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DTSTART;TZID=America/New_York:20230403T110000
DTEND;TZID=America/New_York:20230403T120000
DTSTAMP:20240122T052041Z
CREATED:20230817T181822Z
LAST-MODIFIED:20240122T052041Z
UID:10001280-1680519600-1680523200@cmsa.fas.harvard.edu
SUMMARY:Black hole microstate counting from the gravitational path integral
DESCRIPTION:Colloquium \nSpeaker: Luca Iliesiu\, Stanford \nTitle: Black hole microstate counting from the gravitational path integral \nAbstract: Reproducing the integer count of black hole micro-states from the gravitational path integral is an important problem in quantum gravity. In the first part of the talk\, I will show that\, by using supersymmetric localization\, the gravitational path integral for 1/16-BPS black holes in supergravity can reproduce the index obtained in the string theory construction of such black holes. A more refined argument then shows that not only the black hole index but also the total number of black hole microstates within an energy window above extremality that is polynomially suppressed in the charges also matches this string theory index. In the second part of the talk\, I will present a second perspective on this state count and show how the BPS Hilbert space can be obtained by directly preparing states using the gravitational path integral. While such a preparation naively gives rise to a Hilbert space of BPS states whose dimension is much larger than expected\, I will explain how non-perturbative corrections in the overlap of such states are again responsible for reproducing the correct dimension of the Hilbert space.
URL:https://cmsa.fas.harvard.edu/event/colloquium-4323/
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-04.03.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230404T120000
DTEND;TZID=America/New_York:20230404T130000
DTSTAMP:20240228T092930Z
CREATED:20230817T171014Z
LAST-MODIFIED:20240228T092930Z
UID:10001240-1680609600-1680613200@cmsa.fas.harvard.edu
SUMMARY:Optimal Dynamic Allocation: Simplicity through Information Design
DESCRIPTION:Member Seminar \nSpeaker: Faidra Monachou \nTitle: Optimal Dynamic Allocation: Simplicity through Information Design \nAbstract: We study dynamic nonmonetary markets where objects are allocated to unit-demand agents with private types. An agent’s value for an object is supermodular in her type and the quality of the object\, and her payoff is quasilinear in her waiting cost. The social planner’s objective is a linear combination of allocative efficiency (i.e.\, the sum of values) and welfare (i.e.\, the sum of payoffs). We identify the optimal mechanism in the class of direct-revelation mechanisms that elicit agents’ types and assign them to objects over time. We show that\, when the social planner can design the information disclosed to the agents about the objects\, the optimal mechanism has a simple implementation: a first-come first-served waitlist with deferrals. In this implementation\, the information disclosed about each object is an interval containing the object quality\, rather than the exact quality. These intervals partition the quality space. We also show that when the planner’s objective weight on welfare increases\, these intervals become coarser\, and optimal disclosure policies less informative. A direct corollary is that mechanisms that achieve higher welfare also induce lower distributional inequality\, in terms of the Lorenz order.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-4423/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230411T120000
DTEND;TZID=America/New_York:20230411T130000
DTSTAMP:20240118T070619Z
CREATED:20230817T171211Z
LAST-MODIFIED:20240118T070619Z
UID:10001241-1681214400-1681218000@cmsa.fas.harvard.edu
SUMMARY:Spectral gap and two-point functions in spin glasses
DESCRIPTION:Member Seminar \nSpeaker: Changji Xu \nTitle: Spectral gap and two-point functions in spin glasses \nAbstract: Many have worked on spin glass models over the past 50 years\, including physicists\, mathematicians\, and computers. A question that arises is whether computers yield dependable simulation results. In this talk\, I will discuss some recent mathematical progress on spectral gap and two-point functions in spin glasses models.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-41123/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230412T123000
DTEND;TZID=America/New_York:20230412T133000
DTSTAMP:20240215T103145Z
CREATED:20230817T182227Z
LAST-MODIFIED:20240215T103145Z
UID:10001281-1681302600-1681306200@cmsa.fas.harvard.edu
SUMMARY:Unexpected Uses of Neural Networks: Field Theory and Metric Flows  
DESCRIPTION:Speaker: James Halverson (Northeastern University)\n \nTitle: Unexpected Uses of Neural Networks: Field Theory and Metric Flows\nAbstract:  We are now quite used to the idea that deep neural networks may be trained in a variety of ways to tackle cutting-edge problems in physics and mathematics\, sometimes leading to rigorous results. In this talk\, however\, I will argue that breakthroughs in deep learning theory are also useful for making progress\, focusing on applications to field theory and metric flows. Specifically\, I will introduce a neural network approach to field theory with a different statistical origin\, that exhibits generalized free field behavior at infinite width and interactions at finite width\, and that allows for the study of symmetries via the study of correlation functions in a different duality frame. Then\, I will review recent progress in approximating Calabi-Yau metrics as neural networks and cast that story into the language of neural tangent kernel theory\, yielding a theoretical understanding of neural network metric flows induced by gradient descent and recovering famous metric flows\, such as Perelman’s formulation of Ricci flow\, in particular limits.
