects that are characterised by lacking finiteness under the center of the universal enveloping algebra. \nSlides (pdf) \n\n\n\n\n12:00 – 1:30 pm \n\n\nLunch  \n\n\n\n\n1:30 – 2:30 pm \n\n\nPavel Etingof (MIT) \nTitle: Analytic Langlands correspondence over C and R \nAbstract: I will review the analytic component of the geometric Langlands correspondence\, developed recently in my joint work with E. Frenkel and D. Kazhdan (based on previous works by other authors)\, with a special focus on archimedian local fields\, especially R. This is based on our work with E. Frenkel and D. Kazhdan and insights shared by D. Gaiotto and E. Witten. \nSlides (pdf) \n\n\n\n\n2:30 – 3:00 pm \n\n\nCoffee break \n\n\n\n\n3:00 – 4:00 pm \n\n\nDavide Gaiotto (Perimeter) \nTitle: Unexpected Unitarity \nAbstract: Much of the mathematical content of Supersymmetric Quantum Field Theories can be extracted through “twisted theories”: simplified QFTs which are topological (or holomorphic) in a derived sense and often amenable of a rigorous mathematical treatment. The twisting procedure destroys or obfuscates certain properties of the underlying SQFTs\, including unitarity. I will discuss a variety of situations where some form of unitarity can be restored\, endowing the twisted theories with unexpected structures. This includes the recently developed Analytic Langlands program\, an analytic version of Symplectic Duality\, an A-model description of quantization (as opposed to deformation quantization) and other constructions of Hodge-theoretic or twistorial flavour. \n  \n\n\n\n\nThursday\, March 28\, 2024 \n  \n\n\n\n\n8:30 – 9:00 am \n\n\nBreakfast \n\n\n\n\n9:00 – 10:00 am \n\n\nSpencer Leslie (Boston College) \nTitle: Relative Langlands and endoscopy \nAbstract: Spherical varieties play an important role in the study of periods of automorphic forms. But very closely related varieties can lead to very distinct arithmetic problems. Motivated by applications to relative trace formulas\, we discuss the natural question of distinguishing different forms of a given spherical variety in arithmetic settings\, giving a solution for symmetric varieties. It turns out that the answer is intimately connected with the construction of the dual Hamiltonian variety associated with the symmetric variety by Ben-Zvi\, Sakellaridis\, and Venkatesh. I will explain the source of these questions in the theory of endoscopy for symmetric varieties\, with application to the (pre)-stabilization of relative trace formulas. \n\n\n\n\n10:00 – 10:30 am \n\n\nCoffee break \n\n\n\n\n10:30 – 11:30 am \n\n\nAnne-Marie Aubert (IMJ–PRG) \nTitle: The Local Langlands correspondence: from extended quotients to affine Hecke algebras \nAbstract: We will introduce the notion of extended quotient\, illustrate it on examples\, and show how it can be used to construct the local Langlands correspondence in the nonarchimedean case. Next\, we will connect extended quotients\, that are attached to the Bernstein decomposition of the category of smooth representations of p-adic groups\, and their Langlands duals\, to representations of affine Hecke algebras in order to get a description of the LLC as a correspondence between the categories of modules of two collections of such algebras. \nSlides (pdf) \n\n\n\n\n11:45 – 12:45 pm \n\n\nKobi Kremnitzer (Oxford) \nTitle: Functional analysis over the integers\, L-functions and global Hodge theory  \nAbstract: In this talk I will explain how using bornological methods one can develop functional analysis over the integers unifying Archimedean and non-Archimedean analysis. I will give examples of algebras of functions and distributions defined over the integers which base change to the usual algebras over the reals and p-adics. Using these it is possible to write some version of L-functions over the integers. I will then introduce an analytic stack over the integers for which the category of quasi-coherent sheaves gives global Hodge structures. I will relate the integral L-functions to trivialisations of line bundles on this stack. I will also explain how to define a cohomology theory for schemes valued in global Hodge structures (possibly related to q-deRham) and speculate on the relation between the determinant of cohomology and L-functions. This is work in progress joint with Federico Bambozzi and Jack Kelly. \n\n\n\n\n12:45 – 2:00 pm \n\n\nLunch  \n\n\n\n\n2:00 – 3:00 pm \n\n\nDavid Nadler (Berkeley) \nTitle: Going to the boundary \nAbstract: I’ll describe several situations where degenerating a marked smooth curve to a marked nodal curve leads to interesting structures on automorphic moduli spaces. In particular\, I’ll discuss its implications for the cocenter of the affine Hecke category\, real-symmetric duality in relative Langlands\, and some other conjectural situations. The talk will borrow from joint work with various authors including D. Ben-Zvi\, T.-H. Chen\, P. Li\, and Z. Yun. \n\n\n\n\n3:00 – 3:30 pm \n\n\nCoffee break \n\n\n\n\nFriday\, March 29\, 2024 \n  \n\n\n\n\n9:00 – 9:30 am \n\n\nBreakfast \n\n\n\n\n9:30 – 10:30 am \n\n\nGeorge Pappas (Michigan State) \nTitle: Finite and p-adic Chern-Simons type invariants \nAbstract: We will define arithmetic invariants of Galois covers and of ‘etale local systems which are inspired by the classical constructions of Dijkgraaf-Witten and Chern-Simons. We will discuss various conjectures and recent results about these invariants. \n\n\n\n\n10:30 – 11:00 am \n\n\nCoffee break \n\n\n\n\n11:00 – 12:00 pm \n\n\nSam Raskin (Yale) \nTitle: The geometric Langlands conjecture \nAbstract: I will describe the main ideas that go into the proof of the (unramified\, global) geometric Langlands conjecture. All of this work is joint with Gaitsgory and some parts are joint with Arinkin\, Beraldo\, Chen\, Faergeman\, Lin\, and Rozenblyum. \n\n\n\n\n12:00 – 1:30 pm \n\n\nLunch  \n\n\n\n\n1:30 – 2:30 pm \n\n\nAlejandra Castro (Cambridge) \nTitle: The light we can see: Extracting black holes from weak Jacobi forms \nAbstract: Modular forms play a pivotal role in the counting of black hole microstates. The underlying modular symmetry of counting formulae was key in the precise match between the Bekenstein-Hawking entropy of supersymmetric black holes and Cardy’s formula for the asymptotic growth of states. The goal of this talk is to revisit the connection between modular forms and black hole entropy\, and tie it with other consistency conditions of AdS/CFT. We will focus our attention on weak Jacobi forms.  \nI will quantify how constraints on polar states affect the asymptotic growth of non-polar states in weak Jacobi forms. The constraints I’ll consider are sparseness conditions on the Fourier coefficients of these forms\, which are necessary to interpret them as gravitational path integrals. In short\, the constraints will leave an imprint on the subleading corrections to the asymptotic growth of heavy states. With this we will revisit the UV/IR connection that relates black hole microstate counting to modular forms. In particular\, I’ll provide a microscopic interpretation of the logarithmic corrections to the entropy of supersymmetric black holes and tie it to consistency conditions in AdS_3/CFT_2. \n\n\n\n\n2:30 – 3:00 pm \n\n\nCoffee break \n\n\n\n\n3:00 – 4:00 pm \n\n\nZhiwei Yun (MIT) \nTitle: Theta correspondence and relative Langlands \nAbstract: A reductive dual pair (such as a symplectic group and an orthogonal group) acting on the tensor product of their standard representations is an example of hyperspherical varieties\, and is the geometric avatar for theta correspondence. I will explain two geometric results/constructions motivated by the theta correspondence over finite fields. The first one describes how principal series representations behave under theta correspondence using Springer correspondence (joint with Jiajun Ma\, Congling Qiu and Jialiang Zou). The second one is a definition of character sheaves in the setup of theta correspondence (joint with Shamgar Gurevich). I will speculate how the first result fits into relative Langlands duality. \n\n\n\n\n\nLimited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support\, please register above and send an email to cstillman@math.harvard.eduno later than Sunday\, February 25\, 2024. \nPlease include your name\, address\, current status\, university affiliation\, citizenship\, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student\, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research. If you are a postdoc\, please include a copy of your CV. \n\nThis event will be co-funded by the National Science Foundation.\nThe conference is part of the Arithmetic Quantum Field Theory Program\, Feb 4-March 29\, 2024.
URL:https://cmsa.fas.harvard.edu/event/aqftconf/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Conference
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/AQFT_CONFERENCE_Poster_letter.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20231027
DTEND;VALUE=DATE:20231029
DTSTAMP:20260504T060537
CREATED:20230904T060021Z
LAST-MODIFIED:20240624T182341Z
UID:10000002-1698364800-1698537599@cmsa.fas.harvard.edu
SUMMARY:Mathematics in Science: Perspectives and Prospects
DESCRIPTION:Mathematics in Science: Perspectives and Prospects\nA showcase of mathematics in interaction with physics\, computer science\, biology\, and beyond. \nOctober 27–28\, 2023 \nLocation: Harvard University Science Center Hall D & via Zoom. \nDirections and Recommended Lodging \nMathematics in Science: Perspectives and Prospects Youtube Playlist \n  \n\nSpeakers \n\nNima Arkani-Hamed (IAS)\nConstantinos Daskalakis (MIT)\nAlison Etheridge (Oxford)\nMike Freedman (Harvard CMSA)\nGreg Moore (Rutgers)\nBernd Sturmfels (MPI Leipzig)\n\n\nOrganizers \n\nMichael R. Douglas (Harvard CMSA)\nDan Freed (Harvard Math & CMSA)\nMike Hopkins (Harvard Math)\nCumrun Vafa (Harvard Physics)\nHorng-Tzer Yau (Harvard Math)\n\nSchedule\nFriday\, October 27\, 2023 \n\n\n\n2:00–3:15 pm\n\nGreg Moore (Rutgers) \nTitle: Remarks on Physical Mathematics \nAbstract: I will describe some examples of the vigorous modern dialogue between mathematics and theoretical physics (especially high energy and condensed matter physics). I will begin by recalling Stokes’ phenomenon and explain how it is related to some notable developments in quantum field theory from the past 30 years. Time permitting\, I might also say something about the dialogue between mathematicians working on the differential topology of four-manifolds and physicists working on supersymmetric quantum field theories. But I haven’t finished writing the talk yet\, so I don’t know how it will end any more than you do. \nSlides (PDF) \n \n\n\n\n3:15–3:45 pm\nBreak\n\n\n3:45–5:00 pm\n\nBernd Sturmfels (MPI Leipzig) \nTitle: Algebraic Varieties in Quantum Chemistry \nAbstract: We discuss the algebraic geometry behind coupled cluster (CC) theory of quantum many-body systems. The high-dimensional eigenvalue problems that encode the electronic Schroedinger equation are approximated by a hierarchy of polynomial systems at various levels of truncation. The exponential parametrization of the eigenstates gives rise to truncation varieties. These generalize Grassmannians in their Pluecker embedding. We explain how to derive Hamiltonians\, we offer a detailed study of truncation varieties and their CC degrees\, and we present the state of the art in solving the CC equations. This is joint work with Fabian Faulstich and Svala Sverrisdóttir. \nSlides (PDF) \n \n\n\n\n\n  \nSaturday\, October 28\, 2023 \n\n\n\n9:00 am\nBreakfast\n\n\n9:30–10:45 am\n\nMike Freedman (Harvard CMSA) \nTitle: ML\, QML\, and Dynamics: What mathematics can help us understand and advance machine learning? \nAbstract: Vannila deep neural nets DNN repeatedly stretch and fold. They are reminiscent of the logistic map and the Smale horseshoe.  What kind of dynamics is responsible for their expressivity and trainability. Is chaos playing a role? Is the Kolmogorov Arnold representation theorem relevant? Large language models are full of linear maps. Might we look for emergent tensor structures in these highly trained maps in analogy with emergent tensor structures at local minima of certain loss functions in high-energy physics. \nSlides (PDF) \n \n\n\n\n10:45–11:15 am\nBreak\n\n\n11:15 am–12:30 pmvia Zoom\n\nNima Arkani-Hamed (IAS) \nTitle: All-Loop Scattering as A Counting Problem \nAbstract: I will describe a new understanding of scattering amplitudes based on fundamentally combinatorial ideas in the kinematic space of the scattering data. I first discuss a toy model\, the simplest theory of colored scalar particles with cubic interactions\, at all loop orders and to all orders in the topological ‘t Hooft expansion. I will present a novel formula for loop-integrated amplitudes\, with no trace of the conventional sum over Feynman diagrams\, but instead determined by a beautifully simple counting problem attached to any order of the topological expansion. A surprisingly simple shift of kinematic variables converts this apparent toy model into the realistic physics of pions and Yang-Mills theory. These results represent a significant step forward in the decade-long quest to formulate the fundamental physics of the real world in a new language\, where the rules of spacetime and quantum mechanics\, as reflected in the principles of locality and unitarity\, are seen to emerge from deeper mathematical structures. \n \n\n\n\n12:30–2:00 pm\nLunch break\n\n\n2:00–3:15 pm\n\nConstantinos Daskalakis (MIT) \nTitle: How to train deep neural nets to think strategically \nAbstract: Many outstanding challenges in Deep Learning lie at its interface with Game Theory: from playing difficult games like Go to robustifying classifiers against adversarial attacks\, training deep generative models\, and training DNN-based models to interact with each other and with humans. In these applications\, the utilities that the agents aim to optimize are non-concave in the parameters of the underlying DNNs; as a result\, Nash equilibria fail to exist\, and standard equilibrium analysis is inapplicable. So how can one train DNNs to be strategic? What is even the goal of the training? We shed light on these challenges through a combination of learning-theoretic\, complexity-theoretic\, game-theoretic and topological techniques\, presenting obstacles and opportunities for Deep Learning and Game Theory going forward. \nSlides (PDF) \n \n\n\n\n3:15–3:45 pm\nBreak\n\n\n3:45–5:00 pm\n\nAlison Etheridge (Oxford) \nTitle: Modelling hybrid zones \nAbstract: Mathematical models play a fundamental role in theoretical population genetics and\, in turn\, population genetics provides a wealth of mathematical challenges. In this lecture we investigate the interplay between a particular (ubiquitous) form of natural selection\, spatial structure\, and\, if time permits\, so-called genetic drift. A simple mathematical caricature will uncover the importance of the shape of the domain inhabited by a species for the effectiveness of natural selection. \nSlides (PDF) \n \n\n\n\n\nLimited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support\, please register above and send an email to mathsci2023@cmsa.fas.harvard.edu no later than October 9\, 2023. \nPlease include your name\, address\, current status\, university affiliation\, citizenship\, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student\, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research. If you are a postdoc\, please include a copy of your CV. \n\n 
URL:https://cmsa.fas.harvard.edu/event/mathematics-in-science/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/MathScience2023Poster_8.5x11.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230831T090000
DTEND;TZID=America/New_York:20230901T170000
DTSTAMP:20260504T060537
CREATED:20230904T063654Z
LAST-MODIFIED:20251026T043812Z
UID:10000820-1693472400-1693587600@cmsa.fas.harvard.edu
SUMMARY:Big Data Conference 2023
DESCRIPTION:On August 31-Sep 1\, 2023 the CMSA hosted the ninth annual Conference on Big Data. The Big Data Conference features speakers from the Harvard community as well as scholars from across the globe\, with talks focusing on computer science\, statistics\, math and physics\, and economics. \nSpeakers: \n\nJacob Andreas\, MIT\nMorgane Austern\, Harvard\nAlbert-László Barabási\, Northeastern\nRachel Cummings\, Columbia\nMelissa Dell\, Harvard\nJianqing Fan\, Princeton\nTommi Jaakkola\, MIT\nAnkur Moitra\, MIT\nMark Sellke\, Harvard\nMarinka Zitnik\, Harvard Medical School\n\nOrganizers: \n\nMichael Douglas\, CMSA\, Harvard University\nYannai Gonczarowski\, Economics and Computer Science\, Harvard University\nLucas Janson\, Statistics and Computer Science\, Harvard University\nTracy Ke\, Statistics\, Harvard University\nHorng-Tzer Yau\, Mathematics and CMSA\, Harvard University\nYue Lu\, Electrical Engineering and Applied Mathematics\, Harvard University\n\nSchedule\n(PDF download) \nThursday\, August 31\, 2023 \n\n\n\n9:00 AM\nBreakfast\n\n\n9:30 AM\nIntroductions\n\n\n9:45–10:45 AM\nAlbert-László Barabási (Northeastern\, Harvard) \nTitle: From Network Medicine to the Foodome: The Dark Matter of Nutrition \nAbstract: A disease is rarely a consequence of an abnormality in a single gene but reflects perturbations to the complex intracellular network. Network medicine offer a platform to explore systematically not only the molecular complexity of a particular disease\, leading to the identification of disease modules and pathways\, but also the molecular relationships between apparently distinct (patho) phenotypes. As an application\, I will explore how we use network medicine to uncover the role individual food molecules in our health. Indeed\, our current understanding of how diet affects our health is limited to the role of 150 key nutritional components systematically tracked by the USDA and other national databases in all foods. Yet\, these nutritional components represent only a tiny fraction of the over 135\,000 distinct\, definable biochemicals present in our food. While many of these biochemicals have documented effects on health\, they remain unquantified in any systematic fashion across different individual foods. Their invisibility to experimental\, clinical\, and epidemiological studies defines them as the ‘Dark Matter of Nutrition.’ I will speak about our efforts to develop a high-resolution library of this nutritional dark matter\, and efforts to understand the role of these molecules on health\, opening novel avenues by which to understand\, avoid\, and control disease. \nhttps://youtu.be/UmgzUwi6K3E\n\n\n10:45–11:00 AM\nBreak\n\n\n11:00 AM–12:00 PM\nRachel Cummings (Columbia) \nTitle: Differentially Private Algorithms for Statistical Estimation Problems \nAbstract: Differential privacy (DP) is widely regarded as a gold standard for privacy-preserving computation over users’ data.  It is a parameterized notion of database privacy that gives a rigorous worst-case bound on the information that can be learned about any one individual from the result of a data analysis task. Algorithmically it is achieved by injecting carefully calibrated randomness into the analysis to balance privacy protections with accuracy of the results.\nIn this talk\, we will survey recent developments in the development of DP algorithms for three important statistical problems\, namely online learning with bandit feedback\, causal interference\, and learning from imbalanced data. For the first problem\, we will show that Thompson sampling — a standard bandit algorithm developed in the 1930s — already satisfies DP due to the inherent randomness of the algorithm. For the second problem of causal inference and counterfactual estimation\, we develop the first DP algorithms for synthetic control\, which has been used non-privately for this task for decades. Finally\, for the problem of imbalanced learning\, where one class is severely underrepresented in the training data\, we show that combining existing techniques such as minority oversampling perform very poorly when applied as pre-processing before a DP learning algorithm; instead we propose novel approaches for privately generating synthetic minority points. \nBased on joint works with Marco Avella Medina\, Vishal Misra\, Yuliia Lut\, Tingting Ou\, Saeyoung Rho\, and Ethan Turok. \nhttps://youtu.be/0cPE6rb1Roo\n\n\n12:00–1:30 PM\nLunch\n\n\n1:30–2:30 PM\nMorgane Austern (Harvard) \nTitle: To split or not to split that is the question: From cross validation to debiased machine learning \nAbstract: Data splitting is a ubiquitous method in statistics with examples ranging from cross-validation to cross-fitting. However\, despite its prevalence\, theoretical guidance regarding its use is still lacking. In this talk\, we will explore two examples and establish an asymptotic theory for it. In the first part of this talk\, we study the cross-validation method\, a ubiquitous method for risk estimation\, and establish its asymptotic properties for a large class of models and with an arbitrary number of folds. Under stability conditions\, we establish a central limit theorem and Berry-Esseen bounds for the cross-validated risk\, which enable us to compute asymptotically accurate confidence intervals. Using our results\, we study the statistical speed-up offered by cross-validation compared to a train-test split procedure. We reveal some surprising behavior of the cross-validated risk and establish the statistically optimal choice for the number of folds. In the second part of this talk\, we study the role of cross-fitting in the generalized method of moments with moments that also depend on some auxiliary functions. Recent lines of work show how one can use generic machine learning estimators for these auxiliary problems\, while maintaining asymptotic normality and root-n consistency of the target parameter of interest. The literature typically requires that these auxiliary problems are fitted on a separate sample or in a cross-fitting manner. We show that when these auxiliary estimation algorithms satisfy natural leave-one-out stability properties\, then sample splitting is not required. This allows for sample reuse\, which can be beneficial in moderately sized sample regimes. \nhttps://youtu.be/L_pHxgoQSgU\n\n\n2:30–2:45 PM\nBreak\n\n\n2:45–3:45 PM\nAnkur Moitra (MIT) \nTitle: Learning from Dynamics \nAbstract: Linear dynamical systems are the canonical model for time series data. They have wide-ranging applications and there is a vast literature on learning their parameters from input-output sequences. Moreover they have received renewed interest because of their connections to recurrent neural networks.\nBut there are wide gaps in our understanding. Existing works have only asymptotic guarantees or else make restrictive assumptions\, e.g. that preclude having any long-range correlations. In this work\, we give a new algorithm based on the method of moments that is computationally efficient and works under essentially minimal assumptions. Our work points to several missed connections\, whereby tools from theoretical machine learning including tensor methods\, can be used in non-stationary settings. \nhttps://youtu.be/UmgzUwi6K3E\n\n\n3:45–4:00 PM\nBreak\n\n\n4:00–5:00 PM\nMark Sellke (Harvard) \nTitle: Algorithmic Thresholds for Spherical Spin Glasses \nAbstract: High-dimensional optimization plays a crucial role in modern statistics and machine learning. I will present recent progress on non-convex optimization problems with random objectives\, focusing on the spherical p-spin glass. This model is related to spiked tensor estimation and has been studied in probability and physics for decades. We will see that a natural class of “stable” optimization algorithms gets stuck at an algorithmic threshold related to geometric properties of the landscape. The algorithmic threshold value is efficiently attained via Langevin dynamics or by a second-order ascent method of Subag. Much of this picture extends to other models\, such as random constraint satisfaction problems at high clause density. \nhttps://youtu.be/JoghiwiIbT8\n\n\n6:00 – 8:00 PM\nBanquet for organizers and speakers\n\n\n\n  \nFriday\, September 1\, 2023 \n\n\n\n9:00 AM\nBreakfast\n\n\n9:30 AM\nIntroductions\n\n\n9:45–10:45 AM\nJacob Andreas (MIT) \nTitle: What Learning Algorithm is In-Context Learning? \nAbstract: Neural sequence models\, especially transformers\, exhibit a remarkable capacity for “in-context” learning. They can construct new predictors from sequences of labeled examples (x\,f(x)) presented in the input without further parameter updates. I’ll present recent findings suggesting that transformer-based in-context learners implement standard learning algorithms implicitly\, by encoding smaller models in their activations\, and updating these implicit models as new examples appear in the context\, using in-context linear regression as a model problem. First\, I’ll show by construction that transformers can implement learning algorithms for linear models based on gradient descent and closed-form ridge regression. Second\, I’ll show that trained in-context learners closely match the predictors computed by gradient descent\, ridge regression\, and exact least-squares regression\, transitioning between different predictors as transformer depth and dataset noise vary\, and converging to Bayesian estimators for large widths and depths. Finally\, we present preliminary evidence that in-context learners share algorithmic features with these predictors: learners’ late layers non-linearly encode weight vectors and moment matrices. These results suggest that in-context learning is understandable in algorithmic terms\, and that (at least in the linear case) learners may rediscover standard estimation algorithms. This work is joint with Ekin Akyürek at MIT\, and Dale Schuurmans\, Tengyu Ma and Denny Zhou at Stanford. \nhttps://youtu.be/UNVl64G3BzA\n\n\n10:45–11:00 AM\nBreak\n\n\n11:00 AM–12:00 PM\nTommi Jaakkola (MIT) \nTitle: Generative modeling and physical processes \nAbstract: Rapidly advancing deep distributional modeling techniques offer a number of opportunities for complex generative tasks\, from natural sciences such as molecules and materials to engineering. I will discuss generative approaches inspired from physical processes including diffusion models and more recent electrostatic models (Poisson flow)\, and how they relate to each other in terms of embedding dimension. From the point of view of applications\, I will highlight our recent work on SE(3) invariant distributional modeling over backbone 3D structures with ability to generate designable monomers without relying on pre-trained protein structure prediction methods as well as state of the art image generation capabilities (Poisson flow). Time permitting\, I will also discuss recent analysis of efficiency of sample generation in such models. \nhttps://youtu.be/GLEwQAWQ85E\n\n\n12:00–1:30 PM\nLunch\n\n\n1:30–2:30 PM\nMarinka Zitnik (Harvard Medical School) \nTitle: Multimodal Learning on Graphs \nAbstract: Understanding biological and natural systems requires modeling data with underlying geometric relationships across scales and modalities such as biological sequences\, chemical constraints\, and graphs of 3D spatial or biological interactions. I will discuss unique challenges for learning from multimodal datasets that are due to varying inductive biases across modalities and the potential absence of explicit graphs in the input. I will describe a framework for structure-inducing pretraining that allows for a comprehensive study of how relational structure can be induced in pretrained language models. We use the framework to explore new graph pretraining objectives that impose relational structure in the induced latent spaces—i.e.\, pretraining objectives that explicitly impose structural constraints on the distance or geometry of pretrained models. Applications in genomic medicine and therapeutic science will be discussed. These include TxGNN\, an AI model enabling zero-shot prediction of therapeutic use across over 17\,000 diseases\, and PINNACLE\, a contextual graph AI model dynamically adjusting its outputs to contexts in which it operates. PINNACLE enhances 3D protein structure representations and predicts the effects of drugs at single-cell resolution. \nhttps://youtu.be/hjt4nsN_8iM\n\n\n2:30–2:45 PM\nBreak\n\n\n2:45–3:45 PM\nJianqing Fan (Princeton) \nTitle: UTOPIA: Universally Trainable Optimal Prediction Intervals Aggregation \nAbstract: Uncertainty quantification for prediction is an intriguing problem with significant applications in various fields\, such as biomedical science\, economic studies\, and weather forecasts. Numerous methods are available for constructing prediction intervals\, such as quantile regression and conformal predictions\, among others. Nevertheless\, model misspecification (especially in high-dimension) or sub-optimal constructions can frequently result in biased or unnecessarily-wide prediction intervals. In this work\, we propose a novel and widely applicable technique for aggregating multiple prediction intervals to minimize the average width of the prediction band along with coverage guarantee\, called Universally Trainable Optimal Predictive Intervals Aggregation (UTOPIA). The method also allows us to directly construct predictive bands based on elementary basis functions.  Our approach is based on linear or convex programming which is easy to implement. All of our proposed methodologies are supported by theoretical guarantees on the coverage probability and optimal average length\, which are detailed in this paper. The effectiveness of our approach is convincingly demonstrated by applying it to synthetic data and two real datasets on finance and macroeconomics. (Joint work Jiawei Ge and Debarghya Mukherjee). \nhttps://youtu.be/WY6dr1oEOrk\n\n\n3:45–4:00 PM\nBreak\n\n\n4:00–5:00 PM\nMelissa Dell (Harvard) \nTitle: Efficient OCR for Building a Diverse Digital History \nAbstract: Many users consult digital archives daily\, but the information they can access is unrepresentative of the diversity of documentary history. The sequence-to-sequence architecture typically used for optical character recognition (OCR) – which jointly learns a vision and language model – is poorly extensible to low-resource document collections\, as learning a language-vision model requires extensive labeled sequences and compute. This study models OCR as a character-level image retrieval problem\, using a contrastively trained vision encoder. Because the model only learns characters’ visual features\, it is more sample-efficient and extensible than existing architectures\, enabling accurate OCR in settings where existing solutions fail. Crucially\, it opens new avenues for community engagement in making digital history more representative of documentary history. \nhttps://youtu.be/u0JY9vURUAs\n\n\n\n  \n\nInformation about the 2022 Big Data Conference can be found here.
