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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240925T140000
DTEND;TZID=America/New_York:20240925T150000
DTSTAMP:20260524T182732
CREATED:20240907T180716Z
LAST-MODIFIED:20241002T144226Z
UID:10003454-1727272800-1727276400@cmsa.fas.harvard.edu
SUMMARY:Infinite Limits and Scaling Laws for Deep Neural Networks
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Blake Bordelon \nTitle: Infinite Limits and Scaling Laws for Deep Neural Networks \nAbstract: Scaling up the size and training horizon of deep learning models has enabled breakthroughs in computer vision and natural language processing. Empirical evidence suggests that these neural network models are described by regular scaling laws where performance of finite parameter models improves as model size increases\, eventually approaching a limit described by the performance of an infinite parameter model. In this talk\, we will first examine certain infinite parameter limits of deep neural networks which preserve representation learning and then describe how quickly finite models converge to these limits. Using dynamical mean field theory methods\, we provide an asymptotic description of the learning dynamics of randomly initialized infinite width and depth networks. Next\, we will empirically investigate how close the training dynamics of finite networks are to these idealized limits. Lastly\, we will provide a theoretical model of neural scaling laws which describes how generalization depends on three computational resources: training time\, model size and data quantity. This theory allows analysis of compute optimal scaling strategies and predicts how model size and training time should be scaled together in terms of spectral properties of the limiting kernel. The theory also predicts how representation learning can improve neural scaling laws in certain regimes. For very hard tasks\, the theory predicts that representation learning can approximately double the training-time exponent compared to the static kernel limit.
URL:https://cmsa.fas.harvard.edu/event/newtech_92524/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-9.25.24.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240927T090000
DTEND;TZID=America/New_York:20240927T100000
DTSTAMP:20260524T182732
CREATED:20240907T180338Z
LAST-MODIFIED:20240924T144003Z
UID:10003413-1727427600-1727431200@cmsa.fas.harvard.edu
SUMMARY:Going to the other side .... in algebra\, topology\, and maybe physics
DESCRIPTION:Quantum Field Theory and Physical Mathematics \nSpeaker: Sergei Gukov (Caltech)\n\nTitle: Going to the other side …. in algebra\, topology\, and maybe physics\n\nAbstract: Inspired by Eugene Wigner’s reflections on the ‘unreasonable effectiveness of mathematics in the natural sciences\,’ this talk is about the surprising and pervasive role of a peculiar phenomenon that\, a priori\, seemed to have no reason to exist. Yet\, it emerges across many different areas of mathematics and theoretical physics\, including: \n\nthe Kazhdan-Lusztig correspondence\nquantum invariants of 3-manifolds\nthe study of 2d (0\,2) boundary conditions in 3d N=2 theories\nresurgent analysis\n\nAlthough each of these fields approaches the phenomenon from a different perspective\, the results align in striking and unexpected ways. \n\n 
URL:https://cmsa.fas.harvard.edu/event/qm_92724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QFT-and-Physical-Mathematics-09.27.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241001T161500
DTEND;TZID=America/New_York:20241001T181500
DTSTAMP:20260524T182732
CREATED:20240916T141133Z
LAST-MODIFIED:20240927T182238Z
UID:10003506-1727799300-1727806500@cmsa.fas.harvard.edu
SUMMARY:Topological Invariants of gapped states through cosheaves
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeaker: Bowen Yang\, Harvard CMSA \nTitle: Topological Invariants of gapped states through cosheaves \nAbstract: We provide a proper mathematical framework for the constructions of topological invariants of gapped quantum states and interpret topological invariants of gapped states as lattice analogs of ’t Hooft anomalies in Quantum Field Theory. Our secondary goal is to generalize this construction in various directions. In particular\, we show how to define topological invariants of lattice spin systems living on well-behaved subsets of the lattice.
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_10124/
LOCATION:Science Center Hall E\, 1 Oxford Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Geometry and Quantum Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Geometry-Quantum-Theory-10.1.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241002T120000
DTEND;TZID=America/New_York:20241002T130000
DTSTAMP:20260524T182732
CREATED:20240907T160557Z
LAST-MODIFIED:20240924T194207Z
UID:10003450-1727870400-1727874000@cmsa.fas.harvard.edu
SUMMARY:CMSA Q&A Seminar: Cliff Taubes
DESCRIPTION:CMSA Q&A Seminar \nSpeaker: Cliff Taubes\, Harvard Mathematics \nTopic: What are Z/2 harmonic 1-forms?