URL:https://cmsa.fas.harvard.edu/event/colloquium12523/
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/02CMSA-Colloquium-04.12.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230418T120000
DTEND;TZID=America/New_York:20230418T130000
DTSTAMP:20240228T091907Z
CREATED:20230817T171352Z
LAST-MODIFIED:20240228T091907Z
UID:10001242-1681819200-1681822800@cmsa.fas.harvard.edu
SUMMARY:Recent progress on coupled Einstein-Yang-Mills dynamics
DESCRIPTION:Member Seminar \nSpeaker: Puskar Mondal \nTitle: Recent progress on coupled Einstein-Yang-Mills dynamics \nAbstract: I will discuss my recent work with prof. S.T. Yau on Einstein-Yang-Mills theory. I’ll discuss the main ideas behind the stability of the Minkowski and Milne space time under coupled gauge-gravity perturbations. Construction of the gauge invariant energies that control the suitable norms of the physical degrees of freedom in a double-null framework play an important role. I’ll sketch how the special structure of the Einstein and Yang-Mills nonlinearities play a crucial role in obtaining the stability result of non-expanding spacetimes in particular AF spacetimes.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-41823/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230420T133000
DTEND;TZID=America/New_York:20230420T143000
DTSTAMP:20240216T085423Z
CREATED:20230817T182708Z
LAST-MODIFIED:20240216T085423Z
UID:10001282-1681997400-1682001000@cmsa.fas.harvard.edu
SUMMARY:Black hole collider physics
DESCRIPTION:Speaker: Julio Parra Martinez\, Caltech \nTitle: Black hole collider physics \nAbstract: Despite more than a century since the development of Einstein’s theory\, the general relativistic two-body problem remains unsolved. A precise description of its solution is now essential\, as it is necessary for understanding the strong-gravity dynamics of compact binaries observed at LIGO/VIRGO/KAGRA and in future gravitational wave observatories. In this talk\, I will describe how considering the scattering of black holes and gravitons can shed new light on this problem. I will explain how using modern ideas from collider and particle physics we can calculate scattering observables in classical gravity\, and extract the basic ingredients that describe the bound binary dynamics. Such calculations have produced state-of-art predictions for current and future gravitational wave observatories\, which open the door for further discovery as we enter this new era of precision gravitational physics.