URL:https://cmsa.fas.harvard.edu/event/bigdata_2023/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Big Data Conference,Conference,Event
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230407T140000
DTEND;TZID=America/New_York:20230408T170000
DTSTAMP:20260504T060537
CREATED:20230705T055126Z
LAST-MODIFIED:20240229T095034Z
UID:10000067-1680876000-1680973200@cmsa.fas.harvard.edu
SUMMARY:Current Developments in Mathematics Conference 2023
DESCRIPTION:Current Developments in Mathematics 2023\nHarvard University Science Center\, Lecture Hall C\nApril 7-8\, 2023\nSpeakers: \nAmol Aggarwal – Columbia University\nBhargav Bhatt – Institute for Advanced Study\, Princeton University\, & University of Michigan\nPaul Bourgade – New York University\, Courant Institute\nVesselin Dimitrov – Institute for Advanced Study & Georgia Institute of Technology\nGreta Panova – University of Southern California\n\n\n\n\nFor more information\, and to register\, please visit:\nCurrent Developments in Mathematics 2023 \n \n  \nOrganizers: David Jerison\, Paul Seidel\, Nike Sun (MIT); Denis Auroux\, Mark Kisin\, Lauren Williams\, Horng-Tzer Yau \nSponsored by the National Science Foundation\, Harvard University Mathematics\, Harvard University Center of Mathematical Sciences and Applications\, and the Massachusetts Institute of Technology. \nHarvard University is committed to maintaining a safe and healthy educational and work environment in which no member of the University community is\, on the basis of sex\, sexual orientation\, or gender identity\, excluded from participation in\, denied the benefits of\, or subjected to discrimination in any University program or activity. More information can be found here.
URL:https://cmsa.fas.harvard.edu/event/cdm-2023/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CDM-2023-Poster.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230227T090000
DTEND;TZID=America/New_York:20230301T173000
DTSTAMP:20260504T060537
CREATED:20230705T053135Z
LAST-MODIFIED:20241212T162829Z
UID:10000064-1677488400-1677691800@cmsa.fas.harvard.edu
SUMMARY:Conference on Geometry and Statistics
DESCRIPTION:On Feb 27-March 1\, 2023 the CMSA will host a Conference on Geometry and Statistics. \nLocation: G10\, CMSA\, 20 Garden Street\, Cambridge MA 02138 \nOrganizing Committee:\nStephan Huckemann (Georg-August-Universität Göttingen)\nEzra Miller (Duke University)\nZhigang Yao (Harvard CMSA and Committee Chair) \nScientific Advisors:\nHorng-Tzer Yau (Harvard CMSA)\nShing-Tung Yau (Harvard CMSA) \nSpeakers: \n\nTamara Broderick (MIT)\nDavid Donoho (Stanford)\nIan Dryden (Florida International University in Miami)\nDavid Dunson (Duke)\nCharles Fefferman (Princeton)\nStefanie Jegelka (MIT)\nSebastian Kurtek (OSU)\nLizhen Lin (Notre Dame)\nSteve Marron (U North Carolina)\nEzra Miller (Duke)\nHans-Georg Mueller (UC Davis)\nNicolai Reshetikhin (UC Berkeley)\nWolfgang Polonik (UC Davis)\nAmit Singer (Princeton)\nZhigang Yao (Harvard CMSA)\nBin Yu (Berkeley)\n\nModerator: Michael Simkin (Harvard CMSA) \n  \nSCHEDULE\nMonday\, Feb. 27\, 2023 (Eastern Time) \n\n\n\n8:30 am\nBreakfast\n\n\n8:45–8:55 am\nZhigang Yao\nWelcome Remarks\n\n\n8:55–9:00 am\nShing-Tung Yau*\nRemarks\n\n\n\nMorning Session Chair: Zhigang Yao\n\n\n9:00–10:00 am\nDavid Donoho\nTitle: ScreeNOT: Exact MSE-Optimal Singular Value Thresholding in Correlated Noise \nAbstract: Truncation of the singular value decomposition is a true scientific workhorse. But where to Truncate? \nFor 55 years the answer\, for many scientists\, has been to eyeball the scree plot\, an approach which still generates hundreds of papers per year. \nI will describe ScreeNOT\, a mathematically solid alternative deriving from the many advances in Random Matrix Theory over those 55 years. Assuming a model of low-rank signal plus possibly correlated noise\, and adopting an asymptotic viewpoint with number of rows proportional to the number of columns\, we show that ScreeNOT has a surprising oracle property. \nIt typically achieves exactly\, in large finite samples\, the lowest possible MSE for matrix recovery\, on each given problem instance – i.e. the specific threshold it selects gives exactly the smallest achievable MSE loss among all possible threshold choices for that noisy dataset and that unknown underlying true low rank model. The method is computationally efficient and robust against perturbations of the underlying covariance structure. \nThe talk is based on joint work with Matan Gavish and Elad Romanov\, Hebrew University.\n\n\n10:00–10:10 am\nBreak\n\n\n10:10–11:10 am\nSteve Marron\nTitle: Modes of Variation in Non-Euclidean Spaces \nAbstract: Modes of Variation provide an intuitive means of understanding variation in populations\, especially in the case of data objects that naturally lie in non-Euclidean spaces. A variety of useful approaches to finding useful modes of variation are considered in several non-Euclidean contexts\, including shapes as data objects\, vectors of directional data\, amplitude and phase variation and compositional data.\n\n\n11:10–11:20 am\nBreak\n\n\n11:20 am–12:20 pm\nZhigang Yao\nTitle: Manifold fitting: an invitation to statistics \nAbstract: While classical statistics has dealt with observations which are real numbers or elements of a real vector space\, nowadays many statistical problems of high interest in the sciences deal with the analysis of data which consist of more complex objects\, taking values in spaces which are naturally not (Euclidean) vector spaces but which still feature some geometric structure. This manifold fitting problem can go back to H. Whitney’s work in the early 1930s (Whitney (1992))\, and finally has been answered in recent years by C. Fefferman’s works (Fefferman\, 2006\, 2005). The solution to the Whitney extension problem leads to new insights for data interpolation and inspires the formulation of the Geometric Whitney Problems (Fefferman et al. (2020\, 2021a)): Assume that we are given a set $Y \subset \mathbb{R}^D$. When can we construct a smooth $d$-dimensional submanifold $\widehat{M} \subset \mathbb{R}^D$ to approximate $Y$\, and how well can $\widehat{M}$ estimate $Y$ in terms of distance and smoothness? To address these problems\, various mathematical approaches have been proposed (see Fefferman et al. (2016\, 2018\, 2021b)). However\, many of these methods rely on restrictive assumptions\, making extending them to efficient and workable algorithms challenging. As the manifold hypothesis (non-Euclidean structure exploration) continues to be a foundational element in statistics\, the manifold fitting Problem\, merits further exploration and discussion within the modern statistical community. The talk will be partially based on a recent work Yao and Xia (2019) along with some on-going progress. Relevant reference:https://arxiv.org/abs/1909.10228\n\n\n 12:20–1:50 pm\n12:20 pm Group Photo \nfollowed by Lunch\n\n\n\nAfternoon Session Chair: Stephan Huckemann\n\n\n1:50–2:50 pm\nBin Yu*\nTitle: Interpreting Deep Neural Networks towards Trustworthiness \nAbstract: Recent deep learning models have achieved impressive predictive performance by learning complex functions of many variables\, often at the cost of interpretability. This lecture first defines interpretable machine learning in general and introduces the agglomerative contextual decomposition (ACD) method to interpret neural networks. Extending ACD to the scientifically meaningful frequency domain\, an adaptive wavelet distillation (AWD) interpretation method is developed. AWD is shown to be both outperforming deep neural networks and interpretable in two prediction problems from cosmology and cell biology. Finally\, a quality-controlled data science life cycle is advocated for building any model for trustworthy interpretation and introduce a Predictability Computability Stability (PCS) framework for such a data science life cycle.\n\n\n2:50–3:00 pm\nBreak\n\n\n3:00-4:00 pm\nHans-Georg Mueller\nTitle: Exploration of Random Objects with Depth Profiles and Fréchet Regression \nAbstract: Random objects\, i.e.\, random variables that take values in a separable metric space\, pose many challenges for statistical analysis\, as vector operations are not available in general metric spaces. Examples include random variables that take values in the space of distributions\, covariance matrices or surfaces\, graph Laplacians to represent networks\, trees and in other spaces. The increasing prevalence of samples of random objects has stimulated the development of metric statistics\, an emerging collection of statistical tools to characterize\, infer and relate samples of random objects. Recent developments include depth profiles\, which are useful for the exploration of random objects. The depth profile for any given object is the distribution of distances to all other objects (with P. Dubey\, Y. Chen 2022). \nThese distributions can then be subjected to statistical analysis. Their mutual transports lead to notions of transport ranks\, quantiles and centrality. Another useful tool is global or local Fréchet regression (with A. Petersen 2019) where random objects are responses and scalars or vectors are predictors and one aims at modeling conditional Fréchet means. Recent theoretical advances for local Fréchet regression provide a basis for object time warping (with Y. Chen 2022). These approaches are illustrated with distributional and other data.\n\n\n4:00-4:10 pm\nBreak\n\n\n4:10-5:10 pm\nStefanie Jegelka\nTitle: Some benefits of machine learning with invariances \nAbstract: In many applications\, especially in the sciences\, data and tasks have known invariances. Encoding such invariances directly into a machine learning model can improve learning outcomes\, while it also poses challenges on efficient model design. In the first part of the talk\, we will focus on the invariances relevant to eigenvectors and eigenspaces being inputs to a neural network. Such inputs are important\, for instance\, for graph representation learning. We will discuss targeted architectures that can universally express functions with the relevant invariances – sign flips and changes of basis – and their theoretical and empirical benefits. \nSecond\, we will take a broader\, theoretical perspective. Empirically\, it is known that encoding invariances into the machine learning model can reduce sample complexity. For the simplified setting of kernel ridge regression or random features\, we will discuss new bounds that illustrate two ways in which invariances can reduce sample complexity. Our results hold for learning on manifolds and for invariances to (almost) any group action\, and use tools from differential geometry. \nThis is joint work with Derek Lim\, Joshua Robinson\, Behrooz Tahmasebi\, Lingxiao Zhao\, Tess Smidt\, Suvrit Sra\, and Haggai Maron.\n\n\n\n  \n  \n  \nTuesday\, Feb. 28\, 2023 (Eastern Time) \n\n\n\n8:30-9:00 am\nBreakfast\n\n\n\nMorning Session Chair: Zhigang Yao\n\n\n9:00-10:00 am\nCharles Fefferman*\nTitle: Lipschitz Selection on Metric Spaces \nAbstract: The talk concerns the problem of finding a Lipschitz map F from a given metric space X into R^D\, subject to the constraint that F(x) must lie in a given compact convex “target” K(x) for each point x in X. Joint work with Pavel Shvartsman and with Bernat Guillen Pegueroles.\n\n\n10:00-10:10 am\nBreak\n\n\n10:10-11:10 am\nDavid Dunson\nTitle: Inferring manifolds from noisy data using Gaussian processes \nAbstract: In analyzing complex datasets\, it is often of interest to infer lower dimensional structure underlying the higher dimensional observations. As a flexible class of nonlinear structures\, it is common to focus on Riemannian manifolds. Most existing manifold learning algorithms replace the original data with lower dimensional coordinates without providing an estimate of the manifold in the observation space or using the manifold to denoise the original data. This article proposes a new methodology for addressing these problems\, allowing interpolation of the estimated manifold between fitted data points. The proposed approach is motivated by novel theoretical properties of local covariance matrices constructed from noisy samples on a manifold. Our results enable us to turn a global manifold reconstruction problem into a local regression problem\, allowing application of Gaussian processes for probabilistic manifold reconstruction. In addition to theory justifying the algorithm\, we provide simulated and real data examples to illustrate the performance. Joint work with Nan Wu – see https://arxiv.org/abs/2110.07478\n\n\n11:10-11:20 am\nBreak\n\n\n11:20 am-12:20 pm\nWolfgang Polonik\nTitle: Inference in topological data analysis \nAbstract: Topological data analysis has seen a huge increase in popularity finding applications in numerous scientific fields. This motivates the importance of developing a deeper understanding of benefits and limitations of such methods. Using this angle\, we will present and discuss some recent results on large sample inference in topological data analysis\, including bootstrap for Betti numbers and the Euler characteristics process.\n\n\n\n\n\n\n12:20–1:50 pm\nLunch\n\n\n\nAfternoon Session Chair: Stephan Huckemann\n\n\n1:50-2:50 pm\nEzra Miller\nTitle: Geometric central limit theorems on non-smooth spaces \nAbstract: The central limit theorem (CLT) is commonly thought of as occurring on the real line\, or in multivariate form on a real vector space. Motivated by statistical applications involving nonlinear data\, such as angles or phylogenetic trees\, the past twenty years have seen CLTs proved for Fréchet means on manifolds and on certain examples of singular spaces built from flat pieces glued together in combinatorial ways. These CLTs reduce to the linear case by tangent space approximation or by gluing. What should a CLT look like on general non-smooth spaces\, where tangent spaces are not linear and no combinatorial gluing or flat pieces are available? Answering this question involves figuring out appropriate classes of spaces and measures\, correct analogues of Gaussian random variables\, and how the geometry of the space (think “curvature”) is reflected in the limiting distribution. This talk provides an overview of these answers\, starting with a review of the usual linear CLT and its generalization to smooth manifolds\, viewed through a lens that casts the singular CLT as a natural outgrowth\, and concluding with how this investigation opens gateways to further advances in geometric probability\, topology\, and statistics. Joint work with Jonathan Mattingly and Do Tran.\n\n\n2:50-3:00 pm\nBreak\n\n\n3:00-4:00 pm\nLizhen Lin\nTitle: Statistical foundations of deep generative models \nAbstract: Deep generative models are probabilistic generative models where the generator is parameterized by a deep neural network. They are popular models for modeling high-dimensional data such as texts\, images and speeches\, and have achieved impressive empirical success. Despite demonstrated success in empirical performance\, theoretical understanding of such models is largely lacking. We investigate statistical properties of deep generative models from a nonparametric distribution estimation viewpoint. In the considered model\, data are assumed to be observed in some high-dimensional ambient space but concentrate around some low-dimensional structure such as a lower-dimensional manifold structure. Estimating the distribution supported on this low-dimensional structure is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. We obtain convergence rates with respect to the Wasserstein metric of distribution estimators based on two methods: a sieve MLE based on the perturbed data and a GAN type estimator. Such an analysis provides insights into i) how deep generative models can avoid the curse of dimensionality and outperform classical nonparametric estimates\, and ii) how likelihood approaches work for singular distribution estimation\, especially in adapting to the intrinsic geometry of the data.\n\n\n4:00-4:10 pm\nBreak\n\n\n4:10-5:10 pm\nConversation session\n\n\n\n  \n  \n  \nWednesday\, March 1\, 2023 (Eastern Time) \n\n\n\n8:30-9:00 am\nBreakfast\n\n\n\nMorning Session Chair: Ezra Miller\n\n\n9:00-10:00 am\nAmit Singer*\nTitle: Heterogeneity analysis in cryo-EM by covariance estimation and manifold learning \nAbstract: In cryo-EM\, the 3-D molecular structure needs to be determined from many noisy 2-D tomographic projection images of randomly oriented and positioned molecules. A key assumption in classical reconstruction procedures for cryo-EM is that the sample consists of identical molecules. However\, many molecules of interest exist in more than one conformational state. These structural variations are of great interest to biologists\, as they provide insight into the functioning of the molecule. Determining the structural variability from a set of cryo-EM images is known as the heterogeneity problem\, widely recognized as one of the most challenging and important computational problem in the field. Due to high level of noise in cryo-EM images\, heterogeneity studies typically involve hundreds of thousands of images\, sometimes even a few millions. Covariance estimation is one of the earliest methods proposed for heterogeneity analysis in cryo-EM. It relies on computing the covariance of the conformations directly from projection images and extracting the optimal linear subspace of conformations through an eigendecomposition. Unfortunately\, the standard formulation is plagued by the exorbitant cost of computing the N^3 x N^3 covariance matrix. In the first part of the talk\, we present a new low-rank estimation method that requires computing only a small subset of the columns of the covariance while still providing an approximation for the entire matrix. This scheme allows us to estimate tens of principal components of real datasets in a few minutes at medium resolutions and under 30 minutes at high resolutions. In the second part of the talk\, we discuss a manifold learning approach based on the graph Laplacian and the diffusion maps framework for learning the manifold of conformations. If time permits\, we will also discuss the potential application of optimal transportation to heterogeneity analysis. Based on joint works with Joakim Andén\, Marc Gilles\, Amit Halevi\, Eugene Katsevich\, Joe Kileel\, Amit Moscovich\, and Nathan Zelesko.\n\n\n10:00-10:10 am\nBreak\n\n\n10:10-11:10 am\nIan Dryden\nTitle: Statistical shape analysis of molecule data \nAbstract: Molecular shape data arise in many applications\, for example high dimension low sample size cryo-electron microscopy (cryo-EM) data and large temporal sequences of peptides from molecular dynamics simulations. In both applications it is of interest to summarize the shape evolution of the molecules in a succinct\, low-dimensional representation. However\, Euclidean techniques such as principal components analysis (PCA) can be problematic as the data may lie far from in a flat manifold. Principal nested spheres gives a fundamentally different decomposition of data from the usual Euclidean subspace based PCA. Subspaces of successively lower dimension are fitted to the data in a backwards manner with the aim of retaining signal and dispensing with noise at each stage. We adapt the methodology to 3D sub-shape spaces and provide some practical fitting algorithms. The methodology is applied to cryo-EM data of a large sliding clamp multi-protein complex and to cluster analysis of peptides\, where different states of the molecules can be identified. Further molecular modeling tasks include resolution matching\, where coarse resolution models are back-mapped into high resolution (atomistic) structures. This is joint work with Kwang-Rae Kim\, Charles Laughton and Huiling Le.\n\n\n11:10-11:20 am\nBreak\n\n\n11:20 am-12:20 pm\nTamara Broderick\nTitle: An Automatic Finite-Sample Robustness Metric: Can Dropping a Little Data Change Conclusions? \nAbstract: One hopes that data analyses will be used to make beneficial decisions regarding people’s health\, finances\, and well-being. But the data fed to an analysis may systematically differ from the data where these decisions are ultimately applied. For instance\, suppose we analyze data in one country and conclude that microcredit is effective at alleviating poverty; based on this analysis\, we decide to distribute microcredit in other locations and in future years. We might then ask: can we trust our conclusion to apply under new conditions? If we found that a very small percentage of the original data was instrumental in determining the original conclusion\, we might not be confident in the stability of the conclusion under new conditions. So we propose a method to assess the sensitivity of data analyses to the removal of a very small fraction of the data set. Analyzing all possible data subsets of a certain size is computationally prohibitive\, so we provide an approximation. We call our resulting method the Approximate Maximum Influence Perturbation. Our approximation is automatically computable\, theoretically supported\, and works for common estimators. We show that any non-robustness our method finds is conclusive. Empirics demonstrate that while some applications are robust\, in others the sign of a treatment effect can be changed by dropping less than 0.1% of the data — even in simple models and even when standard errors are small.\n\n\n 12:20-1:50 pm\nLunch\n\n\n\nAfternoon Session Chair: Ezra Miller\n\n\n1:50-2:50 pm\nNicolai Reshetikhin*\nTitle: Random surfaces in exactly solvable models in statistical mechanics. \nAbstract: In the first part of the talk I will be an overview of a few models in statistical mechanics where a random variable is a geometric object such as a random surface or a random curve. The second part will be focused on the behavior of such random surfaces in the thermodynamic limit and on the formation of the so-called “limit shapes”.\n\n\n2:50-3:00 pm\nBreak\n\n\n3:00-4:00 pm\nSebastian Kurtek\nTitle: Robust Persistent Homology Using Elastic Functional Data Analysis \nAbstract: Persistence landscapes are functional summaries of persistence diagrams designed to enable analysis of the diagrams using tools from functional data analysis. They comprise a collection of scalar functions such that birth and death times of topological features in persistence diagrams map to extrema of functions and intervals where they are non-zero. As a consequence\, variation in persistence diagrams is encoded in both amplitude and phase components of persistence landscapes. Through functional data analysis of persistence landscapes\, under an elastic Riemannian metric\, we show how meaningful statistical summaries of persistence landscapes (e.g.\, mean\, dominant directions of variation) can be obtained by decoupling their amplitude and phase variations. This decoupling is achieved via optimal alignment\, with respect to the elastic metric\, of the persistence landscapes. The estimated phase functions are tied to the resolution parameter that determines the filtration of simplicial complexes used to construct persistence diagrams. For a dataset obtained under geometric\, scale and sampling variabilities\, the phase function prescribes an optimal rate of increase of the resolution parameter for enhancing the topological signal in a persistence diagram. The proposed approach adds to the statistical analysis of data objects with rich structure compared to past studies. In particular\, we focus on two sets of data that have been analyzed in the past\, brain artery trees and images of prostate cancer cells\, and show that separation of amplitude and phase of persistence landscapes is beneficial in both settings. This is joint work with Dr. James Matuk (Duke University) and Dr. Karthik Bharath (University of Nottingham).\n\n\n4:00-4:10 pm\nBreak\n\n\n4:10-5:10 pm\nConversation session\n\n\n5:10-5:20 pm\nStephan Huckemann\, Ezra Miller\, Zhigang Yao\nClosing Remarks\n\n\n\n* Virtual Presentation \n\n 
URL:https://cmsa.fas.harvard.edu/event/geometry-and-statistics/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Poster_GeometryStatistics_8.5x11.final_.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220826T090000
DTEND;TZID=America/New_York:20220826T130000
DTSTAMP:20260504T060537
CREATED:20230705T044827Z
LAST-MODIFIED:20250328T145239Z
UID:10000058-1661504400-1661518800@cmsa.fas.harvard.edu
SUMMARY:Big Data Conference 2022