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_10224/
LOCATION:MA
CATEGORIES:CMSA Q&A Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241002T140000
DTEND;TZID=America/New_York:20241002T150000
DTSTAMP:20260524T182732
CREATED:20240907T180645Z
LAST-MODIFIED:20241002T195652Z
UID:10003453-1727877600-1727881200@cmsa.fas.harvard.edu
SUMMARY:Hierarchical data structures through the lenses of diffusion models
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Antonio Sclocchi\, EPFL \nTitle: Hierarchical data structures through the lenses of diffusion models \nAbstract: The success of deep learning with high-dimensional data relies on the fact that natural data are highly structured. A key aspect of this structure is hierarchical compositionality\, yet quantifying it remains a challenge. \nIn this talk\, we explore how diffusion models can serve as a tool to probe the hierarchical structure of data. We consider a context-free generative model of hierarchical data and show the distinct behaviors of high- and low-level features during a noising-denoising process. Specifically\, we find that high-level features undergo a sharp transition in reconstruction probability at a specific noise level\, while low-level features recombine into new data from different classes. This behavior of latent features leads to correlated changes in real-space variables\, resulting in a diverging correlation length at the transition. \nWe validate these predictions in experiments with real data\, using state-of-the-art diffusion models for both images and texts. Remarkably\, both modalities exhibit a growing correlation length in changing features at the transition of the noising-denoising process. \nOverall\, these results highlight the potential of hierarchical models in capturing non-trivial data structures and offer new theoretical insights for understanding generative AI.
URL:https://cmsa.fas.harvard.edu/event/newtech_10224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-10.2.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241004T090000
DTEND;TZID=America/New_York:20241004T103000
DTSTAMP:20260524T182732
CREATED:20240907T190416Z
LAST-MODIFIED:20240930T173743Z
UID:10003465-1728032400-1728037800@cmsa.fas.harvard.edu
SUMMARY:Holography and Regge Phases at Large U(1) Charge
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \nSpeaker: Giulia Fardelli\, Boston University \nTitle: Holography and Regge Phases at Large U(1) Charge \nAbstract: A single Conformal Field Theory (CFT) can have a rich phase diagram with qualitatively different emergent behaviors in a range of different regimes parameterized by the conserved charges of the theory. In this talk\, I will consider a CFT with a global U(1) current and explore the phase diagram as a function of the U(1) charge Q and angular momentum J\, particularly at large J and Q. By taking the large J limit first\, we are able to employ a dual holographic interpretation in AdS_{d+1} to predict the energy spectrum of Q-particle states. This limit has been studied in detail for Q=2\, yielding very general results applicable to unitary CFTs in d>2. When Q is also taken to be large\, the description is more complicated; nevertheless\, we can draw interesting conclusions about the energy spectrum under certain assumptions. I will conclude with a concrete example\, the O(2) model in 3d\, highlighting interesting connections with recent (and less recent) results in this context. \n 
URL:https://cmsa.fas.harvard.edu/event/qm_10424/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QFT-and-Physical-Mathematics-10.4.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241004T120000
DTEND;TZID=America/New_York:20241004T130000
DTSTAMP:20260524T182732
CREATED:20240907T183353Z
LAST-MODIFIED:20240930T155114Z
UID:10003464-1728043200-1728046800@cmsa.fas.harvard.edu
SUMMARY:High-dimensional learning of narrow neural networks
DESCRIPTION:Member Seminar \nSpeaker: Hugo Cui\, CMSA \nTitle: High-dimensional learning of narrow neural networks \nAbstract: This talk explores the interplay between neural network architectures and data structure through the lens of high-dimensional asymptotics. We focus on a class of narrow neural networks\, namely networks possessing a finite number of hidden units\, while operating in high dimensions. In the limit of large data dimension and comparably large number of samples\, we derive a tight asymptotic characterization of the learning of these architectures. As an illustration\, we discuss how this characterization enables the analysis of a solvable model of dot-product attention. We show how the latter can learn to implement either a positional attention mechanism (with tokens attending to each other based on their respective positions)\, or a semantic attention mechanism (with tokens attending to each other based on their meaning)\, and evidence a phase transition with sample complexity from positional to semantic learning.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-10424/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-10.4.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241007T163000
