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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260422T090000
DTEND;TZID=America/New_York:20260422T103000
DTSTAMP:20260501T125227
CREATED:20260130T191058Z
LAST-MODIFIED:20260430T205709Z
UID:10003887-1776848400-1776853800@cmsa.fas.harvard.edu
SUMMARY:CMSA/Tsinghua Math-Science Literature Lecture: Nicolai Reshetikhin (Tsinghua): Asymptotic representation theory
DESCRIPTION:CMSA/Tsinghua Math-Science Literature Lecture \nDate: April 22\, 2026 \nTime: 9:00 – 10:30 am ET \nLocation: via Zoom Webinar \nSpeaker: Nicolai Reshetikhin\, Yau Mathematical Sciences Center\, Tsinghua University \nTitle: Asymptotic representation theory \nAbstract: Loosely speaking asymptotic representation theory studies representations of “large” groups or algebras. One of the first results in this direction is the study of Plancherel measures on the symmetric group $S_N$ in the limit $N\to \infty$ by Vershik and Kerov and Logan and Shepp. The first part of the talk will be an overview of results on statistics of irreducible representations in large tensor products. Then we focus on more modern results on statistics of tilting and projective modules in large tensor products and on how some problems in asymptotic representation theory are related to dimer models in statistical mechanics. \n\nBeginning in Spring 2020\, the CMSA began hosting a lecture series on literature in the mathematical sciences\, with a focus on significant developments in mathematics that have influenced the discipline\, and the lifetime accomplishments of significant scholars. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathscilit2026_nr/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Mathlit_Reshetikhin.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260310T084500
DTEND;TZID=America/New_York:20260310T101500
DTSTAMP:20260501T125227
CREATED:20260127T153158Z
LAST-MODIFIED:20260316T161125Z
UID:10003881-1773132300-1773137700@cmsa.fas.harvard.edu
SUMMARY:CMSA/Tsinghua Math-Science Literature Lecture: Martin Bridson: Profinite rigidity: Chasing finite shadows of infinite groups
DESCRIPTION:CMSA/Tsinghua Math-Science Literature Lecture \n \nDate: March 10\, 2026 \nTime: 8:45 – 10:15 am ET \nLocation: Harvard Science Center Hall A\, 1 Oxford Street\, Cambridge MA &  via Zoom Webinar \nSpeaker: Martin Bridson FRS is the Whitehead Professor of Pure Mathematics at Oxford and President of the Clay Mathematics Institute. \nTitle: Profinite rigidity: Chasing finite shadows of infinite groups \nAbstract: There are many situations in geometry or elsewhere in mathematics where it is natural or convenient to explore infinite groups of symmetries via their actions on finite objects. But how hard is it to find these finite manifestations and to what extent does the collection of all such actions determine the infinite group?\nIn this talk\, I will sketch some of the rich history of such problems and then describe some of the significant advances in recent years. \nWe’ll pay particular attention to groups that arise in 3-dimensional geometry and topology. \n  \n\nBeginning in Spring 2020\, the CMSA began hosting a lecture series on literature in the mathematical sciences\, with a focus on significant developments in mathematics that have influenced the discipline\, and the lifetime accomplishments of significant scholars. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathscilit2026_mb/
CATEGORIES:Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Mathlit_Bridson-poster.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250408T090000
DTEND;TZID=America/New_York:20250408T103000
DTSTAMP:20260501T125227
CREATED:20250331T204029Z
LAST-MODIFIED:20250409T143732Z
UID:10003731-1744102800-1744108200@cmsa.fas.harvard.edu
SUMMARY:CMSA/Tsinghua Math-Science Literature Lecture: Scott Sheffield (MIT): Yang-Mills theory and random surfaces
DESCRIPTION:CMSA/Tsinghua Math-Science Literature Lecture \nDate: April 8\, 2025 \nTime: 9:00 – 10:30 am ET \nLocation: CMSA G10\, 20 Garden Street\, Cambridge MA & via Zoom \nSpeaker: Scott Sheffield (MIT) \nTitle: Yang-Mills theory and random surfaces \nAbstract: The Clay Institute famously offered one million dollars to anyone who could mathematically construct and understand a certain continuum version of “Yang-Mills gauge theory.” This theory is the basis of the standard model of physics\, and the heart of the problem is to understand the so-called “Wilson loop expectations.” Following recent work with Sky Cao and Minjae Park\, I will explain how the “Wilson loop expectations” in a lattice Yang-Mills model are equivalent to “insertion costs” of loops in a related random-closed-surface-ensemble model. In a sense\, these results allow us to convert one famously hard problem into another presumably hard problem. But the new problem is all about random surfaces and random permutations\, and it has a lot of relationships with and similarities to other problems we understand (think domino tilings\, random planar maps\, Young tableaux and symmetric group representation theory\, and the Weingarten calculus). It gives us some intuition for *why* certain things should be true like the “area law” or “exponential correlation decay” (what physicists call “quark confinement” or “mass gap”) even if we can’t prove all of them yet. \n\nBeginning in Spring 2020\, the CMSA began hosting a lecture series on literature in the mathematical sciences\, with a focus on significant developments in mathematics that have influenced the discipline\, and the lifetime accomplishments of significant scholars.