DESCRIPTION:On August 26\, 2022 the CMSA hosted our eighth annual Conference on Big Data. The Big Data Conference features speakers from the Harvard community as well as scholars from across the globe\, with talks focusing on computer science\, statistics\, math and physics\, and economics. \nThe 2022 Big Data Conference took place virtually on Zoom. \nOrganizers: \n\nScott Duke Kominers\, MBA Class of 1960 Associate Professor\, Harvard Business\nHorng-Tzer Yau\, Professor of Mathematics\, Harvard University\nSergiy Verstyuk\, CMSA\, Harvard University\n\nSpeakers: \n\nXiaohong Chen\, Yale\nMiles Cranmer\, Princeton\nJessica Jeffers\, University of Chicago\nDan Roberts\, MIT\n\nSchedule \n\n\n\n\n9:00 am\nConference Organizers\nIntroduction and Welcome\n\n\n9:10 am – 9:55 am\nXiaohong Chen\nTitle: On ANN optimal estimation and inference for policy functionals of nonparametric conditional moment restrictions \nAbstract:  Many causal/policy parameters of interest are expectation functionals of unknown infinite-dimensional structural functions identified via conditional moment restrictions. Artificial Neural Networks (ANNs) can be viewed as nonlinear sieves that can approximate complex functions of high dimensional covariates more effectively than linear sieves. In this talk we present ANN optimal estimation and inference on  policy functionals\, such as average elasticities or value functions\, of unknown structural functions of endogenous covariates. We provide ANN efficient estimation and optimal t based confidence interval for regular policy functionals such as average derivatives in nonparametric instrumental variables regressions. We also present ANN quasi likelihood ratio based inference for possibly irregular policy functionals of general nonparametric conditional moment restrictions (such as quantile instrumental variables models or Bellman equations) for time series data. We conduct intensive Monte Carlo studies to investigate computational issues with ANN based optimal estimation and inference in economic structural models with endogeneity. For economic data sets that do not have very high signal to noise ratios\, there are current gaps between theoretical advantage of ANN approximation theory vs inferential performance in finite samples.\nSome of the results are applied to efficient estimation and optimal inference for average price elasticity in consumer demand and BLP type demand. \nThe talk is based on two co-authored papers:\n(1) Efficient Estimation of Average Derivatives in NPIV Models: Simulation Comparisons of Neural Network Estimators\n(Authors: Jiafeng Chen\, Xiaohong Chen and Elie Tamer)\nhttps://arxiv.org/abs/2110.06763 \n(2) Neural network Inference on Nonparametric conditional moment restrictions with weakly dependent data\n(Authors: Xiaohong Chen\, Yuan Liao and Weichen Wang). \nView/Download Lecture Slides (pdf)\n\n\n10:00 am – 10:45 am\nJessica Jeffers\nTitle: Labor Reactions to Credit Deterioration: Evidence from LinkedIn Activity \nAbstract: We analyze worker reactions to their firms’ credit deterioration. Using weekly networking activity on LinkedIn\, we show workers initiate more connections immediately following a negative credit event\, even at firms far from bankruptcy. Our results suggest that workers are driven by concerns about both unemployment and future prospects at their firm. Heightened networking activity is associated with contemporaneous and future departures\, especially at financially healthy firms. Other negative events like missed earnings and equity downgrades do not trigger similar reactions. Overall\, our results indicate that the build-up of connections triggered by credit deterioration represents a source of fragility for firms.\n\n\n10:50 am – 11:35 am\nMiles Cranmer\nTitle: Interpretable Machine Learning for Physics \nAbstract: Would Kepler have discovered his laws if machine learning had been around in 1609? Or would he have been satisfied with the accuracy of some black box regression model\, leaving Newton without the inspiration to discover the law of gravitation? In this talk I will explore the compatibility of industry-oriented machine learning algorithms with discovery in the natural sciences. I will describe recent approaches developed with collaborators for addressing this\, based on a strategy of “translating” neural networks into symbolic models via evolutionary algorithms. I will discuss the inner workings of the open-source symbolic regression library PySR (github.com/MilesCranmer/PySR)\, which forms a central part of this interpretable learning toolkit. Finally\, I will present examples of how these methods have been used in the past two years in scientific discovery\, and outline some current efforts. \nView/Download Lecture Slides (pdf) \n\n\n11:40 am – 12:25 pm\nDan Roberts\nTitle: A Statistical Model of Neural Scaling Laws \nAbstract: Large language models of a huge number of parameters and trained on near internet-sized number of tokens have been empirically shown to obey “neural scaling laws” for which their performance behaves predictably as a power law in either parameters or dataset size until bottlenecked by the other resource. To understand this better\, we first identify the necessary properties allowing such scaling laws to arise and then propose a statistical model — a joint generative data model and random feature model — that captures this neural scaling phenomenology. By solving this model using tools from random matrix theory\, we gain insight into (i) the statistical structure of datasets and tasks that lead to scaling laws (ii) how nonlinear feature maps\, i.e the role played by the deep neural network\, enable scaling laws when trained on these datasets\, and (iii) how such scaling laws can break down\, and what their behavior is when they do. A key feature is the manner in which the power laws that occur in the statistics of natural datasets are translated into power law scalings of the test loss\, and how the finite extent of such power laws leads to both bottlenecks and breakdowns. \nView/Download Lecture Slides (pdf) \n \n\n\n12:30 pm\nConference Organizers\nClosing Remarks\n\n\n\n\n  \nInformation about last year’s conference can be found here.
URL:https://cmsa.fas.harvard.edu/event/big-data-conference-2022/
LOCATION:Virtual
CATEGORIES:Big Data Conference,Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Big-Data-2022_web.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220730T090000
DTEND;TZID=America/New_York:20220801T134500
DTSTAMP:20260504T060537
CREATED:20230705T041718Z
LAST-MODIFIED:20250305T170940Z
UID:10000056-1659171600-1659361500@cmsa.fas.harvard.edu
SUMMARY:Advances in Mathematical Physics
DESCRIPTION:A Conference in Honor of Elliott H. Lieb on his 90th Birthday\nOn July 30 – Aug 1\, 2022 the Harvard Mathematics Department and the CMSA co-hosted a birthday conference in honor of Elliott Lieb. \nThis meeting highlights Elliott’s vast contribution to math and physics. Additionally\, this meeting features Prof. Lieb’s more recent impact in strong subadditivity of entropy and integrable systems (ice model\, Temperley-Lieb algebra etc.). \nVenue:\nJuly 30–31\, 2022: Hall B\, Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138\nAugust 1\, 2022: Hall C\, Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138 \nSchedule (pdf) \nOrganizers:\nMichael Aizenman\, Princeton University\nJoel Lebowitz\, Rutgers University\nRuedi Seiler\, Technische Universität Berlin\nHerbert Spohn\, Technical University of Munich\nHorng-Tzer Yau\, Harvard University\nShing-Tung Yau\, Harvard University\nJakob Yngvason\, University of Vienna \nSPEAKERS:\nRafael Benguria\, Pontificia Universidad Catolica de Chile\nEric Carlen\, Rutgers University\nPhilippe Di Francesco\, University of Illinois\nHugo Duminil-Copin\, IHES\nLászló Erdös\, Institute of Science and Technology Austria\nRupert Frank\, Ludwig Maximilian University of Munich\nJürg Fröhlich\, ETH Zurich\nAlessandro Giuliani\, Università degli Studi Roma Tre\nBertrand Halperin\, Harvard University\nKlaus Hepp\, Institute for Theoretical Physics\, ETH Zurich\nSabine Jansen\, Ludwig Maximilian University of Munich\nMathieu Lewin\, Université Paris-Dauphine\nBruno Nachtergaele\, The University of California\, Davis\nYoshiko Ogata\, University of Tokyo\nRon Peled\, Tel Aviv University\nBenjamin Schlein\, University of Zurich\nRobert Seiringer\, Institute of Science and Technology Austria\nJan Philip Solovej\, University of Copenhagen\nHal Tasaki\, Gakushuin University\nSimone Warzel\, Technical University of Munich\nJun Yin\, The University of California\, Los Angeles \n 
URL:https://cmsa.fas.harvard.edu/event/advances-in-mathematical-physics/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Elliott-Lieb-conference-2022_banner-2-1536x734-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220621T090000
DTEND;TZID=America/New_York:20220624T170000
DTSTAMP:20260504T060537
CREATED:20230706T183302Z
LAST-MODIFIED:20250305T175141Z
UID:10000894-1655802000-1656090000@cmsa.fas.harvard.edu
SUMMARY:Joint BHI/CMSA Conference on Flat Holography
DESCRIPTION:On June 21–24\, 2022\, the Harvard Black Hole Initiative and the CMSA hosted the Joint BHI/CMSA Conference on Flat Holography (and related topics). \nThe recent discovery of infinitely-many soft symmetries for all quantum theories of gravity in asymptotically flat space has provided a promising starting point for a bottom-up construction of a holographic dual for the real world. Recent developments have brought together previously disparate studies of soft theorems\, asymptotic symmetries\, twistor theory\, asymptotically flat black holes and their microscopic duals\, self-dual gravity\, and celestial scattering amplitudes\, and link directly to AdS/CFT. \nThe conference was held in room G10 of the CMSA\, 20 Garden Street\, Cambridge\, MA. \nOrganizers: \n\nDaniel Kapec\, CMSA\nAndrew Strominger\, BHI\nShing-Tung Yau\, Harvard & Tsinghua\n\nConfirmed Speakers: \n\nNima Arkani-Hamed\, IAS\nShamik Banerjee\, Bhubaneswar\, Inst. Phys.\nMiguel Campiglia\, Republica U.\, Montevido\nGeoffrey Compere\, Brussels\nLaura Donnay\, Vienna\nNetta Engelhardt\, MIT\nLaurent Freidel\, Perimeter\nAlex Lupsasca\, Princeton\nJuan Maldacena\, IAS\nLionel Mason\, Oxford\nNatalie Paquette\, U. Washington\nSabrina Pasterski\, Princeton/Perimeter\nAndrea Puhm\, Ecole Polytechnique\nAna-Maria Raclariu\, Perimeter\nMarcus Spradlin\, Brown\nTomasz Taylor\, Northeastern\nHerman Verlinde\, Princeton\nAnastasia Volovich\, Brown\nBin Zhu\, Northeastern\n\nShort talks by: Gonçalo Araujo-Regado (Cambridge)\, Adam Ball (Harvard)\, Eduardo Casali (Harvard)\, Jordan Cotler (Harvard)\, Erin Crawley (Harvard)\, Stéphane Detournay (Brussels)\, Alfredo Guevara (Harvard)\, Temple He (UC Davis)\, Elizabeth Himwich (Harvard)\, Yangrui Hu (Brown)\, Daniel Kapec (Harvard)\, Rifath Khan (Cambridge)\, Albert Law (Harvard)\, Luke Lippstreu (Brown)\, Noah Miller (Harvard)\, Sruthi Narayanan (Harvard)\, Lecheng Ren (Brown)\, Francisco Rojas (UAI)\, Romain Ruzziconi (Vienna)\, Andrew Strominger (Harvard)\, Adam Tropper (Harvard)\, Tianli Wang (Harvard)\, Walker Melton (Harvard) \n\n\nSchedule\nMonday\, June 20\, 2022 \n\n\n\n\n\nArrival\n\n\n7:00–9:00 pm\nWelcome Reception at Andy’s residence\n\n\n\n\n  \nTuesday\, June 21\, 2022 \n\n\n\n\n9:00–9:30 am\nBreakfast\nlight breakfast provided\n\n\n\nMorning Session\nChair: Dan Kapec\n\n\n9:30–10:00 am\nHerman Verlinde\nTitle: Comments on Celestial Dynamics\n\n\n10:00–10:30 am\nJuan Maldacena\nTitle: What happens when you spend too much time looking at supersymmetric\nblack holes?\n\n\n10:30–11:00\nCoffee break\n\n\n\n11:00–11:30 am\nMiguel Campiglia\nTitle: Asymptotic symmetries and loop corrections to soft theorems\n\n\n11:30–12:00 pm\nGeoffrey Compere\nTitle: Metric reconstruction from $Lw_{1+\infty}$ multipoles \nAbstract: The most general vacuum solution to Einstein’s field equations with no incoming radiation can be constructed perturbatively from two infinite sets of canonical multipole moments\, which are found to be exchanged under gravitational electric-magnetic duality at the non-linear level. We demonstrate that in non-radiative regions such spacetimes are completely determined by a set of conserved celestial charges\, which uniquely label transitions among non-radiative regions caused by radiative processes. The algebra of the conserved celestial charges is derived from the real $Lw_{1+\infty}$ algebra. The celestial charges are expressed in terms of multipole moments\, which allows to holographically reconstruct the metric in de Donder\, Newman-Unti or Bondi gauge outside of sources.\n\n\n12:00–2:00 pm\nLunch break\n\n\n\n\nAfternoon Session\nChair: Eduardo Casali\n\n\n2:00–2:30 pm\nNatalie Paquette\nTitle: New thoughts on old gauge amplitudes\n\n\n2:30–3:00 pm\nLionel Mason\nTitle: An open sigma model for celestial gravity \nAbstract: A global twistor construction for conformally self-dual split signature metrics on $S2\times S2$  was developed 15 years ago by Claude LeBrun and the speaker.  This encodes the conformal metric into the location of a finite deformation of the real twistor space inside the flat complex twistor space\, $\mathbb{CP}3$. This talk adapts the construction to construct global SD Einstein metrics from conformal boundary data and perturbations around the self-dual sector.  The construction entails determining a family of holomorphic discs in $\mathbb{CP}3$ whose boundaries lie on the deformed real slice and the (chiral) sigma model controls these discs in the Einstein case and provides amplitude formulae.\n\n\n3:00–3:30 pm\nCoffee break\n\n\n\n3:30–4:30 pm\nShort Talks\nDaniel Kapec: Soft Scalars and the Geometry of the Space of Celestial CFTs \nAlbert Law: Soft Scalars and the Geometry of the Space of Celestial CFTs \nSruthi Narayanan: Soft Scalars and the Geometry of the Space of Celestial CFTs \nStéphane Detournay: Non-conformal symmetries and near-extremal black holes \nFrancisco Rojas: Celestial string amplitudes beyond tree level \nTemple He: An effective description of energy transport from holography\n\n\n4:30–5:00 pm\nNima Arkani-Hamed\n(Dual) surfacehedra and flow particles know about strings\n\n\n\n\n  \nWednesday\, June 22\, 2022 \n\n\n\n\n9:00–9:30 am\nBreakfast\nlight breakfast provided\n\n\n\nMorning Session\nChair: Alfredo Guevara\n\n\n9:30–10:00 am\nLaurent Freidel\nTitle: Higher spin symmetry in gravity \nAbstract: In this talk\, I will review how the gravitational conservation laws at infinity reveal a tower of symmetry charges in an asymptotically flat spacetime.\nI will show how the conservation laws\, at spacelike infinity\, give a tower of soft theorems that connect to the ones revealed by celestial holography.\nI’ll present the expression for the symmetry charges in the radiative phase space\, which opens the way to reveal the structure of the algebra beyond the positive helicity sector. Then\, if time permits I’ll browse through many questions that these results raise:\nsuch as the nature of the spacetime symmetry these charges represent\, the nature of the relationship with multipole moments\, and the insights their presence provides for quantum gravity.\n\n\n10:00–10:30 am\nAna-Maria Raclariu\nTitle: Eikonal approximation in celestial CFT\n\n\n10:30–11:00 am\nCoffee break\n\n\n\n11:00–11:30 am\nAnastasia Volovich\nTitle: Effective Field Theories with Celestial Duals\n\n\n11:30–12:00 pm\nMarcus Spradlin\nTitle: Loop level gluon OPE’s in celestial holography\n\n\n12:00–2:00 pm\nLunch break\n\n\n\n\nAfternoon Session\nChair: Chiara Toldo\n\n\n2:00–2:30 pm\nNetta Engelhardt\nTitle: Wormholes from entanglement: true or false?\n\n\n2:30–3:00 pm\nShort Talks\nLuke Lippstreu: Loop corrections to the OPE of celestial gluons \nYangrui Hu: Light transforms of celestial amplitudes \nLecheng Ren: All-order OPE expansion of celestial gluon and graviton primaries from MHV amplitudes\n\n\n3:00–3:30 pm\nCoffee break\n\n\n\n3:30–4:30 pm\nShort Talks\nNoah Miller: C Metric Thermodynamics \nErin Crawley: Kleinian black holes \nRifath Khan: Cauchy Slice Holography: A New AdS/CFT Dictionary \nGonçalo Araujo-Regado: Cauchy Slice Holography: A New AdS/CFT Dictionary \nTianli Wang: Soft Theorem in the BFSS Matrix Model \nAdam Tropper: Soft Theorem in the BFSS Matrix Model\n\n\n7:00–9:00 pm\nBanquet\nMaharaja Restaurant\, 57 JFK Street\, Cambridge\, MA\n\n\n\n\n  \nThursday\, June 23\, 2022 \n\n\n\n\n9:00–9:30 am\nBreakfast\nlight breakfast provided\n\n\n\nMorning Session\nChair: Jordan Cotler\n\n\n9:30–10:00 am\nLaura Donnay\nTitle: A Carrollian road to flat space holography\n\n\n10:00–10:30 am\nAndrea Puhm\nTitle: Celestial wave scattering on Kerr-Schild backgrounds\n\n\n10:30–11:00 am\nCoffee break\n\n\n\n11:00–11:30 am\nSabrina Pasterski\nTitle: Mining Celestial Symmetries \nAbstract: The aim of this talk is to delve into the common thread that ties together recent work with H. Verlinde\, L. Donnay\, A. Puhm\, and S. Banerjee exploring\, explaining\, and exploiting the symmetries encoded in the conformally soft sector. \nCome prepared to debate the central charge\, loop corrections\, contour prescriptions\, and orders of limits!\n\n\n11:30–12:00 pm\nShamik Banerjee\nTitle: Virasoro and other symmetries in CCFT \nAbstract:  In this talk I will briefly describe my ongoing work with Sabrina Pasterski. In this work we revisit the standard construction of the celestial stress tensor as a shadow of the subleading conformally soft graviton.  In its original formulation\, we find that there is an obstruction to reproducing the expected $TT$ OPE in the double soft limit. This obstruction is related to the existence of the $SL_2$ current algebra symmetry of the CCFT. We propose a modification to the definition of the stress tensor which circumvents this obstruction and also discuss its implications for the existence of other current algebra (w_{1+\infty}) symmetries in CCFT.\n\n\n12:00–2:00 pm\nLunch break\n\n\n\n\nAfternoon Session\nChair: Albert Law\n\n\n2:00–2:30 pm\nTomasz Taylor\nTitle: Celestial Yang-Mills amplitudes and D=4 conformal blocks\n\n\n2:30–3:00 pm\nBin Zhu\nTitle:  Single-valued correlators and Banerjee-Ghosh equations \nAbstract:  Low-point celestial amplitudes are plagued with singularities resulting from spacetime translation. We consider a marginal deformation of the celestial CFT which is realized by coupling Yang-Mills theory to a background dilaton field\, with the (complex) dilaton source localized on the celestial sphere. This picture emerges from the physical interpretation of the solutions of the system of differential equations discovered by Banerjee and Ghosh. We show that the solutions can be written as Mellin transforms of the amplitudes evaluated in such a dilaton background. The resultant three-gluon and four-gluon amplitudes are single-valued functions of celestial coordinates enjoying crossing symmetry and all other properties expected from standard CFT correlators.\n\n\n3:00–3:30 pm\nCoffee break\n\n\n\n3:30–4:00 pm\nAlex Lupsasca\nTitle: Holography of the Photon Ring\n\n\n4:00–5:30 pm\nShort Talks\nElizabeth Himwich: Celestial OPEs and w(1+infinity) symmetry of massless and massive amplitudes \nAdam Ball: Perturbatively exact $w_{1+\infty}$ asymptotic symmetry of quantum self-dual gravity \nRomain Ruzziconi: A Carrollian Perspective on Celestial Holography \nJordan Cotler: Soft Gravitons in 3D \nAlfredo Guevara: Comments on w_1+\inf \nAndrew Strominger: Top-down celestial holograms \nEduardo Casali: Celestial amplitudes as AdS-Witten diagrams \nWalker Melton: Top-down celestial holograms\n\n\n\n\n  \nFriday\, June 24\, 2022 \n\n\n\n\n9:00–9:30 am\nBreakfast\n\n\n9:30–12:30 pm\nOpen Discussion\n\n\n12:30–2:30 pm\nLunch provided at the BHI\n\n\n\nDeparture\n\n\n\n\n 
URL:https://cmsa.fas.harvard.edu/event/joint-bhi-cmsa-conference-on-flat-holography/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Flat-Holography_2022_small.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220606T090000
DTEND;TZID=America/New_York:20220608T170000
DTSTAMP:20260504T060537
CREATED:20230706T182850Z
LAST-MODIFIED:20250305T172950Z
UID:10000893-1654506000-1654707600@cmsa.fas.harvard.edu
SUMMARY:Symposium on Foundations of Responsible Computing (FORC)
DESCRIPTION:On June 6-8\, 2022\, the CMSA hosted the 3rd annual Symposium on Foundations of Responsible Computing (FORC). \nThe Symposium on Foundations of Responsible Computing (FORC) is a forum for mathematical research in computation and society writ large.  The Symposium aims to catalyze the formation of a community supportive of the application of theoretical computer science\, statistics\, economics and other relevant analytical fields to problems of pressing and anticipated societal concern. \nOrganizers: Cynthia Dwork\, Harvard SEAS | Omer Reingold\, Stanford | Elisa Celis\, Yale \nSchedule\nJune 6\, 2022 \n\n\n\n\n9:15 am–10:15 am\nOpening Remarks \nKeynote Speaker: Caroline Nobo\, Yale University\nTitle: From Theory to Impact: Why Better Data Systems are Necessary for Criminal Legal Reform \nAbstract: This talk will dive into the messy\, archaic\, and siloed world of local criminal justice data in America. We will start with a 30\,000 foot discussion about the current state of criminal legal data systems\, then transition to the challenges of this broken paradigm\, and conclude with a call to measure new things – and to measure them better! This talk will leave you with an understanding of criminal justice data infrastructure and transparency in the US\, and will discuss how expensive case management software and other technology are built on outdated normative values which impede efforts to reform the system. The result is an infuriating paradox: an abundance of tech products built without theoretical grounding\, in a space rich with research and evidence.\n\n\n10:15 am–10:45 am\nCoffee Break\n\n\n\n10:45 am–12:15 pm\nPaper Session 1\nSession Chair: Ruth Urner\n\n\n\nGeorgy Noarov\, University of Pennsylvania\nTitle: Online Minimax Multiobjective Optimization \nAbstract: We introduce a simple but general online learning framework in which a learner plays against an adversary in a vector-valued game that changes every round. The learner’s objective is to minimize the maximum cumulative loss over all coordinates. We give a simple algorithm that lets the learner do almost as well as if she knew the adversary’s actions in advance. We demonstrate the power of our framework by using it to (re)derive optimal bounds and efficient algorithms across a variety of domains\, ranging from multicalibration to a large set of no-regret algorithms\, to a variant of Blackwell’s approachability theorem for polytopes with fast convergence rates. As a new application\, we show how to “(multi)calibeat” an arbitrary collection of forecasters — achieving an exponentially improved dependence on the number of models we are competing against\, compared to prior work.\n\n\n\nMatthew Eichhorn\, Cornell University\nTitle: Mind your Ps and Qs: Allocation with Priorities and Quotas \nAbstract: In many settings\, such as university admissions\, the rationing of medical supplies\, and the assignment of public housing\, decision-makers use normative criteria (ethical\, financial\, legal\, etc.) to justify who gets an allocation. These criteria can often be translated into quotas for the number of units available to particular demographics and priorities over agents who qualify in each demographic. Each agent may qualify in multiple categories at different priority levels\, so many allocations may conform to a given set of quotas and priorities. Which of these allocations should be chosen? In this talk\, I’ll formalize this reserve allocation problem and motivate Pareto efficiency as a natural desideratum. I’ll present an algorithm to locate efficient allocations that conform to the quota and priority constraints. This algorithm relies on beautiful techniques from integer and linear programming\, and it is both faster and more straightforward than existing techniques in this space. Moreover\, its clean formulation allows for further refinement\, such as the secondary optimization of some heuristics for fairness.\n\n\n\nHaewon Jeong\, Harvard University\nTitle: Fairness without Imputation: A Decision Tree Approach for Fair Prediction with Missing Values \nAbstract: We investigate the fairness concerns of training a machine learning model using data with missing values. Even though there are a number of fairness intervention methods in the literature\, most of them require a complete training set as input. In practice\, data can have missing values\, and data missing patterns can depend on group attributes (e.g. gender or race). Simply applying off-the-shelf fair learning algorithms to an imputed dataset may lead to an unfair model. In this paper\, we first theoretically analyze different sources of discrimination risks when training with an imputed dataset. Then\, we propose an integrated approach based on decision trees that does not require a separate process of imputation and learning. Instead\, we train a tree with missing incorporated as attribute (MIA)\, which does not require explicit imputation\, and we optimize a fairness-regularized objective function. We demonstrate that our approach outperforms existing fairness intervention methods applied to an imputed dataset\, through several experiments on real-world datasets.\n\n\n\nEmily Diana\, University of Pennsylvania\nTitle: Multiaccurate Proxies for Downstream Fairness \nAbstract: We study the problem of training a model that must obey demographic fairness conditions when the sensitive features are not available at training time — in other words\, how can we train a model to be fair by race when we don’t have data about race? We adopt a fairness pipeline perspective\, in which an “upstream” learner that does have access to the sensitive features will learn a proxy model for these features from the other attributes. The goal of the proxy is to allow a general “downstream” learner — with minimal assumptions on their prediction task — to be able to use the proxy to train a model that is fair with respect to the true sensitive features. We show that obeying multiaccuracy constraints with respect to the downstream model class suffices for this purpose\, provide sample- and oracle efficient-algorithms and generalization bounds for learning such proxies\, and conduct an experimental evaluation. In general\, multiaccuracy is much easier to satisfy than classification accuracy\, and can be satisfied even when the sensitive features are hard to predict.\n\n\n12:15 pm–1:45 pm\nLunch Break\n\n\n\n1:45–3:15 pm\nPaper Session 2\nSession Chair: Guy Rothblum\n\n\n\nElbert Du\, Harvard University\nTitle: Improved Generalization Guarantees in Restricted Data Models \nAbstract: Differential privacy is known to protect against threats to validity incurred due to adaptive\, or exploratory\, data analysis — even when the analyst adversarially searches for a statistical estimate that diverges from the true value of the quantity of interest on the underlying population. The cost of this protection is the accuracy loss incurred by differential privacy. In this work\, inspired by standard models in the genomics literature\, we consider data models in which individuals are represented by a sequence of attributes with the property that where distant attributes are only weakly correlated. We show that\, under this assumption\, it is possible to “re-use” privacy budget on different portions of the data\, significantly improving accuracy without increasing the risk of overfitting.