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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240920T103000
DTEND;TZID=America/New_York:20240920T120000
DTSTAMP:20260503T230724
CREATED:20240912T144302Z
LAST-MODIFIED:20240912T144302Z
UID:10003498-1726828200-1726833600@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_92024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240920T120000
DTEND;TZID=America/New_York:20240920T130000
DTSTAMP:20260503T230724
CREATED:20240907T183145Z
LAST-MODIFIED:20240916T164559Z
UID:10003462-1726833600-1726837200@cmsa.fas.harvard.edu
SUMMARY:Communication Complexity of Combinatorial Auctions
DESCRIPTION:Member Seminar \nSpeaker: Tomer Ezra (CMSA) \nTitle: Communication Complexity of Combinatorial Auctions \nAbstract: We study the communication complexity of welfare maximization in combinatorial auctions with m items and two subadditive bidders. A 2-approximation can be guaranteed by a trivial randomized protocol with zero communication\, or a trivial deterministic protocol with O(1) communication. We show that outperforming these trivial protocols requires exponential communication\, settling an open question of [DobzinskiNS10\, Feige09]. \nSpecifically\, we show that any (randomized) protocol guaranteeing a o(logm)-approximation requires communication exponential in m. We complement it by presenting an O(logm)-approximation in poly(m) communication.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-92024/
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-09.20.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240920T140000
DTEND;TZID=America/New_York:20240920T153000
DTSTAMP:20260503T230724
CREATED:20240907T191849Z
LAST-MODIFIED:20240918T134041Z
UID:10003467-1726840800-1726846200@cmsa.fas.harvard.edu
SUMMARY:Classification and Construction of crystalline topological superconductors and insulators in interacting fermion systems
DESCRIPTION:Quantum Matter Seminar \nSpeaker: Zhengcheng Gu\, Chinese University of Hong Kong \nTitle: Classification and construction of crystalline topological superconductors and insulators in interacting fermion systems \nAbstract: The construction and classification of crystalline symmetry protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Crystalline SPT phases are not only of conceptual importance\, but also provide us great opportunities towards experimental realization since space group symmetries naturally exist for any realistic material. In this talk\, I will discuss how to construct and classify crystalline topological superconductors (TSC) and topological insulators (TI) in interacting fermion systems. I will also discuss the relationship between internal symmetry protected SPT phases and crystalline symmetry protected SPT Phases.
URL:https://cmsa.fas.harvard.edu/event/qm_92024/
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-QMMP-09.20.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240923T103000
DTEND;TZID=America/New_York:20240923T120000
DTSTAMP:20260503T230724
CREATED:20240911T153551Z
LAST-MODIFIED:20240912T154245Z
UID:10003478-1727087400-1727092800@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_92324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240923T163000
DTEND;TZID=America/New_York:20240923T173000
DTSTAMP:20260503T230724
CREATED:20240903T194207Z
LAST-MODIFIED:20240918T190927Z
UID:10003431-1727109000-1727112600@cmsa.fas.harvard.edu
SUMMARY:Symmetry groups in infinite dimensions
DESCRIPTION:Colloquium \nSpeaker: Lisa Carbone\, Rutgers University \nTitle: Symmetry groups in infinite dimensions \nAbstract: The study of many physical theories requires an understanding of symmetries of infinite dimensional Lie algebras. The construction of groups of automorphisms for infinite dimensional Lie algebras is challenging\, but there is well established theory for the class of Kac-Moody algebras. A generalization of Kac-Moody algebras known as Borcherds algebras arise in string theory models\, but the methods for constructing Kac-Moody groups break down for this more general class. We discuss the challenges that arise and describe several approaches to constructing groups for Borcherds algebras. Our main example is the Monster Lie algebra which plays an important role in the solution of Monstrous Moonshine and which is a symmetry algebra of a model of the compactified Heterotic String.