DTEND;TZID=America/New_York:20241007T173000
DTSTAMP:20260524T182732
CREATED:20240903T194924Z
LAST-MODIFIED:20241003T160128Z
UID:10003433-1728318600-1728322200@cmsa.fas.harvard.edu
SUMMARY:Local complexity measures in modern parameterized function classes for supervised learning
DESCRIPTION:Colloquium \nSpeaker: Elisenda Grigsby\, Boston College \nTitle: Local complexity measures in modern parameterized function classes for supervised learning \nAbstract: The parameter space for any fixed architecture of neural networks serves as a proxy during training for the associated class of functions – but how faithful is this representation? For any fixed feedforward ReLU network architecture\, it is well-known that many different parameter settings can determine the same function. It is less well-known that the degree of this redundancy is inhomogeneous across parameter space. I’ll discuss two locally-applicable complexity measures for ReLU network classes and what we know about the relationship between them: (1) the local functional dimension\, and (2) a local version of VC dimension called persistent pseudodimension. The former is easy to compute on finite batches of points\, the latter should give local bounds on the generalization gap. I’ll speculate about how this circle of ideas might help guide our understanding of the double descent phenomenon. All of the work described in this talk is joint with Kathryn Lindsey. Some portions are also joint with Rob Meyerhoff\, David Rolnick\, and Chenxi Wu.
URL:https://cmsa.fas.harvard.edu/event/colloquium-10724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=application/pdf:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.7.2024.docx.pdf
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241008T161500
DTEND;TZID=America/New_York:20241008T181500
DTSTAMP:20260524T182732
CREATED:20240917T160554Z
LAST-MODIFIED:20241004T150540Z
UID:10003509-1728404100-1728411300@cmsa.fas.harvard.edu
SUMMARY:Skein traces and curve counting
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeaker: Sunghyuk Park\, Harvard CMSA \nTitle: Skein traces and curve counting \nAbstract: Skein modules are vector space-valued invariants of 3-manifolds describing the space of line defects modulo skein relations (determined by a choice of a ribbon category). When the 3-manifold is S x I for some surface S\, the skein module has a natural algebra structure and is called the skein algebra of S. \nIn 2010\, Bonahon and Wong constructed an algebra embedding (named “quantum trace”) of the sl_2 skein algebra into a quantum cluster variety called the “quantum Teichmuller space” for punctured surfaces\, which has applications to the representation theory of skein algebras. \nIn the first half of this talk\, I will give an overview of these concepts and explain how the quantum trace map can be generalized to the 3-dimensional setup. \nIn the second half\, I will discuss how everything above can be generalized to HOMFLYPT skeins and has natural interpretation in terms of counts of holomorphic curves.
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_10824/
LOCATION:Science Center Hall E\, 1 Oxford Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Geometry and Quantum Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Geometry-Quantum-Theory-10.8.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241009T120000
DTEND;TZID=America/New_York:20241009T130000
DTSTAMP:20260524T182732
CREATED:20241007T141752Z
LAST-MODIFIED:20241007T195958Z
UID:10003529-1728475200-1728478800@cmsa.fas.harvard.edu
SUMMARY:CMSA Q&A Seminar: Laura DeMarco
DESCRIPTION:CMSA Q&A Seminar \nSpeaker: Laura DeMarco\, Harvard University \nTopic: What is Teichmuller geometry and why is it important?
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_10924-2/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:CMSA Q&A Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Q-A-Seminar-10.9.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241011T090000
DTEND;TZID=America/New_York:20241011T100000
DTSTAMP:20260524T182732
CREATED:20240912T173151Z
LAST-MODIFIED:20241003T205732Z
UID:10003505-1728637200-1728640800@cmsa.fas.harvard.edu
SUMMARY:Dolbeault Virasoro algebra and M5 branes
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \nSpeaker: Brian Williams\, Boston University \nTitle: Dolbeault Virasoro algebra and M5 branes \nAbstract: The worldvolume theory on a stack of M5 branes in M-theory is superconformal. We propose a conjecture that in the holomorphic twist of the theory on a stack of M5 branes an infinite-dimensional enhancement of the (twisted) superconformal algebra is a symmetry. This algebra is closely related to the exceptional infinite-dimensional Lie superalgebra called E(3|6). We show that under the usual AGT correspondence this enhanced algebra degenerates to the Virasoro algebra at a particular central charge.