\n\n\n\nRuth Urner\, York University\nTitle: Robustness Should not be at Odds with Accuracy \nAbstract: The phenomenon of adversarial examples in deep learning models has caused substantial concern over their reliability and trustworthiness: in many instances an imperceptible perturbation can falsely flip a neural network’s prediction. Applied research in this area has mostly focused on developing novel adversarial attack strategies or building better defenses against such. It has repeatedly been pointed out that adversarial robustness may be in conflict with requirements for high accuracy. In this work\, we take a more principled look at modeling the phenomenon of adversarial examples. We argue that deciding whether a model’s label change under a small perturbation is justified\, should be done in compliance with the underlying data-generating process. Through a series of formal constructions\, systematically analyzing the the relation between standard Bayes classifiers and robust-Bayes classifiers\, we make the case for adversarial robustness as a locally adaptive measure. We propose a novel way defining such a locally adaptive robust loss\, show that it has a natural empirical counterpart\, and develop resulting algorithmic guidance in form of data-informed adaptive robustness radius. We prove that our adaptive robust data-augmentation maintains consistency of 1-nearest neighbor classification under deterministic labels and thereby argue that robustness should not be at odds with accuracy.\n\n\n\nSushant Agarwal\, University of Waterloo\nTitle: Towards the Unification and Robustness of Perturbation and Gradient Based Explanations \nAbstract: As machine learning black boxes are increasingly being deployed in critical domains such as healthcare and criminal justice\, there has been a growing emphasis on developing techniques for explaining these black boxes in a post hoc manner. In this work\, we analyze two popular post hoc interpretation techniques: SmoothGrad which is a gradient based method\, and a variant of LIME which is a perturbation based method. More specifically\, we derive explicit closed form expressions for the explanations output by these two methods and show that they both converge to the same explanation in expectation\, i.e.\, when the number of perturbed samples used by these methods is large. We then leverage this connection to establish other desirable properties\, such as robustness and linearity\, for these techniques. We also derive finite sample complexity bounds for the number of perturbations required for these methods to converge to their expected explanation. Finally\, we empirically validate our theory using extensive experimentation on both synthetic and real world datasets.\n\n\n\nTijana Zrnic\, University of California\, Berkeley\nTitle: Regret Minimization with Performative Feedback \nAbstract: In performative prediction\, the deployment of a predictive model triggers a shift in the data distribution. As these shifts are typically unknown ahead of time\, the learner needs to deploy a model to get feedback about the distribution it induces. We study the problem of finding near-optimal models under performativity while maintaining low regret. On the surface\, this problem might seem equivalent to a bandit problem. However\, it exhibits a fundamentally richer feedback structure that we refer to as performative feedback: after every deployment\, the learner receives samples from the shifted distribution rather than only bandit feedback about the reward. Our main contribution is regret bounds that scale only with the complexity of the distribution shifts and not that of the reward function. The key algorithmic idea is careful exploration of the distribution shifts that informs a novel construction of confidence bounds on the risk of unexplored models. The construction only relies on smoothness of the shifts and does not assume convexity. More broadly\, our work establishes a conceptual approach for leveraging tools from the bandits literature for the purpose of regret minimization with performative feedback.\n\n\n3:15 pm–3:45 pm\nCoffee Break\n\n\n\n3:45 pm–5:00 pm\nPanel Discussion\nTitle: What is Responsible Computing? \nPanelists: Jiahao Chen\, Cynthia Dwork\, Kobbi Nissim\, Ruth Urner \nModerator: Elisa Celis\n\n\n\n\n  \nJune 7\, 2022 \n\n\n\n\n9:15 am–10:15 am\nKeynote Speaker: Isaac Kohane\, Harvard Medical School\nTitle: What’s in a label? The case for and against monolithic group/ethnic/race labeling for machine learning \nAbstract: Populations and group labels have been used and abused for thousands of years. The scale at which AI can incorporate such labels into its models and the ways in which such models can be misused are cause for significant concern. I will describe\, with examples drawn from experiments in precision medicine\, the task dependence of how underserved and oppressed populations can be both harmed and helped by the use of group labels. The source of the labels and the utility models underlying their use will be particularly emphasized.\n\n\n10:15 am–10:45 am\nCoffee Break\n\n\n\n10:45 am–12:15 pm\nPaper Session 3\nSession Chair: Ruth Urner\n\n\n\nRojin Rezvan\, University of Texas at Austin\nTitle: Individually-Fair Auctions for Multi-Slot Sponsored Search \nAbstract: We design fair-sponsored search auctions that achieve a near-optimal tradeoff between fairness and quality. Our work builds upon the model and auction design of Chawla and Jagadeesan\, who considered the special case of a single slot. We consider sponsored search settings with multiple slots and the standard model of click-through rates that are multiplicatively separable into an advertiser-specific component and a slot-specific component. When similar users have similar advertiser-specific click-through rates\, our auctions achieve the same near-optimal tradeoff between fairness and quality. When similar users can have different advertiser-specific preferences\, we show that a preference-based fairness guarantee holds. Finally\, we provide a computationally efficient algorithm for computing payments for our auctions as well as those in previous work\, resolving another open direction from Chawla and Jagadeesan.\n\n\n\nJudy Hanwen Shen\, Stanford\nTitle: Leximax Approximations and Representative Cohort Selection \nAbstract: Finding a representative cohort from a broad pool of candidates is a goal that arises in many contexts such as choosing governing committees and consumer panels. While there are many ways to define the degree to which a cohort represents a population\, a very appealing solution concept is lexicographic maximality (leximax) which offers a natural (pareto-optimal like) interpretation that the utility of no population can be increased without decreasing the utility of a population that is already worse off. However\, finding a leximax solution can be highly dependent on small variations in the utility of certain groups. In this work\, we explore new notions of approximate leximax solutions with three distinct motivations: better algorithmic efficiency\, exploiting significant utility improvements\, and robustness to noise. Among other definitional contributions\, we give a new notion of an approximate leximax that satisfies a similarly appealing semantic interpretation and relate it to algorithmically-feasible approximate leximax notions. When group utilities are linear over cohort candidates\, we give an efficient polynomial-time algorithm for finding a leximax distribution over cohort candidates in the exact as well as in the approximate setting. Furthermore\, we show that finding an integer solution to leximax cohort selection with linear utilities is NP-Hard.\n\n\n\nJiayuan Ye\,\nNational University of Singapore\nTitle: Differentially Private Learning Needs Hidden State (or Much Faster Convergence) \nAbstract: Differential privacy analysis of randomized learning algorithms typically relies on composition theorems\, where the implicit assumption is that the internal state of the iterative algorithm is revealed to the adversary. However\, by assuming hidden states for DP algorithms (when only the last-iterate is observable)\, recent works prove a converging privacy bound for noisy gradient descent (on strongly convex smooth loss function) that is significantly smaller than composition bounds after a few epochs. In this talk\, we extend this hidden-state analysis to various stochastic minibatch gradient descent schemes (such as under “shuffle and partition” and “sample without replacement”)\, by deriving novel bounds for the privacy amplification by random post-processing and subsampling. We prove that\, in these settings\, our privacy bound is much smaller than composition for training with a large number of iterations (which is the case for learning from high-dimensional data). Our converging privacy analysis\, thus\, shows that differentially private learning\, with a tight bound\, needs hidden state privacy analysis or a fast convergence. To complement our theoretical results\, we present experiments for training classification models on MNIST\, FMNIST and CIFAR-10 datasets\, and observe a better accuracy given fixed privacy budgets\, under the hidden-state analysis.\n\n\n\nMahbod Majid\, University of Waterloo\nTitle: Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism \nAbstract: We give the first polynomial-time algorithm to estimate the mean of a d-variate probability distribution from O(d) independent samples (up to logarithmic factors) subject to pure differential privacy. \nOur main technique is a new approach to use the powerful Sum of Squares method (SoS) to design differentially private algorithms. SoS proofs to algorithms is a key theme in numerous recent works in high-dimensional algorithmic statistics – estimators which apparently require exponential running time but whose analysis can be captured by low-degree Sum of Squares proofs can be automatically turned into polynomial-time algorithms with the same provable guarantees. We demonstrate a similar proofs to private algorithms phenomenon: instances of the workhorse exponential mechanism which apparently require exponential time but which can be analyzed with low-degree SoS proofs can be automatically turned into polynomial-time differentially private algorithms. We prove a meta-theorem capturing this phenomenon\, which we expect to be of broad use in private algorithm design.\n\n\n12:15 pm–1:45 pm\nLunch Break\n\n\n\n1:45–3:15 pm\nPaper Session 4\nSession Chair: Kunal Talwar\n\n\n\nKunal Talwar\,\nApple\nTitle: Differential Secrecy for Distributed Data and Applications to Robust Differentially Secure Vector Summation \nAbstract: Computing the noisy sum of real-valued vectors is an important primitive in differentially private learning and statistics. In private federated learning applications\, these vectors are held by client devices\, leading to a distributed summation problem. Standard Secure Multiparty Computation (SMC) protocols for this problem are susceptible to poisoning attacks\, where a client may have a large influence on the sum\, without being detected.\nIn this work\, we propose a poisoning-robust private summation protocol in the multiple-server setting\, recently studied in PRIO. We present a protocol for vector summation that verifies that the Euclidean norm of each contribution is approximately bounded. We show that by relaxing the security constraint in SMC to a differential privacy like guarantee\, one can improve over PRIO in terms of communication requirements as well as the client-side computation. Unlike SMC algorithms that inevitably cast integers to elements of a large finite field\, our algorithms work over integers/reals\, which may allow for additional efficiencies.\n\n\n\nGiuseppe Vietri\, University of Minnesota\nTitle: Improved Regret for Differentially Private Exploration in Linear MDP \nAbstract: We study privacy-preserving exploration in sequential decision-making for environments that rely on sensitive data such as medical records. In particular\, we focus on solving the problem of reinforcement learning (RL) subject to the constraint of (joint) differential privacy in the linear MDP setting\, where both dynamics and rewards are given by linear functions. Prior work on this problem due to Luyo et al. (2021) achieves a regret rate that has a dependence of O(K^{3/5}) on the number of episodes K. We provide a private algorithm with an improved regret rate with an optimal dependence of O(K^{1/2}) on the number of episodes. The key recipe for our stronger regret guarantee is the adaptivity in the policy update schedule\, in which an update only occurs when sufficient changes in the data are detected. As a result\, our algorithm benefits from low switching cost and only performs O(log(K)) updates\, which greatly reduces the amount of privacy noise. Finally\, in the most prevalent privacy regimes where the privacy parameter ? is a constant\, our algorithm incurs negligible privacy cost — in comparison with the existing non-private regret bounds\, the additional regret due to privacy appears in lower-order terms.\n\n\n\nMingxun Zhou\,\nCarnegie Mellon University\nTitle: The Power of the Differentially Oblivious Shuffle in Distributed Privacy MechanismsAbstract: The shuffle model has been extensively investigated in the distributed differential privacy (DP) literature. For a class of useful computational tasks\, the shuffle model allows us to achieve privacy-utility tradeoff similar to those in the central model\, while shifting the trust from a central data curator to a “trusted shuffle” which can be implemented through either trusted hardware or cryptography. Very recently\, several works explored cryptographic instantiations of a new type of shuffle with relaxed security\, called differentially oblivious (DO) shuffles. These works demonstrate that by relaxing the shuffler’s security from simulation-style secrecy to differential privacy\, we can achieve asymptotical efficiency improvements. A natural question arises\, can we replace the shuffler in distributed DP mechanisms with a DO-shuffle while retaining a similar privacy-utility tradeoff?\nIn this paper\, we prove an optimal privacy amplification theorem by composing any locally differentially private (LDP) mechanism with a DO-shuffler\, achieving parameters that tightly match the shuffle model. Moreover\, we explore multi-message protocols in the DO-shuffle model\, and construct mechanisms for the real summation and histograph problems. Our error bounds approximate the best known results in the multi-message shuffle-model up to sub-logarithmic factors. Our results also suggest that just like in the shuffle model\, allowing each client to send multiple messages is fundamentally more powerful than restricting to a single message.\n\n\n\nBadih Ghazi\,\nGoogle Research\nTitle: Differentially Private Ad Conversion Measurement \nAbstract: In this work\, we study conversion measurement\, a central functionality in the digital advertising space\, where an advertiser seeks to estimate advertiser site conversions attributed to ad impressions that users have interacted with on various publisher sites. We consider differential privacy (DP)\, a notion that has gained in popularity due to its strong and rigorous guarantees\, and suggest a formal framework for DP conversion measurement\, uncovering a subtle interplay between attribution and privacy. We define the notion of an operationally valid configuration of the attribution logic\, DP adjacency relation\, privacy\nbudget scope and enforcement point\, and provide\, for a natural space of configurations\, a complete characterization.\n\n\n3:15 pm–3:45 pm\nCoffee Break\n\n\n\n3:45 pm–5:00 pm\nOpen Poster Session\n\n\n\n\n\n  \nJune 8\, 2022 \n\n\n\n\n9:15 am–10:15 am\nKeynote Speaker: Nuria Oliver\, Data-Pop Alliance\nTitle: Data Science against COVID-19 \nAbstract: In my talk\, I will describe the work that I have been doing since March 2020\, leading a multi-disciplinary team of 20+ volunteer scientists working very closely with the Presidency of the Valencian Government in Spain on 4 large areas: (1) human mobility modeling; (2) computational epidemiological models (both metapopulation\, individual and LSTM-based models); (3) predictive models; and (4) citizen surveys via the COVID19impactsurvey with over 600\,000 answers worldwide. \nI will describe the results that we have produced in each of these areas\, including winning the 500K XPRIZE Pandemic Response Challenge and best paper award at ECML-PKDD 2021. I will share the lessons learned in this very special initiative of collaboration between the civil society at large (through the survey)\, the scientific community (through the Expert Group) and a public administration (through the Commissioner at the Presidency level). WIRED magazine just published an article describing our story.\n\n\n10:15 am–10:45 am\nCoffee Break\n\n\n\n10:45 am–12:15 pm\nPaper Session 5\nSession Chair: Kunal Talwar\n\n\n\nShengyuan Hu\, Carnegie Mellon University\nTitle: Private Multi-Task Learning: Formulation and Applications to Federated Learning \nAbstract: Many problems in machine learning rely on multi-task learning (MTL)\, in which the goal is to solve multiple related machine learning tasks simultaneously. MTL is particularly relevant for privacy-sensitive applications in areas such as healthcare\, finance\, and IoT computing\, where sensitive data from multiple\, varied sources are shared for the purpose of learning. In this work\, we formalize notions of task-level privacy for MTL via joint differential privacy (JDP)\, a relaxation of differential privacy for mechanism design and distributed optimization. We then propose an algorithm for mean-regularized MTL\, an objective commonly used for applications in personalized federated learning\, subject to JDP. We analyze our objective and solver\, providing certifiable guarantees on both privacy and utility. Empirically\, our method allows for improved privacy/utility trade-offs relative to global baselines across common federated learning benchmarks\n\n\n\nChristina Yu\,\nCornell University\nTitle: Sequential Fair Allocation: Achieving the Optimal Envy-Efficiency Tradeoff Curve \nAbstract: We consider the problem of dividing limited resources to individuals arriving over T rounds with a goal of achieving fairness across individuals. In general there may be multiple resources and multiple types of individuals with different utilities. A standard definition of `fairness’ requires an allocation to simultaneously satisfy envy-freeness and Pareto efficiency. However\, in the online sequential setting\, the social planner must decide on a current allocation before the downstream demand is realized\, such that no policy can guarantee these desiderata simultaneously with probability 1\, requiring a modified metric of measuring fairness for online policies. We show that in the online setting\, the two desired properties (envy-freeness and efficiency) are in direct contention\, in that any algorithm achieving additive counterfactual envy-freeness up to L_T necessarily suffers an efficiency loss of at least 1 / L_T. We complement this uncertainty principle with a simple algorithm\, HopeGuardrail\, which allocates resources based on an adaptive threshold policy and is able to achieve any fairness-efficiency point on this frontier. Our result is the first to provide guarantees for fair online resource allocation with high probability for multiple resource and multiple type settings. In simulation results\, our algorithm provides allocations close to the optimal fair solution in hindsight\, motivating its use in practical applications as the algorithm is able to adapt to any desired fairness efficiency trade-off.\n\n\n\nHedyeh Beyhaghi\, Carnegie Mellon University\nTitle: On classification of strategic agents who can both game and improve \nAbstract: In this work\, we consider classification of agents who can both game and improve. For example\, people wishing to get a loan may be able to take some actions that increase their perceived credit-worthiness and others that also increase their true credit-worthiness. A decision-maker would like to define a classification rule with few false-positives (does not give out many bad loans) while yielding many true positives (giving out many good loans)\, which includes encouraging agents to improve to become true positives if possible. We consider two models for this problem\, a general discrete model and a linear model\, and prove algorithmic\, learning\, and hardness results for each. For the general discrete model\, we give an efficient algorithm for the problem of maximizing the number of true positives subject to no false positives\, and show how to extend this to a partial-information learning setting. We also show hardness for the problem of maximizing the number of true positives subject to a nonzero bound on the number of false positives\, and that this hardness holds even for a finite-point version of our linear model. We also show that maximizing the number of true positives subject to no false positive is NP-hard in our full linear model. We additionally provide an algorithm that determines whether there exists a linear classifier that classifies all agents accurately and causes all improvable agents to become qualified\, and give additional results for low-dimensional data.\n\n\n\nKeegan Harris\, Carnegie Mellon University\nTitle: Bayesian Persuasion for Algorithmic Recourse \nAbstract: When subjected to automated decision-making\, decision subjects may strategically modify their observable features in ways they believe will maximize their chances of receiving a favorable decision. In many practical situations\, the underlying assessment rule is deliberately kept secret to avoid gaming and maintain competitive advantage. The resulting opacity forces the decision subjects to rely on incomplete information when making strategic feature modifications. We capture such settings as a game of Bayesian persuasion\, in which the decision maker offers a form of recourse to the decision subject by providing them with an action recommendation (or signal) to incentivize them to modify their features in desirable ways. We show that when using persuasion\, both the decision maker and decision subject are never worse off in expectation\, while the decision maker can be significantly better off. While the decision maker’s problem of finding the optimal Bayesian incentive-compatible (BIC) signaling policy takes the form of optimization over infinitely-many variables\, we show that this optimization can be cast as a linear program over finitely-many regions of the space of possible assessment rules. While this reformulation simplifies the problem dramatically\, solving the linear program requires reasoning about exponentially-many variables\, even under relatively simple settings. Motivated by this observation\, we provide a polynomial-time approximation scheme that recovers a near-optimal signaling policy. Finally\, our numerical simulations on semi-synthetic data empirically illustrate the benefits of using persuasion in the algorithmic recourse setting.\n\n\n12:15 pm–1:45 pm\nLunch Break\n\n\n\n1:45–3:15 pm\nPaper Session 6\nSession Chair: Elisa Celis\n\n\n\nMark Bun\, Boston University\nTitle: Controlling Privacy Loss in Sampling Schemes: An Analysis of Stratified and Cluster Sampling \nAbstract: Sampling schemes are fundamental tools in statistics\, survey design\, and algorithm design. A fundamental result in differential privacy is that a differentially private mechanism run on a simple random sample of a population provides stronger privacy guarantees than the same algorithm run on the entire population. However\, in practice\, sampling designs are often more complex than the simple\, data-independent sampling schemes that are addressed in prior work. In this work\, we extend the study of privacy amplification results to more complex\, data-dependent sampling schemes. We find that not only do these sampling schemes often fail to amplify privacy\, they can actually result in privacy degradation. We analyze the privacy implications of the pervasive cluster sampling and stratified sampling paradigms\, as well as provide some insight into the study of more general sampling designs.\n\n\n\nSamson Zhou\, Carnegie Mellon University\nTitle: Private Data Stream Analysis for Universal Symmetric Norm Estimation \nAbstract: We study how to release summary statistics on a data stream subject to the constraint of differential privacy. In particular\, we focus on releasing the family of symmetric norms\, which are invariant under sign-flips and coordinate-wise permutations on an input data stream and include L_p norms\, k-support norms\, top-k norms\, and the box norm as special cases. Although it may be possible to design and analyze a separate mechanism for each symmetric norm\, we propose a general parametrizable framework that differentially privately releases a number of sufficient statistics from which the approximation of all symmetric norms can be simultaneously computed. Our framework partitions the coordinates of the underlying frequency vector into different levels based on their magnitude and releases approximate frequencies for the “heavy” coordinates in important levels and releases approximate level sizes for the “light” coordinates in important levels. Surprisingly\, our mechanism allows for the release of an arbitrary number of symmetric norm approximations without any overhead or additional loss in privacy. Moreover\, our mechanism permits (1+\alpha)-approximation to each of the symmetric norms and can be implemented using sublinear space in the streaming model for many regimes of the accuracy and privacy parameters.