URL:https://cmsa.fas.harvard.edu/event/collquium-42023/
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-04.20.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230425T120000
DTEND;TZID=America/New_York:20230425T130000
DTSTAMP:20240118T071815Z
CREATED:20230817T171725Z
LAST-MODIFIED:20240118T071815Z
UID:10001243-1682424000-1682427600@cmsa.fas.harvard.edu
SUMMARY:On complete Calabi-Yau metrics and some related Monge-Ampere equations
DESCRIPTION:Member Seminar \nSpeaker: Freid Tong \nTitle: On complete Calabi-Yau metrics and some related Monge-Ampere equations \nAbstract: We will give a basic introduction to constructions for complete Calabi-Yau metrics. A systematic approach to construct such metrics using PDE methods was proposed in the work of Tian-Yau in the 90s and have attracted a lot of attention in recent years. I will discuss some joint work with B. Guo and T. Collins on a singular version of such a construction\, as well as some ongoing work with Prof. Yau on some related boundary value problems. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-42523/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230426T123000
DTEND;TZID=America/New_York:20230426T133000
DTSTAMP:20240122T053311Z
CREATED:20230817T183259Z
LAST-MODIFIED:20240122T053311Z
UID:10001283-1682512200-1682515800@cmsa.fas.harvard.edu
SUMMARY:Boundary behavior at classical and quantum phase transitions
DESCRIPTION:Speaker: Max Metlitski (MIT) \nTitle: Boundary behavior at classical and quantum phase transitions \nAbstract: There has been a lot of recent interest in the boundary behavior of materials. This interest is driven in part by the field of topological states of quantum matter\, where exotic protected boundary states are ubiquitous. In this talk\, I’ll ask: what happens at a boundary of a system\, when the bulk goes through a phase transition. While this question was studied in the context of classical statistical mechanics in the 70s and 80s\, basic aspects of the boundary phase diagram for the simplest classical phase transitions have been missed until recently. I’ll describe progress in this field\, as well as some extensions to quantum phase transitions. \n 
URL:https://cmsa.fas.harvard.edu/event/collquium-42623/
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-04.26.2023.rev2_.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230426T140000
DTEND;TZID=America/New_York:20230426T150000
DTSTAMP:20240209T151145Z
CREATED:20230809T103350Z
LAST-MODIFIED:20240209T151145Z
UID:10001224-1682517600-1682521200@cmsa.fas.harvard.edu
SUMMARY:Toolformer: Language Models Can Teach Themselves to Use Tools
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Timo Schick\, Meta AI \nTitle: Toolformer: Language Models Can Teach Themselves to Use Tools \nAbstract: Language models exhibit remarkable abilities to solve new tasks from just a few examples or textual instructions\, especially at scale. They also\, paradoxically\, struggle with basic functionality\, such as arithmetic or factual lookup\, where much simpler and smaller models excel. In this talk\, we show how these limitations can be overcome by letting language models teach themselves to use external tools via simple APIs. We discuss Toolformer\, a model trained to independently decide which APIs to call\, when to call them\, what arguments to pass\, and how to best incorporate the results into future token prediction. Through this\, it achieves substantially improved zero-shot performance across a variety of downstream tasks without sacrificing its core language modeling abilities. \n 
URL:https://cmsa.fas.harvard.edu/event/nt-42623/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-04.26.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230502T120000
DTEND;TZID=America/New_York:20230502T130000
DTSTAMP:20240118T085308Z
CREATED:20230817T171918Z
LAST-MODIFIED:20240118T085308Z
UID:10001244-1683028800-1683032400@cmsa.fas.harvard.edu
SUMMARY:Toroidal Positive Mass Theorem
DESCRIPTION:Member Seminar \nSpeaker: Aghil Alaee \nTitle: Toroidal Positive Mass Theorem \nAbstract: In this talk\, we review the positive mass conjecture in general relativity and prove a toroidal version of this conjecture in an asymptotically hyperbolic setting.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-5223/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230503T123000
DTEND;TZID=America/New_York:20230503T133000
DTSTAMP:20240216T085646Z
CREATED:20230817T183740Z
LAST-MODIFIED:20240216T085646Z
UID:10001284-1683117000-1683120600@cmsa.fas.harvard.edu
SUMMARY:Generative Adversarial Networks (GANs): An Analytical Perspective
DESCRIPTION:Speaker: Xin Guo\, UC Berkeley \nTitle: Generative Adversarial Networks (GANs): An Analytical Perspective \nAbstract: Generative models have attracted intense interests recently. In this talk\, I will discuss one class of generative models\, Generative Adversarial Networks (GANs).  I will first provide a gentle review of the mathematical framework behind GANs. I will then proceed to discuss a few challenges in GANs training from an analytical perspective. I will finally report some recent progress for GANs training in terms of its stability and convergence analysis. \n 
URL:https://cmsa.fas.harvard.edu/event/collquium-5323/
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-05.03.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230510T140000
DTEND;TZID=America/New_York:20230510T150000
DTSTAMP:20240228T104953Z
CREATED:20230809T105349Z
LAST-MODIFIED:20240228T104953Z
UID:10001225-1683727200-1683730800@cmsa.fas.harvard.edu
SUMMARY:Modern Hopfield Networks for Novel Transformer Architectures
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Dmitry Krotov\, IBM Research – Cambridge \nTitle: Modern Hopfield Networks for Novel Transformer Architectures \nAbstract: Modern Hopfield Networks or Dense Associative Memories are recurrent neural networks with fixed point attractor states that are described by an energy function. In contrast to conventional Hopfield Networks\, which were popular in the 1980s\, their modern versions have a very large memory storage capacity\, which makes them appealing tools for many problems in machine learning and cognitive and neurosciences. In this talk\, I will introduce an intuition and a mathematical formulation of this class of models and will give examples of problems in AI that can be tackled using these new ideas. Particularly\, I will introduce an architecture called Energy Transformer\, which replaces the conventional attention mechanism with a recurrent Dense Associative Memory model. I will explain the theoretical principles behind this architectural choice and show promising empirical results on challenging computer vision and graph network tasks.