URL:https://cmsa.fas.harvard.edu/event/qm_101124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics,Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QFT-and-Physical-Mathematics-10.11.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241011T120000
DTEND;TZID=America/New_York:20241011T130000
DTSTAMP:20260524T182732
CREATED:20240919T144307Z
LAST-MODIFIED:20241008T132658Z
UID:10003520-1728648000-1728651600@cmsa.fas.harvard.edu
SUMMARY:Scattering Amplitude from a Twistor Point of View
DESCRIPTION:Member Seminar \nSpeaker: Keyou Zeng \nTitle: Scattering Amplitude from a Twistor Point of View \nAbstract: Scattering amplitude is a key quantity in quantum field theory. Although challenging to compute at higher loops and for large particle numbers\, physicists have developed various tools to gain a deeper understanding of amplitudes. In this seminar\, I will introduce a novel approach\, initiated by K. Costello and N. Paquette\, which makes use of twistor correspondence. This approach enables the computation of certain amplitudes using chiral algebra. I will also present an upcoming work that constructs a top-down holography model for computing tree and loop amplitudes of certain non-SUSY theories in various self-dual backgrounds.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-101124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-10.11.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241015T161500
DTEND;TZID=America/New_York:20241015T181500
DTSTAMP:20260524T182732
CREATED:20240917T162135Z
LAST-MODIFIED:20240927T182405Z
UID:10003514-1729008900-1729016100@cmsa.fas.harvard.edu
SUMMARY:Topological Modular Forms\, its equivariant refinements and relation with supersymmetric quantum field theories
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeaker: Mayuko Yamashita\, Kyoto University \nTitle: Topological Modular Forms\, its equivariant refinements and relation with supersymmetric quantum field theories \nAbstract: This talk is about the Segal-Stolz-Teichner program\, which is one of the most deep and interesting topics relating homotopy theory and physics. Mathematically\, they propose a geometric model of TMF\, the spectrum (in homotopy theory) of Topological Modular Forms\, in terms of supersymmetric quantum field theories. Their proposal\, although far from solid formulation or a proof\, has been a guiding principle leading us to many new interesting ideas and discoveries in both mathematics and physics. In this talk\, I will give an overview of this topic\, as well as my current works using equivariant twisted TMF.
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_101524/
LOCATION:Science Center Hall E\, 1 Oxford Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Geometry and Quantum Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Geometry-Quantum-Theory-10.15.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241016T120000
DTEND;TZID=America/New_York:20241016T130000
DTSTAMP:20260524T182732
CREATED:20241015T133229Z
LAST-MODIFIED:20241015T133655Z
UID:10003530-1729080000-1729083600@cmsa.fas.harvard.edu
SUMMARY:CMSA Q&A Seminar: Nazim Bouatta
DESCRIPTION:CMSA Q&A Seminar \nSpeaker: Nazim Bouatta (HMS) \nTopic: What are AlphaFold2 and OpenFold
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_101624/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:CMSA Q&A Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Q-A-Seminar-10.16.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241016T140000
DTEND;TZID=America/New_York:20241016T150000
DTSTAMP:20260524T182732
CREATED:20241010T152711Z
LAST-MODIFIED:20241108T192805Z
UID:10003612-1729087200-1729090800@cmsa.fas.harvard.edu
SUMMARY:From Word Prediction to Complex Skills: Data Flywheels for Mathematical Reasoning
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Anirudh Goyal (University of Montreal) \nTitle: From Word Prediction to Complex Skills: Data Flywheels for Mathematical Reasoning \nAbstract: This talk examines how large language models (LLMs) evolve from simple word prediction to complex skills\, with a focus on mathematical problem solving. A major driver of AI products today is the fact that new skills emerge in language models when their parameter set and training corpora are scaled up. This phenomenon is poorly understood\, and a mechanistic explanation via mathematical analysis of gradient-based training seems difficult. The first part of the talk focuses on analysing emergence using the famous (and empirical) Scaling Laws of LLMs. Then I talk about howc LLMs can verbalize these skills by assigning labels to problems and clustering them into interpretable categories. This metacognitive ability allows us to leverage skill-based prompting\, significantly improving performance on mathematical reasoning. I then present a framework that combines LLMs with human oversight to generate challenging\, out-of-distribution math questions. This process led to the creation of the MATH^2 dataset\, which enhances both model and human performance\, driving further advances in mathematical reasoning capabilities. \n 