URL:https://cmsa.fas.harvard.edu/event/colloquium-92324/
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-09.23.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240924T110000
DTEND;TZID=America/New_York:20240924T120000
DTSTAMP:20260503T230724
CREATED:20240903T181518Z
LAST-MODIFIED:20240917T155135Z
UID:10003421-1727175600-1727179200@cmsa.fas.harvard.edu
SUMMARY:New Energy Inequality in AdS
DESCRIPTION:General Relativity Seminar \nSpeaker: Diandian Wang\, Harvard University \nTitle: New Energy Inequality in AdS \nAbstract: I will describe evidence for a new energy inequality in asymptotically AdS spacetimes whose conformal boundary contains a spatial circle. It is in some sense analogous but crucially different to the Penrose inequality. In the AdS4 case\, this generalizes the Horowitz-Myers conjecture. I will show how static solutions play an interesting role in determining the shape of the function that bounds the gravitational energy.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-92417/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-09.24.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240924T143000
DTEND;TZID=America/New_York:20240924T154500
DTSTAMP:20260503T230724
CREATED:20240907T181436Z
LAST-MODIFIED:20240907T181436Z
UID:10003457-1727188200-1727192700@cmsa.fas.harvard.edu
SUMMARY:Topics in Deep Learning Theory
DESCRIPTION:Topics in Deep Learning Theory \nEli Grigsby
URL:https://cmsa.fas.harvard.edu/event/deeplearning_92424/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Topics in Deep Learning Theory
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240924T160000
DTEND;TZID=America/New_York:20240924T170000
DTSTAMP:20260503T230724
CREATED:20240911T201722Z
LAST-MODIFIED:20240911T201722Z
UID:10003485-1727193600-1727197200@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Open Discussion/Tea
DESCRIPTION:Open Discussion/Tea
URL:https://cmsa.fas.harvard.edu/event/mml_tea_92424/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240924T161500
DTEND;TZID=America/New_York:20240924T181500
DTSTAMP:20260503T230724
CREATED:20240907T180814Z
LAST-MODIFIED:20240924T145311Z
UID:10003455-1727194500-1727201700@cmsa.fas.harvard.edu
SUMMARY:Symplectic duality in examples
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeaker: Vasily Krylov\, Harvard CMSA & Math \nTitle: Symplectic duality in examples \nAbstract: Over the past twenty years\, mathematicians and physicists have shown increasing interest in studying certain Poisson varieties\, known as “symplectic singularities.” Many of these objects naturally arise as Higgs or Coulomb branches of certain TQFTs and\, therefore\, fall within the framework of 3D mirror symmetry\, also known as symplectic duality. The first part of the talk will provide a gentle introduction to the theory of symplectic singularities\, with an emphasis on various examples. In the second part\, we will discuss how the symplectic duality works in examples\, beginning with the simplest cases. We will then discuss a particular phenomenon called the Hikita-Nakajima conjecture\, which predicts a deep and nontrivial relationship between dual varieties. It is particularly intriguing that this conjecture was formulated by mathematicians and still requires further understanding from a physical perspective.
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_92424/
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-09.24.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240925T103000
DTEND;TZID=America/New_York:20240925T120000
DTSTAMP:20260503T230724
CREATED:20240911T204040Z
LAST-MODIFIED:20240911T204040Z
UID:10003491-1727260200-1727265600@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_92524/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240925T140000
DTEND;TZID=America/New_York:20240925T150000
DTSTAMP:20260503T230724
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:20240926T100000
DTEND;TZID=America/New_York:20240926T110000
DTSTAMP:20260503T230724
CREATED:20240917T135417Z
LAST-MODIFIED:20240920T143613Z
UID:10003508-1727344800-1727348400@cmsa.fas.harvard.edu
SUMMARY:Witten deformation for non-Morse functions and gluing formulas 
DESCRIPTION:Mathematical Physics and Algebraic Geometry \nSpeaker: Junrong Yan (Northeastern University) \nTitle: Witten deformation for non-Morse functions and gluing formulas \nAbstract: Witten deformation is a versatile tool with numerous applications in mathematical physics and geometry. In this talk\, we will focus on the analysis of Witten deformation for a family of non-Morse functions\, which leads to a new technique for studying the gluing formulas of global spectral invariants (such as eta invariants\, analytic torsions\, and some invariants related to Feynman diagrams\, etc.). We will then discuss some applications of this new method. \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_92624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-09.26.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240926T143000