URL:https://cmsa.fas.harvard.edu/event/nt-51023/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-05.10.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230515T120000
DTEND;TZID=America/New_York:20230515T130000
DTSTAMP:20240216T105142Z
CREATED:20230817T172120Z
LAST-MODIFIED:20240216T105142Z
UID:10001245-1684152000-1684155600@cmsa.fas.harvard.edu
SUMMARY:Quantum information and extended topological quantum field theory 
DESCRIPTION:Member Seminar \nSpeaker: Gabriel Wong \nTitle: Quantum information and extended topological quantum field theory \nAbstract: Recently\, ideas from quantum information theory have played an important role in condensed matter and quantum gravity research. Most of these applications focus on the entanglement structure of quantum states\, and the computation of entanglement measures such as entanglement entropy has been an essential part of the story. In this talk\, we will address some subtleties that arise when trying to define entanglement entropy in quantum field theory and quantum gravity. In particular\, we will explain why extended topological field theory provides a useful framework to define and compute entanglement entropy in a continuous system. Time permitting\, we will explain some recent applications of these ideas in low dimensional quantum gravity and to topological string theory. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-51523/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230915T120000
DTEND;TZID=America/New_York:20230915T130000
DTSTAMP:20240223T112851Z
CREATED:20240223T112851Z
LAST-MODIFIED:20240223T112851Z
UID:10002864-1694779200-1694782800@cmsa.fas.harvard.edu
SUMMARY:Quantum UV-IR map and curve counts in skeins
DESCRIPTION:Member Seminar \nSpeaker: Sunghyuk Park \nTitle: Quantum UV-IR map and curve counts in skeins \nAbstract: Quantum UV-IR map (a.k.a. q-nonabelianization map)\, introduced by Neitzke and Yan\, is a map from UV line defects in a 4d N=2 theory of class S to those of the IR. Mathematically\, it can be described as a map between skein modules and is a close cousin of quantum trace map of Bonahon and Wong. \nIn this talk\, I will discuss how quantum UV-IR map can be generalized to a map between HOMFLYPT skein modules\, using skein-valued curve counts of Ekholm and Shende.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-91523/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230919T123000
DTEND;TZID=America/New_York:20230919T133000
DTSTAMP:20240223T080443Z
CREATED:20240223T080443Z
LAST-MODIFIED:20240223T080443Z
UID:10002832-1695126600-1695130200@cmsa.fas.harvard.edu
SUMMARY:CMSA Q and A Seminar 9/19/2023
DESCRIPTION:Speakers: Dan Freed (Harvard Math and CMSA)\, Denis Auroux (Harvard Math)
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_91923/
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:20230920T140000
DTEND;TZID=America/New_York:20230920T150000
DTSTAMP:20240227T083355Z
CREATED:20240227T083355Z
LAST-MODIFIED:20240227T083355Z
UID:10002873-1695218400-1695222000@cmsa.fas.harvard.edu
SUMMARY:The TinyStories Dataset: How Small Can Language Models Be And Still Speak Coherent
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Ronen Eldan\, Microsoft Research \nTitle: The TinyStories Dataset: How Small Can Language Models Be And Still Speak Coherent \nAbstract: While generative language models exhibit powerful capabilities at large scale\, when either the model or the number of training steps is too small\, they struggle to produce coherent and fluent text: Existing models whose size is below a few billion parameters often do not generate coherent text beyond a few sentences. Hypothesizing that one of the main reasons for the strong reliance on size is the vast breadth and abundance of patterns in the datasets used to train those models\, this motivates the following question: Can we design a dataset that preserves the essential elements of natural language\, such as grammar\, vocabulary\, facts\, and reasoning\, but that is much smaller and more refined in terms of its breadth and diversity? \nIn this talk\, we