URL:https://cmsa.fas.harvard.edu/event/newtech_101624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-10.16.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241018T090000
DTEND;TZID=America/New_York:20241018T100000
DTSTAMP:20260524T182732
CREATED:20240907T193958Z
LAST-MODIFIED:20241015T143755Z
UID:10003468-1729242000-1729245600@cmsa.fas.harvard.edu
SUMMARY:Bosonic and fermionic 1-form symmetries and anomaly matching
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \n*via Zoom only* \nSpeaker: Rajath Radhakrishnan (ICTP\, Trieste) \nTitle: Bosonic and fermionic 1-form symmetries and anomaly matching \nAbstract: In this talk\, I will consider bosonic and fermionic (non-invertible) 1-form symmetries in 2+1d QFTs. These are 1-form symmetries implemented by topological line operators with real spins. I will present a classification of topological quantum field theories in which all line operators have real topological spins\, and use this framework to classify the anomalies associated with these 1-form symmetries. Additionally\, I will discuss the anomaly matching condition for these symmetries under an RG flow. I will illustrate this condition in concrete examples.
URL:https://cmsa.fas.harvard.edu/event/qm_101824/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QFT-10.18.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241018T120000
DTEND;TZID=America/New_York:20241018T130000
DTSTAMP:20260524T182732
CREATED:20240919T144412Z
LAST-MODIFIED:20241015T180358Z
UID:10003521-1729252800-1729256400@cmsa.fas.harvard.edu
SUMMARY:Positive mass and rigidity theorems in Riemannian geometry  
DESCRIPTION:Member Seminar \nSpeaker: Puskar Mondal \nTitle: Positive mass and rigidity theorems in Riemannian geometry \nAbstract: Positive mass theorem proved by Schoen-Yau\, Witten\, Taubes-Parker is one of the most important results in scalar curvature geometry in asymptotically flat settings. Since then several versions have been proven and generalized to other geometries such as asymptotically hyperbolic manifolds. The analogous theorem for strictly positive curvature geometries is absent. There have been counterexamples but a precise quantification does not exist.I prove a scalar curvature rigidity theorem for spheres. In particular\, I prove that $n+1~(n\geq 2)$ dimensional spherical caps with constant positive mean curvature totally umbilic boundaries are rigid under smooth perturbations\, and such rigidity results fail for the hemisphere. The assertion of this result is based on the notion of a real Killing connection and solution of the boundary value problem associated with its Dirac operator. Additionally\, an improved eigenvalue estimate for the Dirac operator on hypersurfaces in positively curved manifolds is obtained.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-101824/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-10.18.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241021T093000
DTEND;TZID=America/New_York:20241021T103000
DTSTAMP:20260524T182732
CREATED:20240907T155707Z
LAST-MODIFIED:20241018T171738Z
UID:10003446-1729503000-1729506600@cmsa.fas.harvard.edu
SUMMARY:Foundation Seminar: Singularity Theorems\, Part I
DESCRIPTION:Foundation Seminar (Joint Seminar with BHI) \nLocation: BHI \nTitle: Singularity Theorems\, Part I \nJournal Club Discussion
URL:https://cmsa.fas.harvard.edu/event/foundation-seminar_102124/
LOCATION:Black Hole Initiative\, 20 Garden Street\, Cambridge MA\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Foundation Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/10.28.24_Singularity-Theorems-Part-II-4.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241021T163000
DTEND;TZID=America/New_York:20241021T173000
DTSTAMP:20260524T182732
CREATED:20240903T195022Z
LAST-MODIFIED:20241016T144838Z
UID:10003435-1729528200-1729531800@cmsa.fas.harvard.edu
SUMMARY:Higher Vapnik–Chervonenkis theory
DESCRIPTION:Colloquium \nSpeaker: Artem Chernikov\, University of Maryland \nTitle: Higher Vapnik–Chervonenkis theory \nAbstract: Finite VC-dimension\, a combinatorial property of families of sets\, was discovered simultaneously by Vapnik and Chervonenkis in probabilistic learning theory\, and by Shelah in model theory (where it is called NIP). It plays an important role in several areas including machine learning\, combinatorics\, mathematical logic\, functional analysis and topological dynamics. We develop aspects of higher-order VC-theory\, in particular establishing a generalization of the epsilon-net theorem for families of sets (and functions) on n-fold product spaces with bounded VC_n-dimension (i.e. there is a bound on the sizes of n-dimensional boxes that can be shattered). We obtain some applications in combinatorics and in model theory\, including a strong version of Szemerdi’s regularity lemma for hypergraphs omitting a fixed finite n-partite n-hypergraph. Joint work with Henry Towsner.