DTEND;TZID=America/New_York:20240926T154500
DTSTAMP:20260503T230724
CREATED:20240907T181953Z
LAST-MODIFIED:20240907T182537Z
UID:10003460-1727361000-1727365500@cmsa.fas.harvard.edu
SUMMARY:Topics in Deep Learning Theory
DESCRIPTION:Topics in Deep Learning Theory \nEli Grigsby
URL:https://cmsa.fas.harvard.edu/event/deeplearning_92624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Topics in Deep Learning Theory
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240927T090000
DTEND;TZID=America/New_York:20240927T100000
DTSTAMP:20260503T230724
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:20240927T103000
DTEND;TZID=America/New_York:20240927T120000
DTSTAMP:20260503T230724
CREATED:20240912T144322Z
LAST-MODIFIED:20240912T144322Z
UID:10003499-1727433000-1727438400@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_92724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240930T103000
DTEND;TZID=America/New_York:20240930T120000
DTSTAMP:20260503T230724
CREATED:20240911T160033Z
LAST-MODIFIED:20240911T162524Z
UID:10003479-1727692200-1727697600@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_93024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240930T153000
DTEND;TZID=America/New_York:20240930T173000
DTSTAMP:20260503T230724
CREATED:20240912T152420Z
LAST-MODIFIED:20250328T150047Z
UID:10003504-1727710200-1727717400@cmsa.fas.harvard.edu
SUMMARY:Machine Learning in Science Education Panel Discussion
DESCRIPTION:Machine Learning in Science Education Panel Discussion\nMonday\, Sep. 30\, 2024\n3:30-5:30 pm ET \nMachine Learning is rapidly influencing many spheres of human activity. As part of the CMSA Mathematics and Machine Learning Program\, this panel discussion will explore current and future uses of Machine Learning in science education. Panelists will make brief presentations\, which will be followed by discussion and audience questions. \nGregory Kestin (Harvard University)\n AI-Supported Activities: Design Principles and Impact on Student Learning \nLogan McCarty (Harvard University)\nSurveying the Landscape: Teaching and Learning with AI \nAlexis Ross (Massachusetts Institute of Technology)\nAdaptive Teaching towards Misconceptions with LLMs \nIlia Sucholutsky (New York University)\n Why should machines have human-like  representations? Towards  student-centric AI tutors \n  \nOrganizers: \n\nDan Freed (Harvard University and CMSA)\nMichael Douglas (CMSA)
URL:https://cmsa.fas.harvard.edu/event/teachingmachinelearning_93024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,MML Meeting,Special Lectures
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/ML_9.30.24_Machine-Learning-in-Science-Education.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241001T110000
DTEND;TZID=America/New_York:20241001T120000
DTSTAMP:20260503T230724
CREATED:20240903T181544Z
LAST-MODIFIED:20240926T185818Z
UID:10003422-1727780400-1727784000@cmsa.fas.harvard.edu
SUMMARY:Quasinormal Corrections to Near-Extremal Black Hole Thermodynamics
DESCRIPTION:General Relativity Seminar \nSpeaker: Daniel Kapec\, Harvard \nTitle: Quasinormal Corrections to Near-Extremal Black Hole Thermodynamics \nAbstract: Recent work on the quantum mechanics of near-extremal non-supersymmetric black holes has identified a characteristic  scaling of the low temperature black hole partition function. This result has only been derived using the path integral in the near-horizon region and relies on many assumptions. We discuss how to derive the  scaling for the near-extremal rotating BTZ black hole from a calculation in the full black hole background using the Denef-Hartnoll-Sachdev (DHS) formula\, which expresses the 1-loop determinant of a thermal geometry in terms of a product over the quasinormal mode spectrum. We also derive the spectral measure for fields of any spin in Euclidean BTZ and use it to provide a new proof of the DHS formula and a new\, direct derivation of the BTZ heat kernel. The computations suggest a path to proving the  scaling for the asymptotically flat 4d Kerr black hole.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-10124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-10.1.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241001T143000