introduce TinyStories\, a synthetic dataset of short stories that only contain words that 3 to 4-year-olds typically understand\, generated by GPT-3.5/4. We show that TinyStories can be used to train and analyze language models that are much smaller than the state-of-the-art models (below 10 million parameters)\, or have much simpler architectures (with only one transformer block)\, yet still produce fluent and consistent stories with several paragraphs that are diverse and have almost perfect grammar\, and demonstrate certain reasoning capabilities. We also show that the trained models are substantially more interpretable than larger ones\, as we can visualize and analyze the attention and activation patterns of the models\, and show how they relate to the generation process and the story content. We hope that TinyStories can facilitate the development\, analysis and research of language models\, especially for low-resource or specialized domains\, and shed light on the emergence of language capabilities in LMs. \n 
URL:https://cmsa.fas.harvard.edu/event/nt-92023/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-09.20.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230922T120000
DTEND;TZID=America/New_York:20230922T130000
DTSTAMP:20240223T112106Z
CREATED:20240223T112106Z
LAST-MODIFIED:20240223T112106Z
UID:10002861-1695384000-1695387600@cmsa.fas.harvard.edu
SUMMARY:Modularity of Landau-Ginzburg Models
DESCRIPTION:Member Seminar \nSpeaker: Chuck Doran \nTitle: Modularity of Landau-Ginzburg Models \nAbstract:  Fano varieties are the basic building blocks of algebraic varieties.  Smooth Fano varieties have been classified in dimensions one (the projective line)\, two (del Pezzo surfaces)\, and three (Mori-Mukai classification).  What does Mirror Symmetry have to say about such classifications?  By studying the Landau-Ginzburg models mirror to smooth Fano threefolds we can transform the Mori-Mukai classification into an effective uniruledness result for moduli spaces of certain K3 and abelian surfaces.  This is joint work with Andrew Harder\, Ludmil Katzarkov\, Mikhail Ovcharenko\, and Victor Przjalkowski (arXiv:2307.15607). \n  \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-92223/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230926T123000
DTEND;TZID=America/New_York:20230926T133000
DTSTAMP:20240223T081646Z
CREATED:20240223T081626Z
LAST-MODIFIED:20240223T081646Z
UID:10002835-1695731400-1695735000@cmsa.fas.harvard.edu
SUMMARY:CMSA Q and A Seminar 9/26/2023
DESCRIPTION:CMSA Q and A Seminar \nSpeakers: Michael Douglas (CMSA) and Mayuko Yamashita (Kyoto University) \nTopics: \nMichael Douglas: “What is non-commutative field theory?”\n\nMayuko Yamashita: “What is differential cohomology?”
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_92623/
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:20230927T140000
DTEND;TZID=America/New_York:20230927T150000
DTSTAMP:20240227T082824Z
CREATED:20240227T082824Z
LAST-MODIFIED:20240227T082824Z
UID:10002872-1695823200-1695826800@cmsa.fas.harvard.edu
SUMMARY:Transformers for maths\, and maths for transformers
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: François Charton\, Meta AI \nTitle:  Transformers for maths\, and maths for transformers \nAbstract: Transformers can be trained to solve problems of mathematics. I present two recent applications\, in mathematics and physics: predicting integer sequences\, and discovering the properties of scattering amplitudes in a close relative of Quantum ChromoDynamics. \nProblems of mathematics can also help understand transformers. Using two examples from linear algebra and integer arithmetic\, I show that model predictions can be explained\, that trained models do not confabulate\, and that carefully choosing the training distributions can help achieve better\, and more robust\, performance. \n  \n  \n 
URL:https://cmsa.fas.harvard.edu/event/nt-92723/
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-09.27.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230929T120000
DTEND;TZID=America/New_York:20230929T130000