URL:https://cmsa.fas.harvard.edu/event/colloquium-102124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.21.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241022T161500
DTEND;TZID=America/New_York:20241022T181500
DTSTAMP:20260524T182732
CREATED:20240917T160638Z
LAST-MODIFIED:20241007T195901Z
UID:10003510-1729613700-1729620900@cmsa.fas.harvard.edu
SUMMARY:Fusion 2-Categories and their Classification
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeaker: Thibault Décoppet\, Harvard University \nTitle: Fusion 2-Categories and their Classification \nAbstract: Categorifying the classical notion of fusion (1-)category\, fusion 2-categories were recently introduced. These objects have found many applications in Physics\, most notably to the classification of topological orders\, but also to the description of non-invertible symmetries in 2+1 dimensions. The first part of this talk will be devoted to reviewing the definition of a fusion 2-category and giving many examples. In the second half\, I will present a remarkable result concerning the Morita theory of fusion 2-categories and explain how it can be used to give a homotopy coherent classification of fusion 2-categories. \n 
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_102224/
LOCATION:Science Center Hall E\, 1 Oxford Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Geometry and Quantum Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Geometry-Quantum-Theory-10.22.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241023T120000
DTEND;TZID=America/New_York:20241023T130000
DTSTAMP:20260524T182732
CREATED:20241016T180943Z
LAST-MODIFIED:20241016T182816Z
UID:10003531-1729684800-1729688400@cmsa.fas.harvard.edu
SUMMARY:CMSA Q&A Seminar: Dan Freed
DESCRIPTION:CMSA Q&A Seminar \nSpeaker: Dan Freed\, Harvard Mathematics & CMSA \nTopic: What are topological phases of matter?
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_102324/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:CMSA Q&A Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Q-A-Seminar-10.23.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241023T140000
DTEND;TZID=America/New_York:20241023T150000
DTSTAMP:20260524T182732
CREATED:20241021T140701Z
LAST-MODIFIED:20241108T192710Z
UID:10003616-1729692000-1729695600@cmsa.fas.harvard.edu
SUMMARY:How Far Can Transformers Reason? The Globality Barrier and Inductive Scratchpad
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Aryo Lotfi (EPFL) \nTitle: How Far Can Transformers Reason? The Globality Barrier and Inductive Scratchpad \nAbstract: Can Transformers predict new syllogisms by composing established ones? More generally\, what type of targets can be learned by such models from scratch? Recent works show that Transformers can be Turing-complete in terms of expressivity\, but this does not address the learnability objective. This paper puts forward the notion of ‘globality degree’ of a target distribution to capture when weak learning is efficiently achievable by regular Transformers\, where the latter measures the least number of tokens required in addition to the tokens histogram to correlate nontrivially with the target. As shown experimentally and theoretically under additional assumptions\, distributions with high globality cannot be learned efficiently. In particular\, syllogisms cannot be composed on long chains. Furthermore\, we show that (i) an agnostic scratchpad cannot help to break the globality barrier\, (ii) an educated scratchpad can help if it breaks the globality at each step\, however not all such scratchpads can generalize to out-of-distribution (OOD) samples\, (iii) a notion of ‘inductive scratchpad’\, that composes the prior information more efficiently\, can both break the globality barrier and improve the OOD generalization. In particular\, some inductive scratchpads can achieve length generalizations of up to 6x for some arithmetic tasks depending on the input formatting.