\n\n\n\nAloni Cohen\, University of Chicago\nTitle: Attacks on Deidentification’s Defenses \nAbstract: Quasi-identifier-based deidentification techniques (QI-deidentification) are widely used in practice\, including k-anonymity\, ?-diversity\, and t-closeness. We present three new attacks on QI-deidentification: two theoretical attacks and one practical attack on a real dataset. In contrast to prior work\, our theoretical attacks work even if every attribute is a quasi-identifier. Hence\, they apply to k-anonymity\, ?-diversity\, t-closeness\, and most other QI-deidentification techniques.\nFirst\, we introduce a new class of privacy attacks called downcoding attacks\, and prove that every QI-deidentification scheme is vulnerable to downcoding attacks if it is minimal and hierarchical. Second\, we convert the downcoding attacks into powerful predicate singling-out (PSO) attacks\, which were recently proposed as a way to demonstrate that a privacy mechanism fails to legally anonymize under Europe’s General Data Protection Regulation. Third\, we use LinkedIn.com to reidentify 3 students in a k-anonymized dataset published by EdX (and show thousands are potentially vulnerable)\, undermining EdX’s claimed compliance with the Family Educational Rights and Privacy Act. \nThe significance of this work is both scientific and political. Our theoretical attacks demonstrate that QI-deidentification may offer no protection even if every attribute is treated as a quasi-identifier. Our practical attack demonstrates that even deidentification experts acting in accordance with strict privacy regulations fail to prevent real-world reidentification. Together\, they rebut a foundational tenet of QI-deidentification and challenge the actual arguments made to justify the continued use of k-anonymity and other QI-deidentification techniques.\n\n\n\nSteven Wu\,\nCarnegie Mellon University\nTitle: Fully Adaptive Composition in Differential Privacy \nAbstract: Composition is a key feature of differential privacy. Well-known advanced composition theorems allow one to query a private database quadratically more times than basic privacy composition would permit. However\, these results require that the privacy parameters of all algorithms be fixed before interacting with the data. To address this\, Rogers et al. introduced fully adaptive composition\, wherein both algorithms and their privacy parameters can be selected adaptively. The authors introduce two probabilistic objects to measure privacy in adaptive composition: privacy filters\, which provide differential privacy guarantees for composed interactions\, and privacy odometers\, time-uniform bounds on privacy loss. There are substantial gaps between advanced composition and existing filters and odometers. First\, existing filters place stronger assumptions on the algorithms being composed. Second\, these odometers and filters suffer from large constants\, making them impractical. We construct filters that match the tightness of advanced composition\, including constants\, despite allowing for adaptively chosen privacy parameters. We also construct several general families of odometers. These odometers can match the tightness of advanced composition at an arbitrary\, preselected point in time\, or at all points in time simultaneously\, up to a doubly-logarithmic factor. We obtain our results by leveraging recent advances in time-uniform martingale concentration. In sum\, we show that fully adaptive privacy is obtainable at almost no loss\, and conjecture that our results are essentially not improvable (even in constants) in general.\n\n\n3:15 pm–3:45 pm\nFORC Reception\n\n\n\n3:45 pm–5:00 pm\nSocial Hour
URL:https://cmsa.fas.harvard.edu/event/symposium-on-foundations-of-responsible-computing-forc/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/FORC22_poster.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220517T090000
DTEND;TZID=America/New_York:20220517T180000
DTSTAMP:20260504T060537
CREATED:20230706T181958Z
LAST-MODIFIED:20240229T102937Z
UID:10000146-1652778000-1652810400@cmsa.fas.harvard.edu
SUMMARY:SMaSH: Symposium for Mathematical Sciences at Harvard
DESCRIPTION:SMaSH: Symposium for Mathematical Sciences at Harvard\nOn Tuesday\, May 17\, 2022\, from 9:00 am – 5:30 pm\, the Harvard John A Paulson School of Engineering and Applied Sciences (SEAS) and the Harvard Center of Mathematical Sciences and Applications (CMSA) held a Symposium for Mathematical Sciences for the mathematical sciences community at Harvard. \nOrganizing Committee \n\nMichael Brenner\, Applied Mathematics (SEAS)\nMichael Desai\, Organismic and Evolutionary Biology (FAS)\nSam Gershman\, Psychology (FAS)\nMichael Hopkins\, Mathematics (FAS)\nGary King\, Government (FAS)\nPeter Koellner\, Philosophy (FAS)\nScott Kominers\, Economics (FAS) & Entrepreneurial Management (HBS)\nXihong Lin\, Biostatistics (HSPH) & Statistics (FAS)\nYue Lu\, Electrical Engineering (SEAS)\nSusan Murphy\, Statistics (FAS) & Computer Science (SEAS)\nLisa Randall\, Physics (SEAS)\nEugene Shakhnovich\, Chemistry (FAS)\nSalil Vadhan\, Computer Science (SEAS)\nHorng-Tzer Yau\, Mathematics (FAS)\n\n\nThis event was held in-person at the Science and Engineering Complex (SEC) at 150 Western Ave\, Allston\, MA 02134\, and streamed on Zoom. \nHarvard graduate students and postdocs presented Poster Sessions. \n\nVenue: Science and Engineering Complex (SEC) \n\nSpeakers\n\nAnurag Anshu\, Computer Science (SEAS)\nMorgane Austern\, Statistics (FAS)\nDemba Ba\, Electrical Engineering & Bioengineering (SEAS)\nMichael Brenner\, Applied Mathematics (SEAS)\nRui Duan\, Biostatistics (HSPH)\nYannai A. Gonczarowski\, Economics (FAS) & Computer Science (SEAS)\nKosuke Imai\, Government & Statistics (FAS)\nSham M. Kakade\, Computer Science (SEAS) & Statistics (FAS)\nSeth Neel\, Technology & Operations Management (HBS)\nMelanie Matchett Wood\, Mathematics (FAS)\n\nSchedule PDF \nSchedule\n\n\n\n\n9:00–9:30 am\nCoffee and Breakfast\nWest Atrium (ground floor of the SEC)\n\n\n9:30–10:30 am\nFaculty Talks\nWinokur Family Hall Classroom (Room 1.321) located just off of the West AtriumKosuke Imai\, Government & Statistics (FAS): Use of Simulation Algorithms for Legislative Redistricting Analysis and EvaluationYannai A. Gonczarowski\, Economics (FAS) & Computer Science (SEAS): The Sample Complexity of Up-to-ε Multi-Dimensional Revenue Maximization\n\n\n10:30–11:00 am\nCoffee Break\nWest Atrium (ground floor of the SEC)\n\n\n11:00–12:00 pm\nFaculty Talks\nWinokur Family Hall Classroom (Room 1.321) located just off of the West AtriumSeth Neel\, Technology & Operations Management (HBS): “Machine (Un)Learning” or Why Your Deployed Model Might Violate Existing Privacy LawDemba Ba\, Electrical Engineering & Bioengineering (SEAS): Geometry\, AI\, and the Brain\n\n\n12:00–1:00 pm\nLunch Break\nEngineering Yard Tent\n\n\n1:00–2:30 pm\nFaculty Talks\nWinokur Family Hall Classroom (Room 1.321) located just off of the West AtriumMelanie Matchett Wood\, Mathematics (FAS): Understanding distributions of algebraic structures through their momentsMorgane Austern\, Statistics (FAS): Limit theorems for structured random objectsAnurag Anshu\, Computer Science (SEAS): Operator-valued polynomial approximations and their use.\n\n\n2:30–3:00 pm\nCoffee Break\nWest Atrium (ground floor of the SEC)\n\n\n3:00–4:30 pm\nFaculty Talks\nWinokur Family Hall Classroom (Room 1.321) located just off of the West AtriumMichael Brenner\, Applied Mathematics (SEAS): Towards living synthetic materialsRui Duan\, Biostatistics (HSPH): Federated and transfer learning for healthcare data integrationSham M. Kakade\, Computer Science (SEAS) & Statistics (FAS): What is the Statistical Complexity of Reinforcement Learning?\n\n\n4:30–5:30 pm\nReception with Jazz musicians\n& Poster Session\nEngineering Yard Tent\n\n\n\n\n\nFaculty Talks\n\n\n\n\nSpeaker\nTitle / Abstract / Bio\n\n\nAnurag Anshu\, Computer Science (SEAS)\nTitle: Operator-valued polynomial approximations and their use. \nAbstract: Approximation of complicated functions with low degree polynomials is an indispensable tool in mathematics. This becomes particularly relevant in computer science\, where the complexity of interesting functions is often captured by the degree of the approximating polynomials. This talk concerns the approximation of operator-valued functions (such as the exponential of a hermitian matrix\, or the intersection of two projectors) with low-degree operator-valued polynomials. We will highlight the challenges that arise in achieving similarly good approximations as real-valued functions\, as well as recent methods to overcome them. We will discuss applications to the ground states in physics and quantum complexity theory: correlation lengths\, area laws and concentration bounds. \nBio: Anurag Anshu is an Assistant Professor of computer science at Harvard University. He spends a lot of time exploring the rich structure of quantum many-body systems from the viewpoint of quantum complexity theory\, quantum learning theory and quantum information theory. He held postdoctoral positions at University of California\, Berkeley and University of Waterloo and received his PhD from National University of Singapore\, focusing on quantum communication complexity.\n\n\nMorgane Austern\, Statistics (FAS)\nTitle: Limit theorems for structured random objects \nAbstract: Statistical inference relies on numerous tools from probability theory to study the properties of estimators. Some of the most central ones are the central limit theorem and the free central limit theorem. However\, these same tools are often inadequate to study modern machine problems that frequently involve structured data (e.g networks) or complicated dependence structures (e.g dependent random matrices). In this talk\, we extend universal limit theorems beyond the classical setting. We consider distributionally “structured’ and dependent random object i.e random objects whose distribution is invariant under the action of an amenable group. We show\, under mild moment and mixing conditions\, a series of universal second and third order limit theorems: central-limit theorems\, concentration inequalities\, Wigner semi-circular law and Berry-Esseen bounds. The utility of these will be illustrated by a series of examples in machine learning\, network and information theory. \nBio: Morgane Austern is an assistant professor in the Statistics Department of Harvard University. Broadly\, she is interested in developing probability tools for modern machine learning and in establishing the properties of learning algorithms in structured and dependent data contexts. She graduated with a PhD in statistics from Columbia University in 2019 where she worked in collaboration with Peter Orbanz and Arian Maleki on limit theorems for dependent and structured data. She was a postdoctoral researcher at Microsoft Research New England from 2019 to 2021.\n\n\nDemba Ba\, Electrical Engineering & Bioengineering (SEAS)\nTitle: Geometry\, AI\, and the Brain \nAbstract: A large body of experiments suggests that neural computations reflect\, in some sense\, the geometry of “the world”. How do artificial and neural systems learn representations of “the world” that reflect its geometry? How\, for instance\, do we\, as humans\, learn representations of objects\, e.g. fruits\, that reflect the geometry of object space? Developing artificial systems that can capture/understand the geometry of the data they process may enable them to learn representations useful in many different contexts and tasks. My talk will describe an artificial neural-network architecture that\, starting from a simple union-of-manifold model of data comprising objects from different categories\, mimics some aspects of how primates learn\, organize\, and retrieve concepts\, in a manner that respects the geometry of object space. \nBio: Demba Ba serves as an Associate Professor of electrical engineering and bioengineering in Harvard University’s School of Engineering and Applied Sciences\, where he directs the CRISP group. Recently\, he has taken a keen interest in the connection between artificial neural networks and sparse signal processing. His group leverages this connection to solve data-driven unsupervised learning problems in neuroscience\, to understand the principles of hierarchical representations of sensory signals in the brain\, and to develop explainable AI. In 2016\, he received a Research Fellowship in Neuroscience from the Alfred P. Sloan Foundation. In 2021\, Harvard’s Faculty of Arts and Sciences awarded him the Roslyn Abramson award for outstanding undergraduate teaching.\n\n\nMichael Brenner\, Applied Mathematics (SEAS)\nTitle: Towards living synthetic materials \nAbstract: Biological materials are much more complicated and functional than synthetic ones. Over the past several years we have been trying to figure out why. A sensible hypothesis is that biological materials are programmable. But we are very far from being able to program materials we create with this level of sophistication.  I will discuss our (largely unsuccessful) efforts to bridge this gap\, though as of today I’m somewhat optimistic that we are arriving at a set of theoretical models that is rich enough to produce relevant emergent behavior. \nBio: I’ve been at Harvard for a long time. My favorite part of Harvard is the students.\n\n\nRui Duan\, Biostatistics (HSPH)\nTitle: Federated and transfer learning for healthcare data integration \nAbstract: The growth of availability and variety of healthcare data sources has provided unique opportunities for data integration and evidence synthesis\, which can potentially accelerate knowledge discovery and improve clinical decision-making. However\, many practical and technical challenges\, such as data privacy\, high dimensionality\, and heterogeneity across different datasets\, remain to be addressed. In this talk\, I will introduce several methods for the effective and efficient integration of multiple healthcare datasets in order to train statistical or machine learning models with improved generalizability and transferability. Specifically\, we develop communication-efficient federated learning algorithms for jointly analyzing multiple datasets without the need of sharing patient-level data\, as well as transfer learning approaches that leverage shared knowledge learned across multiple datasets to improve the performance of statistical models in target populations of interest. We will discuss both the theoretical properties and examples of implementation of our methods in real-world research networks and data consortia. \nBio: Rui Duan is an Assistant Professor of Biostatistics at the Harvard T.H. Chan School of Public Health. She received her Ph.D. in Biostatistics in May 2020 from the University of Pennsylvania. Her research interests focus on developing statistical\, machine learning\, and informatics tools for (1) efficient data integration in biomedical research\, (2) understanding and accounting for the heterogeneity of biomedical data\, and improving the generalizability and transferability of models across populations (3) advancing precision medicine research on rare diseases and underrepresented populations.\n\n\nYannai A. Gonczarowski\, Economics (FAS) & Computer Science (SEAS)\nTitle: The Sample Complexity of Up-to-ε Multi-Dimensional Revenue Maximization \nAbstract: We consider the sample complexity of revenue maximization for multiple bidders in unrestricted multi-dimensional settings. Specifically\, we study the standard model of n additive bidders whose values for m heterogeneous items are drawn independently. For any such instance and any ε > 0\, we show that it is possible to learn an ε-Bayesian Incentive Compatible auction whose expected revenue is within ε of the optimal ε-BIC auction from only polynomially many samples. \nOur fully nonparametric approach is based on ideas that hold quite generally\, and completely sidestep the difficulty of characterizing optimal (or near-optimal) auctions for these settings. Therefore\, our results easily extend to general multi-dimensional settings\, including valuations that are not necessarily even subadditive\, and arbitrary allocation constraints. For the cases of a single bidder and many goods\, or a single parameter (good) and many bidders\, our analysis yields exact incentive compatibility (and for the latter also computational efficiency). Although the single-parameter case is already well-understood\, our corollary for this case extends slightly the state-of-the-art. \nJoint work with S. Matthew Weinberg \nBio: Yannai A. Gonczarowski is an Assistant Professor of Economics and of Computer Science at Harvard University—the first faculty member at Harvard to have been appointed to both of these departments. Interested in both economic theory and theoretical computer science\, Yannai explores computer-science-inspired economics: he harnesses approaches\, aesthetics\, and techniques traditionally originating in computer science to derive economically meaningful insights. Yannai received his PhD from the Departments of Math and CS\, and the Center for the Study of Rationality\, at the Hebrew University of Jerusalem\, where he was advised by Sergiu Hart and Noam Nisan. Yannai is also a professionally-trained opera singer\, having acquired a bachelor’s degree and a master’s degree in Classical Singing at the Jerusalem Academy of Music and Dance. Yannai’s doctoral dissertation was recognized with several awards\, including the 2018 Michael B. Maschler Prize of the Israeli Chapter of the Game Theory Society\, and the ACM SIGecom Doctoral Dissertation Award for 2018. For the design and implementation of the National Matching System for Gap-Year Programs in Israel\, he was awarded the Best Paper Award at MATCH-UP’19 and the inaugural INFORMS AMD Michael H. Rothkopf Junior Researcher Paper Prize (first place) for 2020. Yannai is also the recipient of the inaugural ACM SIGecom Award for Best Presentation by a Student or Postdoctoral Researcher at EC’18. His first textbook\, “Mathematical Logic through Python” (Gonczarowski and Nisan)\, which introduces a new approach to teaching the material of a basic Logic course to Computer Science students\, tailored to the unique intuitions and strengths of this cohort of students\, is forthcoming in Cambridge University Press.\n\n\nKosuke Imai\, Government & Statistics (FAS)\nTitle: Use of Simulation Algorithms for Legislative Redistricting Analysis and Evaluation \nAbstract: After the 2020 Census\, many states have been redrawing the boundaries of Congressional and state legislative districts. To evaluate the partisan and racial bias of redistricting plans\, scholars have developed Monte Carlo simulation algorithms. The idea is to generate a representative sample of redistricting plans under a specified set of criteria and conduct a statistical hypothesis test by comparing a proposed plan with these simulated plans. I will give a brief overview of these redistricting simulation algorithms and discuss how they are used in real-world court cases. \nBio: Kosuke Imai is Professor in the Department of Government and Department of Statistics at Harvard University. Before moving to Harvard in 2018\, Imai taught at Princeton University for 15 years where he was the founding director of the Program in Statistics and Machine Learning. Imai specializes in the development of statistical methods and machine learning algorithms and their applications to social science research. His areas of expertise include causal inference\, computational social science\, program evaluation\, and survey methodology.\n\n\nSham M. Kakade\, Computer Science (SEAS) & Statistics (FAS)\nTitle: What is the Statistical Complexity of Reinforcement Learning? \nAbstract: This talk will highlight much of the recent progress on the following fundamental question in the theory of reinforcement learning: what (representational or structural) conditions govern our ability to generalize and avoid the curse of dimensionality?  With regards to supervised learning\, these questions are reasonably well understood\, both practically and theoretically: practically\, we have overwhelming evidence on the value of representational learning (say through modern deep networks) as a means for sample efficient learning\, and\, theoretically\, there are well-known complexity measures (e.g. the VC dimension and Rademacher complexity) that govern the statistical complexity of learning.  Providing an analogous theory for reinforcement learning is far more challenging\, where even characterizing structural conditions which support sample efficient generalization has been far less well understood\, until recently. \nThis talk will survey recent advances towards characterizing when generalization is possible in RL\, focusing on both necessary and sufficient conditions. In particular\, we will introduce a new complexity measure\, the Decision-Estimation Coefficient\, that is proven to be necessary (and\, essentially\, sufficient) for sample-efficient interactive learning. \nBio: Sham Kakade is a professor at Harvard University and a co-director of the Kempner Institute for the Study of Artificial and Natural Intelligence.  He works on the mathematical foundations of machine learning and AI. Sham’s thesis helped lay the statistical foundations of reinforcement learning. With his collaborators\, his additional contributions include foundational results on: policy gradient methods in reinforcement learning; regret bounds for linear bandit and Gaussian process bandit models; the tensor and spectral methods for latent variable models; and a number of convergence analyses for convex and non-convex algorithms.  He is the recipient of the ICML Test of Time Award\, the IBM Pat Goldberg best paper award\, and INFORMS Revenue Management and Pricing Prize. He has been program chair for COLT 2011. \nSham was an undergraduate at Caltech\, where he studied physics and worked under the guidance of John Preskill in quantum computing. He completed his Ph.D. with Peter Dayan in computational neuroscience at the Gatsby Computational Neuroscience Unit. He was a postdoc with Michael Kearns at the University of Pennsylvania.\n\n\nSeth Neel\, Technology & Operations Management (HBS)\nTitle: “Machine (Un)Learning” or Why Your Deployed Model Might Violate Existing Privacy Law \nAbstract:  Businesses like Facebook and Google depend on training sophisticated models on user data. Increasingly—in part because of regulations like the European Union’s General Data Protection Act and the California Consumer Privacy Act—these organizations are receiving requests to delete the data of particular users. But what should that mean? It is straightforward to delete a customer’s data from a database and stop using it to train future models. But what about models that have already been trained using an individual’s data? These are not necessarily safe; it is known that individual training data can be exfiltrated from models trained in standard ways via model inversion attacks. In a series of papers we help formalize a rigorous notion of data-deletion and propose algorithms to efficiently delete user data from trained models with provable guarantees in both convex and non-convex settings. \nBio: Seth Neel is a first-year Assistant Professor in the TOM Unit at Harvard Business School\, and Co-PI of the SAFR ML Lab in the D3 Institute\, which develops methodology to incorporate privacy and fairness guarantees into techniques for machine learning and data analysis\, while balancing other critical considerations like accuracy\, efficiency\, and interpretability. He obtained his Ph.D. from the University of Pennsylvania in 2020 where he was an NSF graduate fellow. His work has focused primarily on differential privacy\, notions of fairness in a variety of machine learning settings\, and adaptive data analysis.\n\n\nMelanie Matchett Wood\, Mathematics (FAS)\nTitle: Understanding distributions of algebraic structures through their moments \nAbstract: A classical tool of probability and analysis is to use the moments (mean\, variance\, etc.) of a distribution to recognize an unknown distribution of real numbers.  In recent work\, we are interested in distributions of algebraic structures that can’t be captured in a single number.  We will explain one example\, the fundamental group\, that captures something about the shapes of possibly complicated or high dimensional spaces.  We are developing a new theory of the moment problem for random algebraic structures which helps to to identify distributions of such\, such as fundamental groups of random three dimensional spaces.  This talk is based partly on joint work with Will Sawin. \nBio: Melanie Matchett Wood is a professor of mathematics at Harvard University and a Radcliffe Alumnae Professor at the Radcliffe Institute for Advanced Study.  Her work spans number theory\, algebraic geometry\, algebraic topology\, additive combinatorics\, and probability. Wood has been awarded a CAREER grant\, a Sloan Research Fellowship\, a Packard Fellowship for Science and Engineering\, and the AWM-Microsoft Research Prize in Algebra and Number Theory\, and she is a Fellow of the American Mathematical Society. In 2021\, Wood received the National Science Foundation’s Alan T. Waterman Award\, the nation’s highest honor for early-career scientists and engineers.