DTSTAMP:20240223T112516Z
CREATED:20240223T112516Z
LAST-MODIFIED:20240223T112516Z
UID:10002863-1695988800-1695992400@cmsa.fas.harvard.edu
SUMMARY:Moduli of vector bundles on curve and semiorthogonal decomposition
DESCRIPTION:Member Seminar \nSpeaker: Kai Xu (CMSA) \nTitle: Moduli of vector bundles on curve and semiorthogonal decomposition \nAbstract: In this talk we construct semiorthogonal decompositions of moduli of vector bundles on a curve into its symmetric powers. The essential ingredients in the proof include Borel-Weil-Bott theory for loop groups\, derived Schur-Weyl duality for current groups and derived Θ-stratification. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-92923/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231002T163000
DTEND;TZID=America/New_York:20231002T173000
DTSTAMP:20240227T095159Z
CREATED:20240227T095159Z
LAST-MODIFIED:20240227T095159Z
UID:10002874-1696264200-1696267800@cmsa.fas.harvard.edu
SUMMARY:Gravitational Instantons
DESCRIPTION:Speaker: Yu-Shen Lin (Boston University) \nTitle: Gravitational Instantons \nAbstract: Gravitational instantons were introduced by Hawking as building blocks of his Euclidean quantum gravity theory back in the 1970s. These are non-compact Calabi-Yau surfaces with L2 curvature and thus can be viewed as the non-compact analogue of K3 surfaces. K3 surfaces are 2-dimensional Calabi-Yau manifolds and are usually the testing stone before conquering the general Calabi-Yau problems. The moduli space of K3 surfaces and its compactification on their own form important problems in various branches in geometry. In this talk\, we will discuss the Torelli theorem of gravitational instantons\, how the cohomological invariants of a gravitational instanton determine them. As a consequence\, this leads to a description of the moduli space of gravitational instantons.
URL:https://cmsa.fas.harvard.edu/event/colloquium-10223/
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-10.02.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231003T123000
DTEND;TZID=America/New_York:20231003T133000
DTSTAMP:20240223T082622Z
CREATED:20240223T082622Z
LAST-MODIFIED:20240223T082622Z
UID:10002836-1696336200-1696339800@cmsa.fas.harvard.edu
SUMMARY:CMSA Q and A Seminar 10/3/2023
DESCRIPTION:CMSA Q and A Seminar \nSpeakers: Dan Freed (Harvard Math & CMSA) and Dan Berwick-Evans (University of Illinois at Urbana-Champaign)\n\nTopics:\nDan Freed: What is framing anomaly? How is it different from other anomalies?\nDan Berwick-Evans: What is Atiyah-Singer index theorem?
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_10323/
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:20231006T120000
DTEND;TZID=America/New_York:20231006T130000
DTSTAMP:20240223T105621Z
CREATED:20240223T105546Z
LAST-MODIFIED:20240223T105621Z
UID:10002854-1696593600-1696597200@cmsa.fas.harvard.edu
SUMMARY:Random matrices and large deviations 
DESCRIPTION:Member Seminar \nSpeaker: Benjamin McKenna \nTitle: Random matrices and large deviations \nAbstract: We give a generalist overview of random matrices and their (a)typical behaviors. In recent years\, classical results have been complemented by a variety of new ones\, in both the math and physics literatures\, whose proofs leverage connections with special integrals over matrix groups. Some of these models exhibit interesting transition points\, whose motivating relationships to eigenvector (de)localization are not yet fully understood. Based on joint work with Jonathan Husson. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-10623/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231010T123000
DTEND;TZID=America/New_York:20231010T133000
DTSTAMP:20240223T103936Z
CREATED:20240223T091026Z
LAST-MODIFIED:20240223T103936Z
UID:10002842-1696941000-1696944600@cmsa.fas.harvard.edu
SUMMARY:CMSA Q and A Seminar 10/10/23
DESCRIPTION:CMSA Q and A Seminar \nSpeakers: Dan Freed (Harvard Math and CMSA) and Sunghyuk Park (CMSA) \nTopics: \nDan Freed: What is Dijkgraaf-Witten theory? \nSunghyuk Park: What happened at the Clay Math Institute Workshop?
