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DTSTART;TZID=America/New_York:20240903T090000
DTEND;TZID=America/New_York:20241101T170000
DTSTAMP:20260430T192658
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UID:10001112-1725354000-1730480400@cmsa.fas.harvard.edu
SUMMARY:Mathematics and Machine Learning Program
DESCRIPTION:Mathematics and Machine Learning Program \nDates: September 3 – November 1\, 2024 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge\, MA 0213 \nMachine learning and AI are increasingly important tools in all fields of research. Recent milestones in machine learning for mathematics include data-driven discovery of theorems in knot theory and representation theory\, the discovery and proof of new singular solutions of the Euler equations\, new counterexamples and lower bounds in graph theory\, and more. Rigorous numerical methods and interactive theorem proving are playing an important part in obtaining these results. Conversely\, much of the spectacular progress in AI has a surprising simplicity at its core. Surely there are remarkable mathematical structures behind this\, yet to be elucidated. \nThe program will begin and end with two week-long workshops\, and will feature focus weeks on number theory\, knot theory\, graph theory\, rigorous numerics in PDE\, and interactive theorem proving\, as well as a course on geometric aspects of deep learning.\n\n  \nSeptember 3–5\, 2024: Opening Workshop: AI for Mathematicians\, with Leon Bottou\, François Charton\, David McAllester\, Adam Wagner and Geordie Williamson.   A series of six lectures covering logic and theorem proving\, AI methods\, theory of machine learning\, two lectures on case studies in math-AI\, and a lecture and discussion on open problems and the ethics of AI in science.\nOpening Workshop Youtube Playlist \n\nSeptember 6–7\, 2024: Big Data Conference \n  \nSeptember 9–13\, 2024: Applying Machine Learning to Math\, with François Charton and Geordie Williamson\nPublic Lecture September 12\, 2024: Geordie Williamson\, University of Sydney: Can AI help with hard mathematics? (Youtube link)\nThe focus of this week will be on practical examples and techniques for the mathematics researcher keen to explore or deepen their use of AI techniques. We will have talks showcasing easily stated problems\, on which machine learning techniques can be employed profitably. These provide excellent toy examples for generating intuition. We will also have expert talks on some of the technical subtleties which arise. There are several instances where the accepted heuristics emerging from the study of large language models (LLM) and image recognition don’t appear to apply on mathematics problems\, and we will try to highlight these subtleties.\nApplying Machine Learning to Math Youtube Playlist \n  \nSeptember 16–20\, 2024: Number theory\, with Drew Sutherland\nThe focus of this week will be on the use of ML as a tool for finding and understanding statistical patterns in number-theoretic datasets\, using the recently discovered (and still largely unexplained) “murmurations” in the distribution of Frobenius traces in families of elliptic curves and other arithmetic L-functions as a motivating example.\nNumber Theory Youtube Playlist \n  \nSeptember 23–27\, 2024: Knot theory\, with Sergei Gukov\nKnot theory is a great source of labeled data that can be synthetically generated. Moreover\, many outstanding problems in knot theory and low-dimensional topology can be formulated as decision and classification tasks\, e.g. “Is the knot 123_45 slice?” or “Can two given Kirby diagrams be related by a sequence of Kirby moves?” During this focus week we will explore various ways in which AI can be applied to problems in knot theory and how\, based on these applications\, mathematical reasoning can advance development of AI algorithms. Another goal will be to develop formal knot theory libraries (e.g. contributions to mathlib) and to apply AI models to formal proof systems\, in particular in the context of knot theory.\nKnot Theory Youtube Playlist \n  \nSeptember 30: Teaching and Machine Learning Panel Discussion\, 3:30-5:30 pm ET \n  \nSeptember 30–October 4\, 2024: Graph theory and combinatorics\, with Adam Wagner\nThis week\, we will consider how machine learning can help us solve problems in combinatorics and graph theory\, broadly interpreted\, in practice. The advantage of these fields is that they deal with finite objects that are simple to set up using computers\, and programs that work for one problem can often be adapted to work for several other related problems as well. Many times\, the best constructions for a problem are easy to interpret\, making it simpler to judge how well a particular algorithm is performing. On the other hand\, there are lots of open conjectures that are simple to state\, for which the best-known constructions are counterintuitive\, making it perhaps more likely that machine learning methods can spot patterns that are difficult to understand otherwise.\nGraph Theory and Combinatorics Youtube Playlist \n  \nOctober 7–11\, 2024: More number theory\, with Drew Sutherland\nThe focus of this week will be on the use of AI as a tool to search for and/or construct interesting or extremal examples in number theory and arithmetic geometry\, using LLM-based genetic algorithms\, generative adversarial networks\, game-theoretic methods\, and heuristic tree pruning as alternatives to conventional local search strategies.\nMore Number Theory Youtube Playlist \n  \nOctober 14 –18\, 2024: Interactive theorem proving\nThis week we will discuss the use of interactive theorem proving systems such as Lean\, Coq and Isabelle in mathematical research\, and AI systems which prove theorems and translate between informal and formal mathematics.\nInteractive Theorem Proving Youtube Playlist \n  \nOctober 21–25\, 2024: Numerical Partial Differential Equations (PDE)\, with Tristan Buckmaster and Javier Gomez-Serrano\nThe focus of this week will be on constructing solutions to partial differential equations and dynamical systems (finite and infinite dimensional) more broadly defined. We will discuss several toy problems and comment on issues like sampling strategies\, optimization algorithms\, ill-posedness\, or convergence. We will also outline strategies about further developing machine-learning findings and turn them into mathematical theorems via computer-assisted approaches.\nNumerical PDEs Youtube Playlist \n  \nOctober 28–Nov. 1\, 2024: Closing Workshop: The closing workshop will provide a forum for discussing the most current research in these areas\, including work in progress and recent results from program participants.\nMath and Machine Learning Closing Workshop Youtube Playlist \n  \nSeptember 3–Nov. 1: Graduate topics in deep learning theory (Boston College) taught by Eli Grigsby\, held at the CMSA Tuesdays and Thursdays 2:30–3:45 pm Eastern Time. Course website (link).