URL:https://cmsa.fas.harvard.edu/event/smash-symposium-for-mathematical-sciences-at-harvard/
LOCATION:Science and Engineering Complex (SEC)\, 150 Western Ave\, Allston\, MA 02134\, MA
CATEGORIES:Conference,Event
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END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220509T090000
DTEND;TZID=America/New_York:20220512T123000
DTSTAMP:20260504T060537
CREATED:20230706T181710Z
LAST-MODIFIED:20231227T082643Z
UID:10000107-1652086800-1652358600@cmsa.fas.harvard.edu
SUMMARY:Conference in Memory of Professor Masatake Kuranishi
DESCRIPTION:On May 9–12\, 2022\, the CMSA hosted the conference Deformations of structures and moduli in geometry and analysis: A Memorial in honor of Professor Masatake Kuranishi. \nOrganizers:  Tristan Collins (MIT) and Shing-Tung Yau (Harvard and Tsinghua) \nVideos are available on the conference playlist. \n  \nSpeakers: \nCharles Fefferman (Princeton University) \nTeng Fei (Rutgers University) \nRobert Friedman (Columbia University) \nKenji Fukaya (Simons Center\, Stony Brook) \nAkito Futaki (Tsinghua University) \nVictor Guillemin (Massachusetts Institute of Technology) \nNigel Hitchin (Oxford University) \nBlaine Lawson (Stony Brook University) \nYu-Shen Lin (Boston University) \nMelissa C.C. Liu (Columbia University) \nTakeo Ohsawa (Nagoya University) \nDuong H. Phong (Columbia University) \nSebastien Picard (University of British Columbia) \nPaul Seidel (Massachusetts Institute of Technology) \nGabor Szekelyhidi (University of Notre Dame) \nClaire Voisin (Institut de Mathematiques\, Jussieu\, France) \nShing-Tung Yau (Harvard University) \n  \n\n\n\nSchedule (download pdf) \n\nMonday\, May 9\, 2022 \n\n\n\n8:15 am\nLight breakfast & coffee/tea\n\n\n8:45–9:00 am\nOpening Remarks\n\n\n9:00–10:00 am\nKenji Fukaya\nTitle: Gromov Hausdorff convergence of filtered A infinity category \nAbstract: In mirror symmetry a mirror to a symplectic manifold is actually believed to be a family of complex manifold parametrized by a disk (of radius 0). The coordinate ring of the parameter space is a kind of formal power series ring the Novikov ring. Novikov ring is a coefficient ring of Floer homology. Most of the works on homological Mirror symmetry so far studies A infinity category over Novikov field\, which corresponds to the study of generic fiber. The study of A infinity category over Novikov ring is related to several interesting phenomenon of Hamiltonian dynamics. In this talk I will explain a notion which I believe is useful to study mirror symmetry. \nVideo\n\n\n10:15–11:15 am\nNigel Hitchin (Zoom)\nTitle: Deformations: A personal perspective \nAbstract: The talk\, largely historical\, will focus on different deformation complexes I have encountered in my work\, starting with instantons on 4-manifolds\, but also monopoles\, Higgs bundles and generalized complex structures. I will also discuss some speculative ideas related to surfaces of negative curvature. \nVideo\n\n\n11:30–12:30 pm\nH. Blaine Lawson\nTitle: Projective Hulls\, Projective Linking\, and Boundaries of Varieties \nAbstract: In 1958 John Wermer proved that the polynomial hull of a compact real analytic curve γ ⊂ Cn was a 1-dim’l complex subvariety of Cn − γ. This result engendered much subsequent activity\, and was related to Gelfand’s spectrum of a Banach algebra. In the early 2000’s Reese Harvey and I found a projective analogue of these concepts and wondered whether Wermer’s Theorem could be generalized to the projective setting. This question turned out to be more subtle and quite intriguing\, with unexpected consequences. We now know a great deal\, a highpoint of which s a result with Harvey and Wermer. It led to conjectures (for Cω-curves in P2C) which imply several results. One says\, roughly\, that a (2p − 1)-cycle Γ in Pn bounds a positive holomorphic p-chain of mass ≤ Λ ⇐⇒ its normalized linking number with all positive (n − p)-cycles in Pn − |Γ| is ≥ −Λ. Another says that a class τ ∈ H2p(Pn\,|Γ|;Z) with ∂τ = Γ contains a positive holomorphic p-chain ⇐⇒ τ•[Z]≥0 for all positive holomorphic (n−p)-cycles Z in Pn−|Γ| \nVideo\n\n\n12:30–2:30 pm\nLunch Break\n\n\n\n2:30–3:30 pm\nGabor Szekelyhidi\nTitle: Singularities along the Lagrangian mean curvature flow. \nAbstract: We study singularity formation along the Lagrangian mean curvature flow of surfaces. On the one hand we show that if a tangent flow at a singularity is the special Lagrangian union of two transverse planes\, then the flow undergoes a “neck pinch”\, and can be continued past the flow. This can be related to the Thomas-Yau conjecture on stability conditions along the Lagrangian mean curvature flow. In a different direction we show that ancient solutions of the flow\, whose blow-down is given by two planes meeting along a line\, must be translators. These are joint works with Jason Lotay and Felix Schulze. \nVideo\n\n\n3:30–4:00 pm\nCoffee Break\n \n\n\n4:00–5:00 pm\nTakeo Ohsawa\nTitle: Glimpses of embeddings and deformations of CR manifolds \nAbstract: Basic results on the embeddings and the deformations of CR manifolds will be reviewed with emphasis on the reminiscences of impressive moments with Kuranishi since his visit to Kyoto in 1975. \nVideo\n\n\n\n  \n  \n  \nTuesday\, May 10\, 2022 \n  \n\n\n\n8:15 am\nLight breakfast & coffee/tea\n\n\n9:00–10:00 am\nCharles Fefferman (Zoom)\nTitle: Interpolation of Data by Smooth Functions \nAbstract: Let X be your favorite Banach space of continuous functions on R^n. Given an (arbitrary) set E in R^n and an arbitrary function f:E->R\, we ask: How can we tell whether f extends to a function F \in X? If such an F exists\, then how small can we take its norm? What can we say about its derivatives (assuming functions in X have derivatives)? Can we take F to depend linearly on f? Suppose E is finite. Can we compute an F as above with norm nearly as small as possible? How many computer operations does it take? What if F is required to agree only approximately with f on E? What if we are allowed to discard a few data points (x\, f(x)) as “outliers”? Which points should we discard? \nThe results were obtained jointly with A. Israel\, B. Klartag\, G.K. Luli and P. Shvartsman over many years. \nVideo\n\n\n10:15–11:15 am\nClaire Voisin\nTitle: Deformations of K-trivial manifolds and applications to hyper-Kähler geometry \nSummary: I will explain the Ran approach via the T^1-lifting principle to the BTT theorem stating that deformations of K-trivial compact Kähler manifolds are unobstructed. I will explain a similar unobstructedness result for Lagrangian submanifolds of hyper-Kähler manifolds and I will describe important consequences on the topology and geometry of hyper-Kähler manifolds. \nVideo\n\n\n11:30– 2:30 pm\nVictor Guillemin\nTitle: Semi-Classical Functions of Isotropic Type \nAbstract: The world of semiclassical analysis is populated by objects of “Lagrangian type.” The topic of this talk however will be objects in semi-classical analysis that live instead on isotropic submanifolds. I will describe in my talk a lot of interesting examples of such objects. \nVideo\n\n\n12:30–2:30 pm\nLunch Break\n\n\n\n2:30–3:30 pm\nTeng Fei\nTitle: Symplectic deformations and the Type IIA flow \nAbstract: The equations of flux compactification of Type IIA superstrings were written down by Tomasiello and Tseng-Yau. To study these equations\, we introduce a natural geometric flow known as the Type IIA flow on symplectic Calabi-Yau 6-manifolds. We prove the wellposedness of this flow and establish the basic estimates. We show that the Type IIA flow can be applied to find optimal almost complex structures on certain symplectic manifolds. We prove the dynamical stability of the Type IIA flow\, which leads to a proof of stability of Kahler property for Calabi-Yau 3-folds under symplectic deformations. This is based on joint work with Phong\, Picard and Zhang. \nVideo\n\n\nSpeakers Banquet\n\n\n\n\n\n  \n  \n  \nWednesday\, May 11\, 2022 \n  \n\n\n\n8:15 am\nLight breakfast & coffee/tea\n\n\n9:00–10:00 am\nShing-Tung Yau (Zoom)\nTitle: Canonical metrics and stability in mirror symmetry \nAbstract: I will discuss the deformed Hermitian-Yang-Mills equation\, its role in mirror symmetry and its connections to notions of stability.  I will review what is known\, and pose some questions for the future. \nVideo\n\n\n10:15–11:15 am\nDuong H. Phong\nTitle: $L^\infty$ estimates for the Monge-Ampere and other fully non-linear equations in complex geometry \nAbstract: A priori estimates are essential for the understanding of partial differential equations\, and of these\, $L^\infty$ estimates are particularly important as they are also needed for other estimates. The key $L^\infty$ estimates were obtained by S.T. Yau in 1976 for the Monge-Ampere equation for the Calabi conjecture\, and sharp estimates obtained later in 1998 by Kolodziej using pluripotential theory. It had been a long-standing question whether a PDE proof of these estimates was possible. We provide a positive answer to this question\, and derive as a consequence sharp estimates for general classes of fully non-linear equations. This is joint work with B. Guo and F. Tong. \nVideo\n\n\n11:30–2:30 pm\nPaul Seidel\nTitle: The quantum connection: familiar yet puzzling \nAbstract: The small quantum connection on a Fano variety is possibly the most basic piece of enumerative geometry. In spite of being really easy to write down\, it is the subject of far-reaching conjectures (Dubrovin\, Galkin\, Iritani)\, which challenge our understanding of mirror symmetry. I will give a gentle introduction to the simplest of these questions. \nVideo\n\n\n12:30–2:30 pm\nLunch Break\n\n\n\n2:30–3:30 pm\nMelissa C.C. Liu\nTitle: Higgs-Coulumb correspondence for abelian gauged linear sigma models \nAbstract: The underlying geometry of a gauged linear sigma model (GLSM) consists of a GIT quotient of a complex vector space by the linear action of a reductive algebraic group G (the gauge group) and a polynomial function (the superpotential) on the GIT quotient. The Higgs-Coulomb correspondence relates (1) GLSM invariants which are virtual counts of curves in the critical locus of the superpotential (Higgs branch)\, and (2) Mellin-Barnes type integrals on the Lie algebra of G (Coulomb branch). In this talk\, I will describe the correspondence when G is an algebraic torus\, and explain how to use the correspondence to study dependence of GLSM invariants on the stability condition. This is based on joint work with Konstantin Aleshkin. \nVideo\n\n\n3:30–4:00 pm\nCoffee Break\n \n\n\n4:00–5:00 pm\nSebastien Picard\nTitle: Topological Transitions of Calabi-Yau Threefolds \nAbstract: Conifold transitions were proposed in the works of Clemens\, Reid and Friedman as a way to travel in the parameter space of Calabi-Yau threefolds with different Hodge numbers. This process may deform a Kahler Calabi-Yau threefold into a non-Kahler complex manifold with trivial canonical bundle. We will discuss the propagation of differential geometric structures such as balanced hermitian metrics\, Yang-Mills connections\, and special submanifolds through conifold transitions. This is joint work with T. Collins\, S. Gukov and S.-T. Yau. \nVideo\n\n\n\n  \n  \n  \nThursday\, May 12\, 2022 \n  \n\n\n\n8:15 am\nLight breakfast & coffee/tea\n\n\n9:00 am–10:00 am\nAkito Futaki (Zoom)\nTitle: Transverse coupled Kähler-Einstein metrics and volume minimization\n\nAbstract: We show that transverse coupled Kähler-Einstein metrics on toric Sasaki manifolds arise as a critical point of a volume functional. As a preparation for the proof\, we re-visit the transverse moment polytopes and contact moment polytopes under the change of Reeb vector fields. Then we apply it to a coupled version of the volume minimization by Martelli-Sparks-Yau. This is done assuming the Calabi-Yau condition of the Kählercone\, and the non-coupled case leads to a known existence result of a transverse Kähler-Einstein metric and a Sasaki-Einstein metric\, but the coupled case requires an assumption related to Minkowski sum to obtain transverse coupled Kähler-Einstein metrics.Video\n\n\n10:15 am–11:15 am\nYu-Shen Lin\nTitle: SYZ Mirror Symmetry of Log Calabi-Yau Surfaces \nAbstract: Strominger-Yau-Zaslow conjecture predicts Calabi-Yau manifolds admits special Lagrangian fibrations. The conjecture serves as one of the guiding principles in mirror symmetry. In this talk\, I will explain the existence of the special Lagrangian fibrations in some log Calabi-Yau surfaces and their dual fibrations in their expected mirrors. The journey leads us to the study of the moduli space of Ricci-flat metrics with certain asymptotics on these geometries and the discovery of new semi-flat metrics. If time permits\, I will explain the application to the Torelli theorem of ALH^* gravitational instantons. The talk is based on joint works with T. Collins and A. Jacob. \nVideo\n\n\n11:30 am – 12:30 pm\nRobert Friedman\nTitle: Deformations of singular Fano and Calabi-Yau varieties \nAbstract: This talk will describe recent joint work with Radu Laza on deformations of generalized Fano and Calabi-Yau varieties\, i.e. compact analytic spaces whose dualizing sheaves are either duals of ample line bundles or are trivial. Under the assumption of isolated hypersurface canonical singularities\, we extend results of Namikawa and Steenbrink in dimension three and discuss various generalizations to higher dimensions. \nVideo\n\n\n12:30 pm\nConcluding Remarks\n\n\n\n 
URL:https://cmsa.fas.harvard.edu/event/conference-in-memory-of-professor-masatake-kuranishi/
LOCATION:Science and Engineering Complex (SEC)\, 150 Western Ave\, Allston\, MA 02134\, MA
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Kuranishi_Harvard_10x12-2.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220404T093000
DTEND;TZID=America/New_York:20220408T170000
DTSTAMP:20260504T060537
CREATED:20230705T082708Z
LAST-MODIFIED:20250305T172217Z
UID:10000087-1649064600-1649437200@cmsa.fas.harvard.edu
SUMMARY:General Relativity Conference
DESCRIPTION:Schedule | April 4–8\, 2022\nMonday\, April 4\, 2022 \n\n\n\n\nTime (ET)\nSpeaker\nTitle/Abstract\n\n\n9:30 am–10:30 am\nPieter Blue\, University of Edinburgh\, UK\n(virtual)\nTitle: Linear stability of the Kerr spacetime in the outgoing radiation gauge \nAbstract: This talk will discuss a new gauge condition (i.e. coordinate condition) for the Einstein equation\, the linearisation of the Einstein equation in this gauge\, and the decay of solutions to the linearised Einstein equation around Kerr black holes in this gauge. The stability of the family of Kerr black holes under the evolution generated by the Einstein equation is a long-standing problem in mathematical relativity. In 1972\, Teukolsky discovered equations governing certain components of the linearised curvature that are invariant under linearised gague transformations. In 1975\, Chrzanowski introduced the “outgoing radiation gauge”\, a condition on the linearised metric that allows for the construction of the linearised metric from the linearised curvature. In 2019\, we proved decay for the metric constructed using Chrzanowski’s outgoing radiation gauge. Recently\, using a flow along null geodesics\, we have constructed a new gauge such that\, in this gauge\, the Einstein equation is well posed and such that the linearisation is Chrzanowski’s outgoing radiation gauge. \nThis is joint work with Lars Andersson\, Thomas Backdahl\, and Siyuan Ma.\n\n\n10:30 am–11:30 am\nPeter Hintz\, ETH Zürich\n(virtual)\nTitle: Mode stability and shallow quasinormal modes of Kerr-de Sitter\nblack holesAbstract: The Kerr-de Sitter metric describes a rotating black hole with mass $m$ and specific angular momentum $a$ in a universe\, such as our own\, with cosmological constant $\Lambda>0$. I will explain a proof of mode stability for the scalar wave equation on Kerr-de Sitter spacetimes in the following setting: fixing $\Lambda$ and the ratio $|a/m|<1$ (related to the subextremality of the black hole in question)\, mode stability holds for sufficiently small black hole mass $m$. We also obtain estimates for the location of quasinormal modes (resonances) $\sigma$ in any fixed half space $\Im\sigma>-C$. Our results imply that solutions of the wave equation decay exponentially in time to constants\, with an explicit exponential rate. The proof is based on careful uniform estimates for the spectral family in the singular limit $m\to 0$ in which\, depending on the scaling\, the Kerr-de Sitter spacetime limits to a Kerr or the de Sitter spacetime.\n\n\n11:30 am–12:30 pm\nLars Andersson\, Albert Einstein Institute\, Germany\n(virtual)\nTitle: Gravitational instantons and special geometry \nAbstract: Gravitational instantons are Ricci flat complete Riemannian 4-manifolds with at least quadratic curvature decay. In this talk\, I will introduce some notions of special geometry\, discuss known examples\, and mention some open questions. The Chen-Teo gravitational instanton is an asymptotically flat\, toric\, Ricci flat family of metrics on $\mathrm{CP}^2 \setminus \mathrm{S}^1$\, that provides a counterexample to the classical Euclidean Black Hole Uniqueness conjecture. I will sketch a proof that the Chen-Teo Instanton is Hermitian and non-Kähler. Thus\, all known examples of gravitational instantons are Hermitian. This talks is based on joint work with Steffen Aksteiner\, cf. https://arxiv.org/abs/2112.11863.\n\n\n12:30 pm–1:30 pm\nbreak\n\n\n\n1:30 pm–2:30 pm\nMartin Taylor\, Imperial College London\n(virtual)\nTitle: The nonlinear stability of the Schwarzschild family of black holes \nAbstract: I will present a theorem on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.  The proof employs a double null gauge\, is expressed entirely in physical space\, and utilises the analysis of Dafermos–Holzegel–Rodnianski on the linear stability of the Schwarzschild family.  This is joint work with M. Dafermos\, G. Holzegel and I. Rodnianski.\n\n\n2:30 pm–3:30 pm\nPo-Ning Chen\, University of California\, Riverside\n(virtual)\nTitle: Angular momentum in general relativity\n\nAbstract: The definition of angular momentum in general relativity has been a subtle issue since the 1960s\, due to the ‘supertranslation ambiguity’. In this talk\, we will discuss how the mathematical theory of quasilocal mass and angular momentum leads to a new definition of angular momentum at null infinity that is free of any supertranslation ambiguity.This is based on joint work with Jordan Keller\, Mu-Tao Wang\, Ye-Kai Wang\, and Shing-Tung Yau.\n\n\n3:30 pm–4:00 pm\nbreak\n\n\n\n4:00 pm–5:00 pm\nDan Lee\, Queens College (CUNY)\n(hybrid: in person & virtual)\nTitle: Stability of the positive mass theorem \nAbstract: We will discuss the problem of stability for the rigidity part of the Riemannian positive mass theorem\, focusing on recent work with Kazaras and Khuri\, in which we proved that if one assumes a lower Ricci curvature bound\, then stability holds with respect to pointed Gromov-Hausdorff convergence.\n\n\n\n\n  \nTuesday\, April 5\, 2022 \n\n\n\n\nTime (ET)\nSpeaker\nTitle/Abstract\n\n\n9:30 am–10:30 am\nXinliang An\, National University of Singapore\n(virtual)\nTitle: Anisotropic dynamical horizons arising in gravitational collapse \nAbstract: Black holes are predicted by Einstein’s theory of general relativity\, and now we have ample observational evidence for their existence. However theoretically there are many unanswered questions about how black holes come into being and about the structures of their inner spacetime singularities. In this talk\, we will present several results in these directions. First\, in a joint work with Qing Han\, with tools from scale-critical hyperbolic method and non-perturbative elliptic techniques\, with anisotropic characteristic initial data we prove that: in the process of gravitational collapse\, a smooth and spacelike apparent horizon (dynamical horizon) emerges from general (both isotropic and anisotropic) initial data. This result extends the 2008 Christodoulou’s monumental work and it connects to black hole thermodynamics along the apparent horizon. Second\, in joint works with Dejan Gajic and Ruixiang Zhang\, for the spherically symmetric Einstein-scalar field system\, we derive precise blow-up rates for various geometric quantities along the inner spacelike singularities. These rates obey polynomial blow-up upper bounds; and when it is close to timelike infinity\, these rates are not limited to discrete finite choices and they are related to the Price’s law along the event horizon. This indicates a new blow-up phenomenon\, driven by a PDE mechanism\, rather than an ODE mechanism. If time permits\, some results on fluid dynamics will also be addressed.\n\n\n10:30 am–11:30 am\nSergiu Klainerman\, Princeton\n(virtual)\nTitle: Nonlinear stability of slowly rotating Kerr solutions \nAbstract: I will talk about the status of the stability of Kerr conjecture in General Relativity based on recent results obtained in collaboration with Jeremie Szeftel and Elena Giorgi.\n\n\n11:30 am–12:30 pm\nSiyuan Ma\, Sorbonne University\n(virtual)\nTitle: Sharp decay for Teukolsky master equation \nAbstract: I will talk about joint work with L. Zhang on deriving the late time dynamics of the spin $s$ components that satisfy the Teukolsky master equation in Kerr spacetimes.\n\n\n12:30 pm–1:30 pm\nBreak\n\n\n\n1:30 pm–2:30 pm\nJonathan Luk\, Stanford\n(virtual)\nTitle: A tale of two tails \nAbstract: Motivated by the strong cosmic censorship conjecture\, we introduce a general method for understanding the late-time tail for solutions to wave equations on asymptotically flat spacetimes in odd spatial dimensions. A particular consequence of the method is a re-proof of Price’s law-type results\, which concern the sharp decay rate of the late-time tails on stationary spacetimes. Moreover\, we show that the late-time tails are in general different from the stationary case in the presence of dynamical and/or nonlinear perturbations. This is a joint work with Sung-Jin Oh (Berkeley).\n\n\n2:30 pm–3:30 pm\nGary Horowitz\, University of California Santa Barbara\n(virtual)\nTitle: A new type of extremal black hole \nAbstract: I describe a family of four-dimensional\, asymptotically flat\, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Surprisingly\, the maximum charge for given mass is a nonsingular hairy black hole with a nondegenerate event horizon. Since the surface gravity is nonzero\, if quantum matter is added\, Hawking radiation does not appear to stop when this new extremal limit is reached. This raises the question of whether Hawking radiation will cause the black hole to turn into a naked singularity. I will argue that does not occur.\n\n\n3:30 pm–4:00 pm\nBreak\n\n\n\n4:00 pm–5:00 pm\nLydia Bieri\, University of Michigan\n(virtual)\nTitle: Gravitational radiation in general spacetimes \nAbstract: Studies of gravitational waves have been devoted mostly to sources such as binary black hole mergers or neutron star mergers\, or generally sources that are stationary outside of a compact set. These systems are described by asymptotically-flat manifolds solving the Einstein equations with sufficiently fast decay of the gravitational field towards Minkowski spacetime far away from the source. Waves from such sources have been recorded by the LIGO/VIRGO collaboration since 2015. In this talk\, I will present new results on gravitational radiation for sources that are not stationary outside of a compact set\, but whose gravitational fields decay more slowly towards infinity. A panorama of new gravitational effects opens up when delving deeper into these more general spacetimes. In particular\, whereas the former sources produce memory effects that are finite and of purely electric parity\, the latter in addition generate memory of magnetic type\, and both types grow. These new effects emerge naturally from the Einstein equations both in the Einstein vacuum case and for neutrino radiation. The latter results are important for sources with extended neutrino halos.