URL:https://cmsa.fas.harvard.edu/event/mathscilit2025_ss/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Mathlit_Sheffield_11x17-2.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241121T090000
DTEND;TZID=America/New_York:20241121T103000
DTSTAMP:20260501T125227
CREATED:20240923T152934Z
LAST-MODIFIED:20241203T144846Z
UID:10003528-1732179600-1732185000@cmsa.fas.harvard.edu
SUMMARY:CMSA/Tsinghua Math-Science Literature Lecture: Bjorn Poonen\, MIT
DESCRIPTION:CMSA/Tsinghua Math-Science Literature Lecture \nDate: November 21\, 2024 \nTime: 9:00 – 10:30 am ET \nLocation: CMSA G10\, 20 Garden Street\, Cambridge MA & via Zoom \nSpeaker: Bjorn Poonen\, MIT \nTitle: Ranks of elliptic curves \nAbstract: Elliptic curves are simplest varieties whose rational points are not fully understood\, and they are the simplest projective varieties with a nontrivial group structure.  In 1922 Mordell proved that the group of rational points on an elliptic curve is finitely generated.  We will survey what is known and what is believed about this group. \n  \n\nBeginning in Spring 2020\, the CMSA began hosting a lecture series on literature in the mathematical sciences\, with a focus on significant developments in mathematics that have influenced the discipline\, and the lifetime accomplishments of significant scholars.
URL:https://cmsa.fas.harvard.edu/event/mathscilit2024_bp/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Math Science Literature Lecture Series
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Mathlit_Poonen_11x17.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240918T090000
DTEND;TZID=America/New_York:20240918T103000
DTSTAMP:20260501T125227
CREATED:20240904T181255Z
LAST-MODIFIED:20250328T150446Z
UID:10003442-1726650000-1726655400@cmsa.fas.harvard.edu
SUMMARY:CMSA/Tsinghua Math-Science Literature Lecture: Marc Lackenby
DESCRIPTION:CMSA/Tsinghua Math-Science Literature Lecture \nDate: Wednesday\, September 18\, 2024 \nTime: 9:00 – 10:30 am ET \nLocation: Via Zoom Webinar \nSpeaker: Marc Lackenby\, University of Oxford \nTitle: The complexity of knots \nAbstract: In his final paper in 1954\, Alan Turing wrote `No systematic method is yet known by which one can tell whether two knots are the same.’ Within the next 20 years\, Wolfgang Haken and Geoffrey Hemion had discovered such a method. However\, the computational complexity of this problem remains unknown. In my talk\, I will give a survey on this area\, that draws on the work of many low-dimensional topologists and geometers. Unfortunately\, the current upper bounds on the computational complexity of the knot equivalence problem remain quite poor. However\, there are some recent results indicating that\, perhaps\, knots are more tractable than they first seem. Specifically\, I will explain a theorem that provides\, for each knot type K\, a polynomial p_K with the property that any two diagrams of K with n_1 and n_2 crossings differ by at most p_K(n_1) + p_K(n_2) Reidemeister moves. \n\nBeginning in Spring 2020\, the CMSA began hosting a lecture series on literature in the mathematical sciences\, with a focus on significant developments in mathematics that have influenced the discipline\, and the lifetime accomplishments of significant scholars.