DTEND;TZID=America/New_York:20241001T154500
DTSTAMP:20260503T230724
CREATED:20240907T181510Z
LAST-MODIFIED:20240907T181538Z
UID:10003458-1727793000-1727797500@cmsa.fas.harvard.edu
SUMMARY:Topics in Deep Learning Theory
DESCRIPTION:Topics in Deep Learning Theory \nEli Grigsby
URL:https://cmsa.fas.harvard.edu/event/deeplearning_10124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Topics in Deep Learning Theory
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241001T160000
DTEND;TZID=America/New_York:20241001T170000
DTSTAMP:20260503T230724
CREATED:20240911T201749Z
LAST-MODIFIED:20240911T201749Z
UID:10003486-1727798400-1727802000@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Open Discussion/Tea
DESCRIPTION:Open Discussion/Tea
URL:https://cmsa.fas.harvard.edu/event/mml_tea_10124/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241001T161500
DTEND;TZID=America/New_York:20241001T181500
DTSTAMP:20260503T230724
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:20241002T103000
DTEND;TZID=America/New_York:20241002T120000
DTSTAMP:20260503T230724
CREATED:20240911T205114Z
LAST-MODIFIED:20240911T205114Z
UID:10003492-1727865000-1727870400@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_10224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241002T120000
DTEND;TZID=America/New_York:20241002T130000
DTSTAMP:20260503T230724
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:Massachusetts
CATEGORIES:CMSA Q&A Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241002T140000
DTEND;TZID=America/New_York:20241002T150000
DTSTAMP:20260503T230724
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:20241003T100000
DTEND;TZID=America/New_York:20241003T110000
DTSTAMP:20260503T230724
CREATED:20240927T144416Z
LAST-MODIFIED:20240927T183006Z
UID:10003592-1727949600-1727953200@cmsa.fas.harvard.edu
SUMMARY:Enumerative geometry and modularity in two-modulus K3-fibered Calabi-Yau threefolds
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Chuck Doran\, Harvard CMSA \nTitle: Enumerative geometry and modularity in two-modulus K3-fibered Calabi-Yau threefolds \nAbstract: Smooth $M_m$-polarized K3-fibered Calabi-Yau (CY) 3-folds have been classified in terms of the choice of a generalized functional invariant and\, in the case $m=1$\, a generalized homological invariant. The resulting geometries generally exhibit a small number of complex structure moduli greater or equal to two. A concrete choice of these invariants realizes (almost all of) the known Calabi-Yau geometries with exactly two moduli and allows us to describe completely the structure of the corresponding moduli spaces. The corresponding variations of Hodge structure are entirely determined by the regular periods\, for which we obtain a generic expression in terms of $m$ and three integers $i\,j\,s$. Using the form of this period and Batyrev-Borisov mirror symmetry we explicitly construct the corresponding mirror CY 3-folds with two Kaehler moduli and show consistency with the DHT conjecture. In the cases with $s=0$\, the mirror CY 3-folds are again K3-fibered but with the mirror $<2m>$-polarization. The generic form of the periods allows us to derive generic modular expressions for the A-model topological string free energies and we argue that those are a consequence of a Tyurin degeneration of the generalized functional invariant with the central fiber being an $M_m$-polarized K3. This is joint work with Boris Pioline and Thorsten Schimannek.
URL:https://cmsa.fas.harvard.edu/event/mathphys_10324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-10.3.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241004T090000
DTEND;TZID=America/New_York:20241004T103000
DTSTAMP:20260503T230724
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:20241004T103000
DTEND;TZID=America/New_York:20241004T120000
DTSTAMP:20260503T230724
CREATED:20240912T145639Z
LAST-MODIFIED:20240912T145639Z
UID:10003502-1728037800-1728043200@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_10424/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241004T120000
DTEND;TZID=America/New_York:20241004T130000
DTSTAMP:20260503T230724
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:20241007T103000
DTEND;TZID=America/New_York:20241007T120000
DTSTAMP:20260503T230724
CREATED:20240911T195632Z
LAST-MODIFIED:20240911T195632Z
UID:10003480-1728297000-1728302400@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_10724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241007T163000
DTEND;TZID=America/New_York:20241007T173000
DTSTAMP:20260503T230724
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
END:VCALENDAR