\n\n\n\n\n  \nWednesday\, April 6\, 2022 \n\n\n\n\nTime (ET)\nSpeaker\nTitle/Abstract\n\n\n9:30 am–10:30 am\nGerhard Huisken\, Mathematisches Forschungsinstitut Oberwolfach\n(virtual)\nTitle: Space-time versions of inverse mean curvature flow \nAbstract: In order to extend the Penrose inequality from a time-symmetric setting to general asymptotically flat initial data sets several anisotropic generalisations of inverse mean curvature flow have been suggested that take the full space-time geometry into account. The lecture describes the properties of such flows and reports on recent joint work with Markus Wolff on inverse flow along the space-time mean curvature.\n\n\n10:30 am–11:30 am\nCarla Cederbaum\, Universität Tübingen\, Germany\n(virtual)\nTitle: Coordinates are messy \nAbstract: Asymptotically Euclidean initial data sets $(M\,g\,K)$ are characterized by the existence of asymptotic coordinates in which the Riemannian metric $g$ and second fundamental form $K$ decay to the Euclidean metric $\delta$ and to $0$ suitably fast\, respectively. Provided their matter densities satisfy suitable integrability conditions\, they have well-defined (ADM-)energy\, (ADM-)linear momentum\, and (ADM-)mass. This was proven by Bartnik using harmonic coordinates. To study their (ADM-)angular momentum and (BORT-)center of mass\, one usually assumes the existence of Regge—Teitelboim coordinates on the initial data set $(M\,g\,K)$ in question. We will give examples of asymptotically Euclidean initial data sets which do not possess any Regge—Teitelboim coordinates We will also show that harmonic coordinates can be used as a tool in checking whether a given asymptotically Euclidean initial data set possesses Regge—Teitelboim coordinates. This is joint work with Melanie Graf and Jan Metzger. We will also explain the consequences these findings have for the definition of the center of mass\, relying on joint work with Nerz and with Sakovich.\n\n\n11:30 am–12:30 pm\nStefanos Aretakis\, University of Toronto\n(virtual)\nTitle: Observational signatures for extremal black holes \nAbstract: We will present results regarding the asymptotics of scalar perturbations on black hole backgrounds. We will then derive observational signatures for extremal black holes that are based on global or localized measurements on null infinity. This is based on joint work with Gajic-Angelopoulos and ongoing work with Khanna-Sabharwal.\n\n\n12:30 pm–1:30 pm\nBreak\n\n\n\n1:30 pm–2:30 pm\nJared Speck\, Vanderbilt University\n(virtual)\nTitle: The mathematical theory of shock waves in multi-dimensional relativistic and non-relativistic compressible Euler flow \nAbstract: In the last two decades\, there have been dramatic advances in the rigorous mathematical theory of shock waves in solutions to the relativistic Euler equations and their non-relativistic analog\, the compressible Euler equations. A lot of the progress has relied on techniques that were developed to study Einstein’s equations. In this talk\, I will provide an overview of the field and highlight some recent progress on problems without symmetry or irrotationality assumptions. I will focus on results that reveal various aspects of the structure of the maximal development of the data and the corresponding implications for the shock development problem\, which is the problem of continuing the solution weakly after a shock. I will also describe various open problems\, some of which are tied to the Einstein–Euler equations. Various aspects of this program are joint with L. Abbrescia\, M. Disconzi\, and J. Luk.\n\n\n2:30 pm–3:30 pm\nLan-Hsuan Huang\, University of Connecticut\n(virtual)\nTitle: Null perfect fluids\, improvability of dominant energy scalar\, and Bartnik mass minimizers \nAbstract: We introduce the concept of improvability of the dominant energy scalar\, and we derive strong consequences of non-improvability. In particular\, we prove that a non-improvable initial data set without local symmetries must sit inside a null perfect fluid spacetime carrying a global Killing vector field. We also show that the dominant energy scalar is always almost improvable in a precise sense. Using these main results\, we provide a characterization of Bartnik mass minimizing initial data sets which makes substantial progress toward Bartnik’s stationary conjecture. \nAlong the way we observe that in dimensions greater than eight there exist pp-wave counterexamples (without the optimal decay rate for asymptotically flatness) to the equality case of the spacetime positive mass theorem. As a consequence\, we find counterexamples to Bartnik’s stationary and strict positivity conjectures in those dimensions. This talk is based on joint work with Dan A. Lee.\n\n\n3:30 pm–4:00 pm\nBreak\n\n\n\n4:00 pm–5:00 pm\nDemetre Kazaras\, Duke University\n(virtual)\nTitle: Comparison geometry for scalar curvature and spacetime harmonic functions \nAbstract: Comparison theorems are the basis for our geometric understanding of Riemannian manifolds satisfying a given curvature condition. A remarkable example is the Gromov-Lawson toric band inequality\, which bounds the distance between the two sides of a Riemannian torus-cross-interval with positive scalar curvature by a sharp constant inversely proportional to the scalar curvature’s minimum. We will give a new qualitative version of this and similar band-type inequalities in dimension 3 using the notion of spacetime harmonic functions\, which recently played the lead role in our recent proof of the positive mass theorem. This is joint work with Sven Hirsch\, Marcus Khuri\, and Yiyue Zhang.\n\n\n\n\n  \nThursday\, April 7\, 2022 \n\n\n\n\nTime (ET)\nSpeaker\nTitle/Abstract\n\n\n9:30 am–10:30 am\nPiotr Chrusciel\, Universitat Wien\n(virtual)\nTitle: Maskit gluing and hyperbolic mass \nAbstract: “Maskit gluing” is a gluing construction for asymptotically locally hyperbolic (ALH) manifolds with negative cosmological constant. I will present a formula for the mass of Maskit-glued ALH manifolds and describe how it can be used to construct general relativistic initial data with negative mass.\n\n\n10:30 am–11:30 am\nGreg Galloway\, University of Miami (virtual)\nTitle:  Initial data rigidity and applications \nAbstract:  We present a result from our work with Michael Eichmair and Abraão Mendes concerning initial data rigidity results (CMP\, 2021)\, and look at some consequences.  In a note with Piotr Chruściel (CQG 2021)\, we showed how to use this result\, together with arguments from Chruściel and Delay’s proof of the their hyperbolic PMT result\, to obtain a hyperbolic PMT result with boundary.  This will also be discussed.\n\n\n11:30 am–12:30 pm\nPengzi Miao\, University of Miami\n(virtual)\nTitle: Some remarks on mass and quasi-local mass \nAbstract: In the first part of this talk\, I will describe how to detect the mass of asymptotically flat and asymptotically hyperbolic manifolds via large Riemannian polyhedra. In the second part\, I will discuss an estimate of the Bartnik quasi-local mass and its geometric implications. This talk is based on several joint works with A. Piubello\, and with H.C. Jang.\n\n\n12:30 pm–1:30 pm\nBreak\n\n\n\n1:30 pm–2:30 pm\nYakov Shlapentokh Rothman\, Princeton\n(hybrid: in person & virtual)\nTitle: Self-Similarity and Naked Singularities for the Einstein Vacuum Equations \nAbstract: We will start with an introduction to the problem of constructing naked singularities for the Einstein vacuum equations\, and then explain our discovery of a fundamentally new type of self-similarity and show how this allows us to construct solutions corresponding to a naked singularity. This is joint work with Igor Rodnianski.\n\n\n2:30 pm–3:30 pm\nMarcelo Disconzi\, Vanderbilt University\n(virtual)\nTitle: General-relativistic viscous fluids. \nAbstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions\, as the quark-gluon plasma is the hottest\, smallest\, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe\, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades\, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments\, theory\, phenomenology\, and numerical simulations. From these investigations\, a coherent picture has emerged\, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently\, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems\, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due\, in part\, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk\, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.\n\n\n3:30 pm–4:00 pm\nBreak\n\n\n\n4:00 pm–5:00 pm\nMaxime van de Moortel\, Princeton\n(hybrid: in person & virtual)\nTitle: Black holes: the inside story of gravitational collapse \nAbstract: What is inside a dynamical black hole? While the local region near time-like infinity is understood for various models\, the global structure of the black hole interior has largely remained unexplored.\nThese questions are deeply connected to the nature of singularities in General Relativity and celebrated problems such as Penrose’s Strong Cosmic Censorship Conjecture.\nI will present my recent resolution of these problems in spherical gravitational collapse\, based on the discovery of a novel phenomenon: the breakdown of weak singularities and the dynamical formation of a strong singularity.\n\n\n\n\n  \nFriday\, April 8\, 2022 \n\n\n\n\nTime (ET)\nSpeaker\nTitle/Abstract\n\n\n9:30 am–10:30 am\nYe-Kai Wang\, National Cheng Kun University\, Taiwan\n(virtual)\nTitle: Supertranslation invariance of angular momentum at null infinity in double null gauge \nAbstract: This talk accompanies Po-Ning Chen’s talk on Monday with the results described in the double null gauge rather than Bondi-Sachs coordinates. Besides discussing\nhow Chen-Wang-Yau angular momentum resolves the supertranslation ambiguity\, we also review the definition of angular momentum defined by A. Rizzi. The talk is based on the joint work with Po-Ning Chen\, Jordan Keller\, Mu-Tao Wang\, and Shing-Tung Yau.\n\n\n10:30 am–11:30 am\nZoe Wyatt\, King’s College London\n(virtual)\nTitle: Global Stability of Spacetimes with Supersymmetric Compactifications \nAbstract: Spacetimes with compact directions which have special holonomy\, such as Calabi-Yau spaces\, play an important role in\nsupergravity and string theory. In this talk I will discuss a recent work with Lars Andersson\, Pieter Blue and Shing-Tung Yau\, where we show the global\, nonlinear stability a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. This stability result is related to a conjecture of Penrose concerning the validity of string theory. Our proof uses the intersection of methods for quasilinear wave and Klein-Gordon equations\, and so towards the end of the talk I will also comment more generally on coupled wave–Klein-Gordon equations.\n\n\n11:30 am–12:30 pm\nElena Giorgi\, Columbia University\n(hybrid: in person & virtual)\nTitle: The stability of charged black holes \nAbstract: Black hole solutions in General Relativity are parametrized by their mass\, spin and charge. In this talk\, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally\, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole\, where the interaction between the radiations prevents the separability in modes.\n\n\n12:30 pm–1:30 pm\nBreak\n\n\n\n1:30 pm–2:30 pm\nMarcus Khuri\, Stony Brook University\n(virtual)\nTitle: The mass-angular momentum inequality for multiple black holes\n\nAbstract: Consider a complete 3-dimensional initial data set for the Einstein equations which has multiple asymptotically flat or asymptotically cylindrical ends. If it is simply connected\, axisymmetric\, maximal\, and satisfies the appropriate energy condition then the ADM mass of any of the asymptotically flat ends is bounded below by the square root of the total angular momentum. This generalizes previous work of Dain\, Chrusciel-Li-Weinstein\, and Schoen-Zhou which treated either the single black hole case or the multiple black hole case without an explicit lower bound. The proof relies on an analysis of the asymptotics of singular harmonic maps from\nR^3 \ \Gamma –>H^2   where \Gamma is a coordinate axis. This is joint work with Q. Han\, G. Weinstein\, and J. Xiong.\n\n\n2:30 pm–3:30 pm\nMartin Lesourd\, Harvard\n(hybrid: in person & virtual)\nTitle:  A Snippet on Mass and the Topology and Geometry of Positive Scalar Curvature \nAbstract:  I will talk about a small corner of the study of Positive Scalar Curvature (PSC) and questions which are most closely related to the Positive Mass Theorem. The classic questions are ”which topologies allow for PSC?” and ”what is the geometry of manifolds with PSC?”. This is based on joint work with Prof. S-T. Yau\, Prof. D. A. Lee\, and R. Unger.\n\n\n3:30 pm–4:00 pm\nBreak\n\n\n\n4:00 pm–5:00 pm\nGeorgios Moschidis\, Princeton\n(virtual)\nTitle: Weak turbulence for the Einstein–scalar field system. \nAbstract: In the presence of confinement\, the Einstein field equations are expected to exhibit turbulent dynamics. In the presence of a negative cosmological constant\, the AdS instability conjecture claims the existence of arbitrarily small perturbations to the initial data of Anti-de Sitter spacetime which\, under evolution by the vacuum Einstein equations with reflecting boundary conditions at conformal infinity\, lead to the formation of black holes after sufficiently long time.\nIn this talk\, I will present a rigorous proof of the AdS instability conjecture in the setting of the spherically symmetric Einstein-scalar field system. The construction of the unstable initial data will require carefully designing a family of initial configurations of localized matter beams and estimating the exchange of energy taking place between interacting beams over long periods of time\, as well as estimating the decoherence rate of those beams.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-conference/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/GR-Conference.png
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20210824
DTEND;VALUE=DATE:20210825
DTSTAMP:20260504T060537
CREATED:20230705T081718Z
LAST-MODIFIED:20250328T145235Z
UID:10000070-1629763200-1629849599@cmsa.fas.harvard.edu
SUMMARY:Big Data Conference 2021
DESCRIPTION:On August 24\, 2021\, the CMSA hosted our seventh annual Conference on Big Data. The Conference features many speakers from the Harvard community as well as scholars from across the globe\, with talks focusing on computer science\, statistics\, math and physics\, and economics. \nThe 2021 Big Data Conference took place virtually on Zoom. \nOrganizers:  \n\nShing-Tung Yau\, William Caspar Graustein Professor of Mathematics\, Harvard University\nScott Duke Kominers\, MBA Class of 1960 Associate Professor\, Harvard Business\nHorng-Tzer Yau\, Professor of Mathematics\, Harvard University\nSergiy Verstyuk\, CMSA\, Harvard University\n\nSpeakers: \n\nAndrew Blumberg\, University of Texas at Austin\nMoran Koren\, Harvard CMSA\nHima Lakkaraju\, Harvard University\nKatrina Ligett\, The Hebrew University of Jerusalem\n\n\n\n\n\nTime (ET; Boston time)\nSpeaker\nTitle/Abstract\n\n\n9:00AM\nConference Organizers\nIntroduction and Welcome\n\n\n9:10AM – 9:55AM\nAndrew Blumberg\, University of Texas at Austin\nTitle: Robustness and stability for multidimensional persistent homology \nAbstract: A basic principle in topological data analysis is to study the shape of data by looking at multiscale homological invariants. The idea is to filter the data using a scale parameter that reflects feature size. However\, for many data sets\, it is very natural to consider multiple filtrations\, for example coming from feature scale and density. A key question that arises is how such invariants behave with respect to noise and outliers. This talk will describe a framework for understanding those questions and explore open problems in the area.\n\n\n10:00AM – 10:45AM\nKatrina Ligett\, The Hebrew University of Jerusalem\nTitle: Privacy as Stability\, for Generalization \nAbstract: Many data analysis pipelines are adaptive: the choice of which analysis to run next depends on the outcome of previous analyses. Common examples include variable selection for regression problems and hyper-parameter optimization in large-scale machine learning problems: in both cases\, common practice involves repeatedly evaluating a series of models on the same dataset. Unfortunately\, this kind of adaptive re-use of data invalidates many traditional methods of avoiding overfitting and false discovery\, and has been blamed in part for the recent flood of non-reproducible findings in the empirical sciences. An exciting line of work beginning with Dwork et al. in 2015 establishes the first formal model and first algorithmic results providing a general approach to mitigating the harms of adaptivity\, via a connection to the notion of differential privacy. In this talk\, we’ll explore the notion of differential privacy and gain some understanding of how and why it provides protection against adaptivity-driven overfitting. Many interesting questions in this space remain open. \nJoint work with: Christopher Jung (UPenn)\, Seth Neel (Harvard)\, Aaron Roth (UPenn)\, Saeed Sharifi-Malvajerdi (UPenn)\, and Moshe Shenfeld (HUJI). This talk will draw on work that appeared at NeurIPS 2019 and ITCS 2020\n\n\n10:50AM – 11:35AM\nHima Lakkaraju\, Harvard University\nTitle: Towards Reliable and Robust Model Explanations \nAbstract: As machine learning black boxes are increasingly being deployed in domains such as healthcare and criminal justice\, there is growing emphasis on building tools and techniques for explaining these black boxes in an interpretable manner. Such explanations are being leveraged by domain experts to diagnose systematic errors and underlying biases of black boxes. In this talk\, I will present some of our recent research that sheds light on the vulnerabilities of popular post hoc explanation techniques such as LIME and SHAP\, and also introduce novel methods to address some of these vulnerabilities. More specifically\, I will first demonstrate that these methods are brittle\, unstable\, and are vulnerable to a variety of adversarial attacks. Then\, I will discuss two solutions to address some of the vulnerabilities of these methods – (i) a framework based on adversarial training that is designed to make post hoc explanations more stable and robust to shifts in the underlying data; (ii) a Bayesian framework that captures the uncertainty associated with post hoc explanations and in turn allows us to generate explanations with user specified levels of confidences. I will conclude the talk by discussing results from real world datasets to both demonstrate the vulnerabilities in post hoc explanation techniques as well as the efficacy of our aforementioned solutions.\n\n\n11:40AM – 12:25PM\nMoran Koren\, Harvard CMSA\nTitle: A Gatekeeper’s Conundrum \nAbstract: Many selection processes contain a “gatekeeper”. The gatekeeper’s goal is to examine an applicant’s suitability to a proposed position before both parties endure substantial costs. Intuitively\, the introduction of a gatekeeper should reduce selection costs as unlikely applicants are sifted out. However\, we show that this is not always the case as the gatekeeper’s introduction inadvertently reduces the applicant’s expected costs and thus interferes with her self-selection. We study the conditions under which the gatekeeper’s presence improves the system’s efficiency and those conditions under which the gatekeeper’s presence induces inefficiency. Additionally\, we show that the gatekeeper can sometimes improve selection correctness by behaving strategically (i.e.\, ignore her private information with some probability).\n\n\n12:25PM\nConference Organizers\nClosing Remarks
URL:https://cmsa.fas.harvard.edu/event/big-data-conference-2021/
LOCATION:Virtual
CATEGORIES:Big Data Conference,Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/BD_21-Poster.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20200824T100000
DTEND;TZID=America/New_York:20200825T140500
DTSTAMP:20260504T060537
CREATED:20230707T104105Z
LAST-MODIFIED:20250305T185337Z
UID:10000137-1598263200-1598364300@cmsa.fas.harvard.edu
SUMMARY:2020 Big Data Conference (Virtual)
DESCRIPTION:On August 24-25\, 2020 the CMSA hosted our sixth annual Conference on Big Data. The Conference featured many speakers from the Harvard community as well as scholars from across the globe\, with talks focusing on computer science\, statistics\, math and physics\, and economics. The 2020 Big Data Conference took place virtually. \n\nVideos of the talks are available in this youtube playlist.\n  \nOrganizers:  \n\nShing-Tung Yau\, William Caspar Graustein Professor of Mathematics\, Harvard University\nScott Duke Kominers\, MBA Class of 1960 Associate Professor\, Harvard Business\nHorng-Tzer Yau\, Professor of Mathematics\, Harvard University\nSergiy Verstyuk\, CMSA\, Harvard University\n\nSpeakers:\n \n\nSanjeev Arora\, Princeton University\nJuan Camilo Castillo\, University of Pennsylvania\nJoseph Dexter\, Dartmouth College\nNicole Immorlica\, Microsoft\nAmin Saberi\, Stanford University\nVira Semenova\, University of California\, Berkeley\nVarda Shalev\, Tel Aviv University
URL:https://cmsa.fas.harvard.edu/event/2020-big-data-conference-virtual/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Big Data Conference,Conference,Event
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Big-Data-2020-pdf.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20191101T090000
DTEND;TZID=America/New_York:20191101T170000
DTSTAMP:20260504T060537
CREATED:20230715T072841Z
LAST-MODIFIED:20250305T211543Z
UID:10000122-1572598800-1572627600@cmsa.fas.harvard.edu
SUMMARY:Learning from health data in the million genome era
DESCRIPTION:On November 1\, 2019 the CMSA will be hosting a conference organized by Seven Bridges Genomics. The workshop will be held in room G10 of the CMSA\, located at 20 Garden Street\, Cambridge\, MA. \nProjects currently underway around the world are collecting detailed health and genomic data from millions of volunteers. In parallel\, numerous healthcare systems have announced commitments to integrate genomic data into the standard of care for select patients. These data have the potential to reveal transformative insights into health and disease. However\, to realize this promise\, novel approaches are required across the full life cycle of data analysis. This symposium will include discussion of advanced statistical and algorithmic approaches to draw insights from petabyte scale genomic and health data; success stories to date; and a view towards the future of clinical integration of genomics in the learning health system. \nSpeakers:  \n\nHeidi Rehm\, Ph.D.\nChief Genomics Officer\, MGH; Professor of Pathology\, MGH\, BWH & Harvard Medical School; Medical Director\, Broad Institute Clinical Research Sequencing Platform.\nSaiju Pyarajan\, Ph.D.\nDirector\, Centre for Data and Computational Sciences\,VABHS\, and Department of Medicine\, BWH and HMS\nTianxi Cai\, Sci.D\nJohn Rock Professor of Population and Translational Data Sciences\, Department of Biostatistics\, Harvard School of Public Health\nSusan Redline\, M.D.\, M.P.H\nFarrell Professor of Sleep MedicineHarvard Medical School\, Brigham and Women’s Hospital and Beth Israel Deaconess Medical Center\nAvinash Sahu\, Ph.D.\nPostdoctoral Research Fellow\, Dana Farber Cancer Institute\, Harvard School of Public Health\nPeter J. Park\, Ph.D.\nProfessor of Biomedical Informatics\, Department of Biomedical Informatics\, Harvard Medical School\nDavid Roberson\nCommunity Engagement Manager\, Seven Bridges
URL:https://cmsa.fas.harvard.edu/event/learning-from-health-data-in-the-million-genome-era/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/SEVENB0051-POSTER-Harvard-Seminar-REV1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190819T083000
DTEND;TZID=America/New_York:20190820T164000
DTSTAMP:20260504T060537
CREATED:20230707T174003Z
LAST-MODIFIED:20250328T145128Z
UID:10000116-1566203400-1566319200@cmsa.fas.harvard.edu
SUMMARY:2019 Big Data Conference
DESCRIPTION:On August 19-20\, 2019 the CMSA hosted the fifth annual Conference on Big Data. The Conference will featured many speakers from the Harvard community as well as scholars from across the globe\, with talks focusing on computer science\, statistics\, math and physics\, and economics. \nThe talks will take place in Science Center Hall D\, 1 Oxford Street. \nVideos can be found in the Youtube playlist.