URL:https://cmsa.fas.harvard.edu/event/newtech_102324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=application/pdf:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-10.23.24.docx-1-1.pdf
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241025T090000
DTEND;TZID=America/New_York:20241025T103000
DTSTAMP:20260524T182732
CREATED:20240907T194046Z
LAST-MODIFIED:20241018T221702Z
UID:10003469-1729846800-1729852200@cmsa.fas.harvard.edu
SUMMARY:The spin-statistics theorem for TFTs
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \nSpeaker: Luuk Stehouwer\, Dalhousie University \nTitle: The spin-statistics theorem for TFTs \nAbstract: In quantum field theory (QFT) the spin-statistics theorem says that in a unitary QFT\, a particle has half-integer spin if and only if it is a fermion. I show how to phrase this statement in the language of functorial field theories. More precisely\, I explain when a functorial field theory “has fermions” and “has spinors” and when they are “related”. I will then restrict to topological field theories (TFTs) and define unitary TFTs. There are counterexamples of the spin-statistics theorem for non-unitary TFTs. I will prove that every unitary TFT satisfies the spin-statistics theorem. \n  \n  \n 
URL:https://cmsa.fas.harvard.edu/event/qm_102524/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QFT-and-Physical-Mathematics-10.25.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241025T120000
DTEND;TZID=America/New_York:20241025T130000
DTSTAMP:20260524T182732
CREATED:20240919T144515Z
LAST-MODIFIED:20241022T155009Z
UID:10003522-1729857600-1729861200@cmsa.fas.harvard.edu
SUMMARY:Formality Theorem and Webs
DESCRIPTION:Member Seminar \nSpeaker: Ahsan Khan \nTitle: Formality Theorem and Webs \nAbstract: The “formality theorem” of Kontsevich was a key result that implies that every Poisson manifold admits a deformation quantization. I will review the ideas behind the formality theorem and discuss a potentially novel viewpoint on it involving webs and twisted masses.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-102524/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=application/pdf:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-10.25.24.docx.pdf
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241025T143000
DTEND;TZID=America/New_York:20241025T173000
DTSTAMP:20260524T182732
CREATED:20240907T191539Z
LAST-MODIFIED:20241010T152044Z
UID:10003466-1729866600-1729877400@cmsa.fas.harvard.edu
SUMMARY:Freedman CMSA Seminar
DESCRIPTION:Freedman CMSA Seminar \n*Note: via Zoom only* \n2:00-3:30 pm ET \nSpeaker: Matt Hastings\, Microsoft Quantum Program \nTitle: Invertible Phases of Matter and Quantum Cellular Automata: Dimensions One to Three \nAbstract: A Quantum Cellular Automaton (QCA) is a *-automorphism of the algebra of local operators. While local quantum circuits provide one example of QCA\, we are most interested in nontrivial QCA which are those which cannot be written as conjugation by a local quantum circuit. For systems in one and two spatial dimensions\, all nontrivial QCA are shifts (i.e.\, translations by some amount)\, up to conjugation by a quantum circuit\, but in three and higher dimensions\, other examples are known. I’ll explain the relation between QCA and a certain “boundary algebra” of operators in one lower spatial dimension\, and also the relation to invertible phases of matter on the boundary\, and use this to explain and motivate some of these results in dimensions one through three. \n  \n3:30-4:00 pm ET \nBreak/Discussion \n  \n4:00-5:30 pm ET \nSpeaker: Lukasz Fidkowski\, U Washington\, Physics \nTitle: Invertible Phases of Matter and Quantum Cellular Automata: Higher dimensions \nAbstract: We discuss the explicit construction of a non-trivial QCA in 3 dimensions\, one which takes the form of multiplication by a discrete Chern-Simons functional in an appropriate basis for the Hilbert space. We relate the non-trivialness of the QCA to the fact that the Chern-Simons action is not the integral of a gauge invariant local quantity. One property of this QCA is that it creates a specific non-trivial time reversal symmetry protected topological (SPT) phase when acting on a non-trivial tensor product state. Motivated by this\, we construct a general class of QCA in arbitrary dimensions based on time reversal protected SPTs\, and conjecture a general correspondence between unoriented cobordism (which classifies such SPTs) and QCA. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/freedman_102524/
LOCATION:Virtual