\nGraduate Topics in Deep Learning Youtube Playlist \nCourse description: This is a course on geometric aspects of deep learning theory. Broadly speaking\, we’ll investigate the question: How might human-interpretable concepts be expressed in the geometry of their data encodings\, and how does this geometry interact with the computational units and higher-level algebraic structures in various parameterized function classes\, especially neural network classes? During the portion of the course Sep. 3-Nov. 1\, the course will be presented as part of the Math and Machine Learning program at the CMSA in Cambridge. During that portion\, we will focus on the current state of research on mechanistic interpretability of transformers\, the architecture underlying large language models like Chat-GPT. \n\n\n\n\nPrerequisites: This course is targeted to graduate students and advanced undergraduates in mathematics and theoretical computer science. No prior background in machine learning or learning theory will be assumed\, but I will assume a degree of mathematical maturity (at the level of–say—the standard undergraduate math curriculum+ first-year graduate geometry/topology sequence)\n\n\n\n\n\nProgram Organizers \n\nFrancois Charton (Meta AI)\nMichael R. Douglas (Harvard CMSA)\nMichael Freedman (Harvard CMSA)\nFabian Ruehle (Northeastern)\nGeordie Williamson (Univ. of Sydney)\n\n\nProgram Schedule  \nMonday\n10:30–noon\nOpen Discussion\nRoom G10 \n12:00–1:30 pm\nGroup lunch\nCMSA Common Room \nTuesday\n2:30–3:45 pm\nTopics in deep learning theory\nRoom G10 \n4:00–5:00 pm\nOpen Discussion/Tea\nCMSA Common Room \nWednesday\n10:30 am–12:00 pm\nOpen Discussion\nRoom G10 \n2:00–3:00 pm\nNew Technologies in Mathematics Seminar\nRoom G10 \nThursday\n2:30–3:45 pm\nTopics in deep learning theory\nRoom G10 \nFriday\n10:30 am–12:00 pm\nOpen Discussion\nRoom G10 \n\nHarvard CMSA thanks Mistral AI for a generous donation of computing credit.
URL:https://cmsa.fas.harvard.edu/event/mml2024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Programs
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Machine-Learning-Program-poster-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240918T090000
DTEND;TZID=America/New_York:20240918T103000
DTSTAMP:20260430T192658
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:20240918T103000
DTEND;TZID=America/New_York:20240918T120000
DTSTAMP:20260430T192658
CREATED:20240910T135135Z
LAST-MODIFIED:20240911T203928Z
UID:10003476-1726655400-1726660800@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_91824/
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:20240918T120000
DTEND;TZID=America/New_York:20240918T130000
DTSTAMP:20260430T192658
CREATED:20240907T160427Z
LAST-MODIFIED:20240924T195406Z
UID:10003409-1726660800-1726664400@cmsa.fas.harvard.edu
SUMMARY:CMSA Q&A Seminar: Noam Elkies
DESCRIPTION:CMSA Q&A Seminar \nSpeaker: Noam Elkies\, Harvard Math \nTopic: How to show E8 and Leech lattices have optimal sphere packings?
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_91824/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:CMSA Q&A Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240919T100000
DTEND;TZID=America/New_York:20240919T110000
DTSTAMP:20260430T192658
CREATED:20240917T135258Z
LAST-MODIFIED:20240917T155533Z
UID:10003507-1726740000-1726743600@cmsa.fas.harvard.edu
SUMMARY:Feynman graph integrals from topological holomorphic theories 
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Minghao Wang (Boston University) \nTitle: Feynman graph integrals from topological holomorphic theories \nAbstract: Feynman graph integrals from topological theories were developed by M. Kontsevich\, S. Axelrod and I. M. Singer in 1990s. These integrals have many mathematical applications\, such as knot invariants\, operad theory and formality theorems. In this talk\, I will talk about Feynman graph integrals from topological-holomorphic theories. In particular\, I will prove the finiteness of Feynman graph integrals when spacetime is flat spaces and a vanishing result of graph integrals. Combining the vanishing result with Batalin-Vilkovisky(BV) formalism\, we can show the absence of anomalies of topological-holomorphic theories on flat spaces with at least two topological dimensions. As a consequence\, we can construct factorization algebras of quantum observables. This is a joint with Brian Williams.
URL:https://cmsa.fas.harvard.edu/event/mathphys_91924/
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-09.19.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240919T143000
DTEND;TZID=America/New_York:20240919T154500
DTSTAMP:20260430T192658
CREATED:20240907T181700Z
LAST-MODIFIED:20240907T182411Z
UID:10003459-1726756200-1726760700@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_91924/
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:20240920T103000
DTEND;TZID=America/New_York:20240920T120000
DTSTAMP:20260430T192658
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:20260430T192658
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:20260430T192658
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:20260430T192658
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:20260430T192658
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:20260430T192658
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:20260430T192658
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:20260430T192659
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:20260430T192659
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:20260430T192659
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:20260430T192659
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:20260430T192659
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:20260430T192659
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:20260430T192659
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:20260430T192659
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:20260430T192659
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:20260430T192659
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:20260430T192659
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:20260430T192659
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:20260430T192659
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:20260430T192659
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:20260430T192659
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:20260430T192659
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/
CATEGORIES:CMSA Q&A Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241002T140000
DTEND;TZID=America/New_York:20241002T150000
DTSTAMP:20260430T192659
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
END:VCALENDAR