URL:https://cmsa.fas.harvard.edu/event/mathscilit2024_ml/
LOCATION:Virtual
CATEGORIES:Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Mathlit_Lackenby_8.5x11.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230227T090000
DTEND;TZID=America/New_York:20230301T173000
DTSTAMP:20260501T125227
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:20220509T090000
DTEND;TZID=America/New_York:20220512T123000
DTSTAMP:20260501T125227
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:20210503T100000
DTEND;TZID=America/New_York:20210503T160000
DTSTAMP:20260501T125227
CREATED:20230707T172813Z
LAST-MODIFIED:20240103T100239Z
UID:10000914-1620036000-1620057600@cmsa.fas.harvard.edu
SUMMARY:Computational Biology Symposium
DESCRIPTION:On May 3\, 2021 the CMSA will be hosting a Computational Biology Symposium virtually on Zoom. This symposium will be organized by Vijay Kuchroo. \nThe symposium will begin at 10:00am ET. There will be a morning and afternoon session\, with an hour break for lunch. \nVideos of the talks can be found in this Youtube playlist. Links are also available in the schedule below.\nConfirmed participants: \n\nUri Alon\, Weizmann Institute\nElana Fertig\, Johns Hopkins\nMartin Hemberg\, Brigham and Women’s Hospital\nPeter Kharchenko\, Harvard University\nSmita Krishnaswamy\, Yale University\nJohn Marioni\, EMBL-EBI\nEran Segal\, Weizmann Institute\nMeromit Singer\, Harvard Medical School\n\nSchedule:\nPDF of the schedule    Download
URL:https://cmsa.fas.harvard.edu/event/computational-biology-symposium/
LOCATION:20 Garden Street\, Cambridge\, MA 02138\, MA\, MA\, 02138\, United States
CATEGORIES:Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Compbiotextlessfeature-600x338-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180324T090000
DTEND;TZID=America/New_York:20180326T181500
DTSTAMP:20260501T125227
CREATED:20230717T174646Z
LAST-MODIFIED:20250304T212149Z
UID:10000074-1521882000-1522088100@cmsa.fas.harvard.edu
SUMMARY:Workshop on Geometry\, Imaging\, and Computing
DESCRIPTION:On March 24-26\, The Center of Mathematical Sciences and Applications will be hosting a workshop on Geometry\, Imaging\, and Computing\, based off  the journal of the same name. The workshop will take place in CMSA building\, G10. \nThe organizing committee consists of Yang Wang (HKUST)\, Ronald Lui (CUHK)\, David Gu (Stony Brook)\, and Shing-Tung Yau (Harvard). \nConfirmed Speakers: \n\nJianfeng Cai (HKUST)\nShikui Chen (Stony Brook)\nJerome Darbon (Brown University)\nLaurent Demanet (MIT)\nDavid Gu (Stony Brook)\nMonica Hurdal (Florida State University)\nRongjie Lai (RPI)\nYue Lu (Harvard)\nRonald Lok Ming Lui (CUHK)\nLakshminarayanan Mahadevan (Harvard)\nEric Miller (Tufts)\nAshley Prater  (AFOSR)\nLixin Shen (Syracuse University)\nAllen Tannenbaum (Stony Brook)\nGuowei Wei (Michigan State)\nStephen Wong (Houston Methodist)\nJun Zhang (University of Michigan\, Ann Arbor)\nSong Zhang (Purdue University)\nHongkai Zhao (University of California\, Irvine)
URL:https://cmsa.fas.harvard.edu/event/workshop-on-geometry-imaging-and-computing/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/GIC-Poster-2-e1520002551865.png
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END:VCALENDAR