CATEGORIES:Freedman Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Freedman-Seminar-10.25.2024.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241028T093000
DTEND;TZID=America/New_York:20241028T103000
DTSTAMP:20260524T182732
CREATED:20240918T132207Z
LAST-MODIFIED:20241018T172052Z
UID:10003518-1730107800-1730111400@cmsa.fas.harvard.edu
SUMMARY:Foundation Seminar: Singularity Theorems\, Part II
DESCRIPTION:Foundation Seminar (Joint Seminar with BHI) \nLocation: BHI \nTitle: Singularity Theorems\, Part II \nJournal Club Discussion
URL:https://cmsa.fas.harvard.edu/event/foundation-seminar_102824/
LOCATION:20 Garden Street\, Cambridge\, MA 02138\, MA\, MA\, 02138\, United States
CATEGORIES:Foundation Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241029T161500
DTEND;TZID=America/New_York:20241029T181500
DTSTAMP:20260524T182732
CREATED:20240917T160658Z
LAST-MODIFIED:20241015T150203Z
UID:10003511-1730218500-1730225700@cmsa.fas.harvard.edu
SUMMARY:Boundaries and duality for 3d gauge theories
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeaker: Ben Gammage\, Harvard University \nTitle: Boundaries and duality for 3d gauge theories \nAbstract: 3d N=4 supersymmetric gauge theory has a pair of topological twists\, the A-model and B-model\, the latter of which is also known as Rozansky-Witten theory. Conjecturally\, boundary conditions for these TFTs ought to admit descriptions in terms of (microlocal) perverse or coherent sheaves of categories\, respectively. Unfortunately\, neither of these admits a general mathematical definition; nevertheless\, in some cases these are well-defined 2-categories. We will survey these situations and the duality\, known as 3d mirror symmetry\, which relates the A- and B-models of different theories\, together with its relation to the relative Langlands duality of Ben-Zvi–Sakellaridis-Venkatesh.
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_102924/
LOCATION:Science Center Hall E\, 1 Oxford Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Geometry and Quantum Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Geometry-Quantum-Theory-10.29.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241030T120000
DTEND;TZID=America/New_York:20241030T130000
DTSTAMP:20260524T182732
CREATED:20241016T181110Z
LAST-MODIFIED:20241024T135640Z
UID:10003532-1730289600-1730293200@cmsa.fas.harvard.edu
SUMMARY:CMSA Q&A Seminar: Michael Freedman
DESCRIPTION:CMSA Q&A Seminar \nSpeaker: Michael Freedman\, Harvard CMSA \nTopic: Broad perspective on manifolds: all dimensions\, all structures\, classification and dynamics
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_103024/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:CMSA Q&A Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Q-A-Seminar-10.30.2024.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241104T093000
DTEND;TZID=America/New_York:20241104T103000
DTSTAMP:20260524T182732
CREATED:20240918T132254Z
LAST-MODIFIED:20241104T150620Z
UID:10003519-1730712600-1730716200@cmsa.fas.harvard.edu
SUMMARY:Foundation Seminar
DESCRIPTION:Foundation Seminar (Joint Seminar with BHI) \nLocation: BHI\n\nSpeaker: Christoph Kehle (MIT)\n\nTitle: On the cosmic censorship conjectures\nAbstract: I will present the modern formulations of the weak and strong cosmic censorship conjectures and discuss some recent developments in the context of gravitational collapse.
URL:https://cmsa.fas.harvard.edu/event/foundation-seminar_11424/
LOCATION:Black Hole Initiative\, 20 Garden Street\, Cambridge MA\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Foundation Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241104T163000
DTEND;TZID=America/New_York:20241104T173000
DTSTAMP:20260524T182733
CREATED:20240903T195045Z
LAST-MODIFIED:20241016T202352Z
UID:10003436-1730737800-1730741400@cmsa.fas.harvard.edu
SUMMARY:The mathematics of evolution
DESCRIPTION:Colloquium \nSpeaker: Martin Nowak (Harvard) \nTitle: The mathematics of evolution \nAbstract: All living systems are guided by evolutionary dynamics. Evolution is a search process which occurs in populations of reproducing individuals. The three fundamental forces of evolution are mutation\, selection and cooperation. I will present basic ideas in the mathematical description of evolutionary dynamics\, including quasi-species theory\, evolutionary game theory\, and evolutionary graph theory. I will discuss specific problems such as origin of life\, emergence of complexity\, mechanisms of cooperation\, evolution of cancer and how to overcome resistance to targeted therapy. \n 
URL:https://cmsa.fas.harvard.edu/event/colloquium-11424/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-11.4.2024.docx.png
END:VEVENT
END:VCALENDAR