URL:https://cmsa.fas.harvard.edu/event/2019-big-data-conference/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Big Data Conference,Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Big-Data-2019-Poster-5-2.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190502T090000
DTEND;TZID=America/New_York:20190505T170000
DTSTAMP:20260504T060537
CREATED:20230715T175235Z
LAST-MODIFIED:20250328T145104Z
UID:10000115-1556787600-1557075600@cmsa.fas.harvard.edu
SUMMARY:Conference on Differential Geometry\, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau
DESCRIPTION:On May 2-5\, 2019 the Harvard Mathematics Department hosted a Conference on Differential Geometry\, Calabi-Yau Theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau. The conference was held in the  Science Center\, Lecture Hall C.  \nOrganizers:\n\nHorng-Tzer Yau (Harvard)\nWilfried Schmid (Harvard)\nClifford Taubes (Harvard)\nCumrun Vafa (Harvard)\n\nSpeakers:\n\nLydia Bieri\, University of Michigan\nTristan Collins\, MIT\nSimon Donaldson\, Imperial College\nFan Chung Graham\, UC San Diego\nNigel Hitchin\, Oxford University\nJun Li\, Stanford University\nKefeng Liu\, UCLA\nChiu-Chu Melissa Liu\, Columbia University\nAlina Marian\, Northeastern University\nXenia de la Ossa\, Oxford University\nDuong H. Phong\, Columbia University\nRichard Schoen\, UC Irvine\nAndrew Strominger\, Harvard University\nNike Sun\, MIT\nClifford Taubes\, Harvard University\nChuu-Lian Terng\, UC Irvine\nValentino Tosatti\, Northwestern University\nKaren Uhlenbeck\, University of Texas\nCumrun Vafa\, Harvard University\nMu Tao Wang\, Columbia University\nEdward Witten\, IAS\nStephen Yau\, Tsinghua University\, P.R. China
URL:https://cmsa.fas.harvard.edu/event/conference-on-differential-geometry-calabi-yau-theory-and-general-relativity-a-conference-in-honor-of-the-70th-birthday-of-shing-tung-yau/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Yau-2-2-791x1024-2.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190429T090000
DTEND;TZID=America/New_York:20190501T170000
DTSTAMP:20260504T060537
CREATED:20230715T174721Z
LAST-MODIFIED:20250304T214254Z
UID:10000114-1556528400-1556730000@cmsa.fas.harvard.edu
SUMMARY:Conference on Algebraic Geometry\, Representation theory and Mathematical Physics
DESCRIPTION:From April 29 to May 1\, 2019 the CMSA will be hosting a Conference on Algebraic Geometry\, Representation theory and Mathematical Physics. This workshop is organized by Bong Lian (Brandeis) and Artan Sheshmani (CMSA) . The workshop will be held in room G10 of the CMSA\, located at 20 Garden Street\, Cambridge\, MA.   \nVideos\nSpeakers: \n\nDan Abramovich\, Brown\nRoman Bezrukavnikov\, MIT\nFedor Bogomolov\, NYU\nQile Chen\, Boston College\nDawei Chen\, Boston College\nAlexander Efimov\, Moscow\nPavel Etingof\, MIT\nMaksym Fedorchuk\, Boston College\nDennis Gaitsgory\, Harvard\nAmin Gholampour\, Maryland\nBrendan Hassett\, Brown\nLudmil Katzarkov\, Miami & Moscow\nSi Li\, Tsinghua\nAndrei Negut\, MIT\nYuri Tschinkel\, NYU\nWei Zhang\, MIT\n\n  \nMonday\, April 29 \n\n\n\nTime\nSpeaker\nTitle/Abstract\n\n\n8:30 – 9:00am\nBreakfast\n\n\n\n9:00 – 10:00am\nWei Zhang\, MIT\nTitle: The arithmetic fundamental lemma for diagonal cycles \nAbstract: I’ll recall the Gross–Zagier theorem and a high dimensional generalization\, the arithmetic Gan-Gross-Prasad conjecture\, which relates the height pairing of arithmetic diagonal cycles on certain shimura varieties to the first order derivative of certain L-functions.  The arithmetic fundamental lemma conjecture arises from the relative trace formula approach to this conjecture. I will recall the statement of the arithmetic fundamental lemma and outline a proof.\n\n\n10:00 – 10:30am\nBreak\n\n\n\n10:30 – 11:30am\nYuri Tschinkel\, NYU\nTitle: Equivariant birational geometry and modular symbols \nAbstract: We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups (joint with M. Kontsevich and V. Pestun).\n\n\n11:30 – 1:30pm\nLunch\n\n\n\n1:30 – 2:30pm\nAlexander Efimov\, Moscow\nTitle: Torsionness for regulators of canonical extensions \nAbstract: I will sketch a generalization of the results of Iyer and Simpson arXiv:0707.0372 to the general case of a normal-crossings divisor at infinity.\n\n\n2:30 – 3:00pm\nBreak\n\n\n\n3:00 – 4:00pm\nAmin Gholampour\, Maryland\nTitle: Euler Characteristics of punctual quot schemes on threefolds \nAbstract: Let F be a homological dimension 1 torsion free sheaf on a nonsingular quasi-projective threefold. The first cohomology of the derived dual of F is a 1-dimension sheaf G supported on the singular locus of F. We prove a wall-crossing formula relating the generating series of the Euler characteristics of Quot(F\, n) and Quot(G\,n)\, where Quot(-\,n) denotes the quot scheme of length n quotients. We will use this relation in studying the Euler characteristics of the moduli spaces of stable torsion free sheaves on nonsingular projective threefolds. This is a joint work with Martijn Kool.\n\n\n4:00 – 4:30pm\nBreak\n\n\n\n4:30 – 5:30pm\nMaksym Fedorchuck\, BC\nTitle:  Stability of one-parameter families of weighted hypersurfaces \nAbstract:  We define a notion of stability for fibrations over a curve with generic fibers being weighted hypersurfaces (in some weighted projective space) generalizing Kollár’s stability for families of hypersurfaces in a projective space.  The stability depends on a choice of an effective line bundle on the parameter space of weighted hypersurfaces and different choices pick out different birational model of the total space of the fibration. I will describe enumerative geometry that goes into understanding these stability conditions\, and\, if time permits\, examples where this machinery can be used to produce birational models with good properties.  Joint work with Hamid Ahmadinezhad and Igor Krylov.\n\n\n\n  \nTuesday\, April 30 \n\n\n\nTime\nSpeaker\nTitle/Abstract\n\n\n8:30 – 9:00am\nBreakfast\n\n\n\n9:00 – 10:00am\nBrendan Hassett\, Brown\nTitle: Rationality for geometrically rational threefolds \nAbstract: We consider rationality questions for varieties over non-closed fields that become rational over an algebraic closure\, like smooth complete intersections of two quadrics.  (joint with Tschinkel)\n\n\n10:00 – 10:30am\nBreak\n\n\n\n10:30 – 11:30am\nDennis Gaitsgory\, Harvard\nTitle: The Fundamental Local Equivalence in quantum geometric Langlands \nAbstract: The Fundamental Local Equivalence is statement that relates the q-twisted  Whittaker category of the affine Grassmannian for the group G and the category of modules over the Langlands dual “big” quantum group. The non-triviaiity of the statement lies is the fact that the relationship between the group and its  dual is combinatorial\, so to prove the FLE one needs to express both sides in combinatorial terms. In the talk we will indicate the proof of a related statement for the “small” quantum group. The combinatorial link is provided by the category of factorization modules over a certain factorization algebra\, which in itself is a geometric device that concisely encodes the root data.\n\n\n11:30 – 1:00pm\nLunch\n\n\n\n1:00- 2:00pm\nAndrei Negut\, MIT\nTitle: AGT relations in geometric representation theory \nAbstract: I will survey a program that seeks to translate the Alday-Gaiotto-Tachikawa correspondence (between gauge theory on R^4 and conformal field theory) into the language of algebraic geometry. The objects of study become moduli spaces of sheaves on surfaces\, and the goal is to connect them with the W-algebra of type gl_n.\n\n\n2:00 – 2:15pm\nBreak\n\n\n\n2:15 – 3:15pm\nDan Abramovich\, Brown\nTitle: Resolution in characteristic 0 using weighted blowing up \nAbstract: Given a variety $X$\, one wants to blow up the worst singular locus\, show that it gets better\, and iterate until the singularities are resolved. \nExamples such as the whitney umbrella show that this iterative process cannot be done by blowing up smooth loci – it goes into a loop. \nWe show that there is a functorial way to resolve varieties using \emph{weighted} blowings up\, in the stack-theoretic sense. To an embedded variety $X \subset Y$ one functorially assigns an invariant $(a_1\,\ldots\,a_k)$\, and a center locally of the form $(x_1^{a_1} \, \ldots \, x_k^{a_k})$\, whose stack-theoretic weighted blowing up has strictly smaller invariant under the lexicographic order. \nThis is joint work with Michael Tëmkin (Jerusalem) and Jaroslaw Wlodarczyk (Purdue)\, a side product of our work on functorial semistable reduction. A similar result was discovered by G. Marzo and M. McQuillan.\n\n\n3:15 – 3:30pm\nBreak\n\n\n\n3:30 – 4:30pm\nFedor Bogomolov\, NYU\nTitle: On the base of a Lagrangian fibration for a compact hyperkahler manifold. \nAbstract: In my talk I will discuss our proof with N. Kurnosov that the base of such fibration for complex projective manifold hyperkahler manifold of dimension $4$ is always a projective plane $P^2$. In fact we show that the base of such fibration can not have a singular point of type $E_8$. It was by the theorem of Matsushita and others that only quotient singularities can occur and if the base is smooth then the it is isomorphic to $P^2$. The absence of other singularities apart from $E_8$ has been already known and we show that $E-8$ can not occur either. Our method can be applied to other types of singularities for the study of  Lagrangian fibrations in higher dimensions More recently similar result was obtained by Huybrechts and Xu.\n\n\n4:30 – 4:45pm\nBreak\n\n\n\n4:45 – 5:45pm\nDawei Chen\, BC\nTitle: Volumes and intersection theory on moduli spaces of Abelian differentials \nAbstract: Computing volumes of moduli spaces has significance in many fields. For instance\, Witten’s conjecture regarding intersection numbers on moduli spaces of Riemann surfaces has a fascinating connection to the Weil-Petersson volume\, which motivated Mirzakhani to give a proof via Teichmueller theory\, hyperbolic geometry\, and symplectic geometry. In this talk I will introduce an analogue of Witten’s intersection numbers on moduli spaces of Abelian differentials to compute the Masur-Veech volumes induced by the flat metric associated with Abelian differentials. This is joint work with Moeller\, Sauvaget\, and Zagier (arXiv:1901.01785).\n\n\n\n  \nWednesday\, May 1 \n\n\n\nTime\nSpeaker\nTitle/Abstract\n\n\n8:30 – 9:00am\nBreakfast\n\n\n\n9:00 – 10:00am\nPavel Etingof\, MIT\nTitle: Short star-products for filtered quantizations \nThis is joint work with Eric Rains and Douglas Stryker.\n\n\n10:00 – 10:30am\nBreak\n\n\n\n10:30 – 11:30am\nRoman Bezrukavnikov\, MIT\nTitle: Stability conditions and representation theory \nAbstract: I will recall the concept of real variation of stabilities (introduced in my work with Anno and Mirkovic)\nand its relation to modular Lie algebra representations. I will also address a potential generalization of that picture\nto modular representations of affine Lie algebras related to the classical limit of geometric Langlands duality and its local counterpart.\n\n\n11:30 – 11:45am\nBreak\n\n\n\n11:45 – 12:45pm\nQile Chen\, BC\nTitle: Counting curves in critical locus via logarithmic compactification \nAbstract: An R-map consists of a pre-stable map to possibly non-GIT quotient together with sections of certain spin bundles. The moduli of R-maps are in general non-compact. When the target of R-maps is equipped with a super-potential W with compact critical locus\, using Kiem-Li cosection localization it has been proved by many authors in various settings that the virtual cycle of R-maps can be represented by the cosection localized virtual cycle which is supported on the proper locus consisting of R-maps in the critical locus of W. Though the moduli of R-maps is equipped with a natural torus action by scaling of the spin bundles\, the non-compactness of the R-maps moduli makes such powerful torus action useless. \nIn this talk\, I will introduce a logarithmic compactification of the moduli of R-maps using certain modifications of stable logarithmic maps. The logarithmic moduli space carries a canonical virtual cycle from the logarithmic deformation theory. In the presence of a super-potential with compact critical locus\, it further carries a reduced virtual cycle. We prove that (1) the reduced virtual cycle of the compactification can be represented by the cosection localized virtual cycle; and (2) the difference of the canonical and reduced virtual cycles is another reduced virtual cycle supported along the logarithmic boundary. As an application\, one recovers the Gromov-Witten invariants of the critical locus as the invariants of logarithmic R-maps of its ambient space in an explicit form. The latter can be calculated using the spin torus action. \nThis is a joint work with Felix Janda and Yongbin Ruan.\n\n\n12:45 – 2:30pm\nLunch\n\n\n\n2:30 – 3:30pm\nSi Li\, Tsinghua\nTitle: Semi-infinite Hodge structure: from BCOV theory to Seiberg-Witten geometry \nAbstract: I will explain how the semi-infinite Hodge theory extends Kodaira-Spencer gravity (Bershadsky-Cecotti-Ooguri-Vafa theory of B-twisted closed topological string field theory) into a full solution of Batalin-Vilkovisky master equation. This allows us to formulate quantum B-model via a rigorous BV quantization method and construct integrable hierarchies arising naturally from the background symmetry. In the second part of the talk\, I will explain the recent discovery of the connection between K.Saito’s primitive form and 4d N=2 Seiberg-Witten geometry arising from singularity theory.\n\n\n3:30 – 4:00pm\nBreak\n\n\n\n4:00 – 5:00pm\nLudmil Katzarkov\, Moscow\nTitle: PDE’s non commutative  motives and HMS. \nAbstract: In this talk we will discuss the theory of central manifolds and the new structures in geometry it produces. Application to Bir.  Geometry will be discussed.\n\n\n\n 
URL:https://cmsa.fas.harvard.edu/event/conference-on-algebraic-geometry-representation-theory-and-mathematical-physics/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/algebraic-geo-conference-final-795x1024-1-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181116T080000
DTEND;TZID=America/New_York:20181117T170000
DTSTAMP:20260504T060537
CREATED:20230715T085736Z
LAST-MODIFIED:20241212T191652Z
UID:10000102-1542355200-1542474000@cmsa.fas.harvard.edu
SUMMARY:Current Developments In Mathematics 2018
DESCRIPTION:Current Developments in Mathematics 2018 Conference. \nFriday\, Nov. 16\, 2018 2:15 pm – 6:00 pm \nSaturday\, Nov. 17\, 2018  9:00 am – 5:00 pm \nHarvard University Science Center\, Hall B \nYoutube Playlist
URL:https://cmsa.fas.harvard.edu/event/current-developments-in-mathematics-2018/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/cdm-2018-poster.jpeg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180823T083000
DTEND;TZID=America/New_York:20180824T163000
DTSTAMP:20260504T060537
CREATED:20230715T083801Z
LAST-MODIFIED:20250415T154139Z
UID:10000086-1535013000-1535128200@cmsa.fas.harvard.edu
SUMMARY:Big Data Conference 2018
DESCRIPTION:On August 23-24\, 2018 the CMSA hosted the fourth annual Conference on Big Data. The Conference featured speakers from the Harvard community as well as scholars from across the globe\, with talks focusing on computer science\, statistics\, math and physics\, and economics. \nThe talks were held in Science Center Hall B\, 1 Oxford Street. \nSpeakers:  \n\nMohammad Akbarpour\, Stanford\nEmily Breza\, Harvard\nFrancesca Dominici\, Harvard\nChiara Farronato\, Harvard\nKobi Gal\, Ben Gurion\nJonah Kallenbach\, Reverie Labs\nSamuel Kou\, Harvard\nLaura Kreidberg\, Harvard\nDanielle Li\, MIT\nLibby Mishkin\, Uber\nJosh Speagle\, Harvard\nWilliam Stein\, University of Washington\nAlex Teyltelboym\, University of Oxford\nSergiy Verstyuk\, CMSA/Harvard\n\nOrganizers:  \n\nShing-Tung Yau\, William Caspar Graustein Professor of Mathematics\, Harvard University\nScott Duke Kominers\, MBA Class of 1960 Associate Professor\, Harvard Business\nRichard Freeman\, Herbert Ascherman Professor of Economics\, Harvard University\nJun Liu\, Professor of Statistics\, Harvard University\nHorng-Tzer Yau\, Professor of Mathematics\, Harvard University
URL:https://cmsa.fas.harvard.edu/event/2018-big-data-conference-2/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Big Data Conference,Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Big-Data-2018-4.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180818T083000
DTEND;TZID=America/New_York:20180820T172000
DTSTAMP:20260504T060537
CREATED:20230715T083526Z
LAST-MODIFIED:20250304T213419Z
UID:10000084-1534581000-1534785600@cmsa.fas.harvard.edu
SUMMARY:From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford
DESCRIPTION:On August 18 and 20\, 2018\, the Center of Mathematic Sciences and Applications and the Harvard University Mathematics Department hosted a conference on From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford. The talks took place in Science Center\, Hall B. \nSaturday\, August 18th:  A day of talks on Vision\, AI and brain sciences \nMonday\, August 20th: a day of talks on Math \nSpeakers: \n\nStuart Geman\, Brown\nJanos Kollar\, Princeton\nTai Sing Lee\, CMU\nEmanuele Macri\, Northeastern\nJitendra Malik\, Berkeley / FAIR\nPeter Michor\, University of Vienna\nMichael Miller\, Johns Hopkins\nAaron Pixton\, MIT\nJayant Shah\, Northeastern\nJosh Tenenbaum\, MIT\nBurt Totaro\, UCLA\nAvi Wigderson\, IAS\nYing Nian Wu\, UCLA\nLaurent Younes\, Johns Hopkins\nSong-Chun Zhu\, UCLA\n\nOrganizers:\n\nChing-Li Chai\, University of Pennsylvania\nDavid Gu\, Stony Brook University\nAmnon Neeman\, Australian National University\nMark Nitzberg\, University of California at Berkeley\nYang Wang\, Hong Kong University of Science and Technology\nShing-Tung Yau\, Harvard University\nSong-Chun Zhu\, University of California\, Los Angeles\n\nPublication: \nPure and Applied Mathematics Quarterly\nSpecial Issue: In Honor of David Mumford\nGuest Editors: Ching-Li Chai\, Amnon Neeman \n 
URL:https://cmsa.fas.harvard.edu/event/from-algebraic-geometry-to-vision-and-ai-a-symposium-celebrating-the-mathematical-work-of-david-mumford/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Mumford-3.png
END:VEVENT
END:VCALENDAR