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_101023/
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:20231011T140000
DTEND;TZID=America/New_York:20231011T150000
DTSTAMP:20240223T114336Z
CREATED:20240223T114336Z
LAST-MODIFIED:20240223T114336Z
UID:10002868-1697032800-1697036400@cmsa.fas.harvard.edu
SUMMARY:LeanDojo: Theorem Proving with Retrieval-Augmented Language Models
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Alex Gu\, MIT Dept. of EE&CS \nTitle: LeanDojo: Theorem Proving with Retrieval-Augmented Language Models \nAbstract: Large language models (LLMs) have shown promise in proving formal theorems using proof assistants such as Lean. However\, existing methods are difficult to reproduce or build on\, due to private code\, data\, and large compute requirements. This has created substantial barriers to research on machine learning methods for theorem proving. We introduce LeanDojo: an open-source Lean playground consisting of toolkits\, data\, models\, and benchmarks. LeanDojo extracts data from Lean and enables interaction with the proof environment programmatically. It contains fine-grained annotations of premises in proofs\, providing valuable data for premise selection: a key bottleneck in theorem proving. Using this data\, we develop ReProver (Retrieval-Augmented Prover): the first LLM-based prover that is augmented with retrieval for selecting premises from a vast math library. It is inexpensive and needs only one GPU week of training. Our retriever leverages LeanDojo’s program analysis capability to identify accessible premises and hard negative examples\, which makes retrieval much more effective. Furthermore\, we construct a new benchmark consisting of 96\,962 theorems and proofs extracted from Lean’s math library. It features a challenging data split requiring the prover to generalize to theorems relying on novel premises that are never used in training. We use this benchmark for training and evaluation\, and experimental results demonstrate the effectiveness of ReProver over non-retrieval baselines and GPT-4. We thus provide the first set of open-source LLM-based theorem provers without any proprietary datasets and release it under a permissive MIT license to facilitate further research. \n 
URL:https://cmsa.fas.harvard.edu/event/nt-101123-2/
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-10.11.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231013T120000
DTEND;TZID=America/New_York:20231013T130000
DTSTAMP:20240223T105527Z
CREATED:20240223T105131Z
LAST-MODIFIED:20240223T105527Z
UID:10002852-1697198400-1697202000@cmsa.fas.harvard.edu
SUMMARY:On the Breakdown of Einstein's Gravity
DESCRIPTION:Member Seminar \nSpeaker: Puskar Mondal (CMSA) \nTitle: On the Breakdown of Einstein’s Gravity \nAbstract: It is important to understand under which conditions\, the solutions of non-linear hyperbolic PDEs break down in finite time. In the context of Einstein’s gravity\, this is very closely tied to naked singularity formation and Penrose’s weak cosmic censorship conjecture. In this talk\, I will give sharp estimates on the relevant geometric entities that allow one to continue the solutions of Einstein’s equations indefinitely in the future in a ‘time’ direction without forming a naked singularity.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-101323/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231016T163000
DTEND;TZID=America/New_York:20231016T173000
DTSTAMP:20251026T063911Z
CREATED:20240223T093426Z
LAST-MODIFIED:20251026T063911Z
UID:10002844-1697473800-1697477400@cmsa.fas.harvard.edu
SUMMARY:An exploration of infinite games—infinite Wordle and the Mastermind numbers
DESCRIPTION:Speaker: Joel D. Hamkins (Notre Dame and Oxford) \nTitle: An exploration of infinite games—infinite Wordle and the Mastermind numbers \nAbstract: Let us explore the nature of strategic reasoning in infinite games\, focusing on the cases of infinite Wordle and infinite Mastermind. The familiar game of Wordle extends naturally to longer words or even infinite words in an idealized language\, and Mastermind similarly has natural infinitary analogues. What is the nature of play in these infinite games? Can the codebreaker play so as to win always at a finite stage of play? The analysis emerges gradually\, and in the talk I shall begin slowly with some easy elementary observations. By the end\, however\, we shall engage with sophisticated ideas in descriptive set theory\, a kind of infinitary information theory. Some assertions about the minimal size of winning sets of guesses\, for example\, turn out to be independent of the Zermelo-Fraenkel ZFC axioms of set theory. Some questions remain open.
URL:https://cmsa.fas.harvard.edu/event/colloquium-101623/
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-10.16.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231018T140000
DTEND;TZID=America/New_York:20231018T150000
DTSTAMP:20240223T114049Z
CREATED:20240223T114049Z
LAST-MODIFIED:20240223T114049Z
UID:10002867-1697637600-1697641200@cmsa.fas.harvard.edu
SUMMARY:Physics of Language Models: Knowledge Storage\, Extraction\, and Manipulation
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Yuanzhi Li\, CMU Dept. of Machine Learning and Microsoft Research \nTitle: Physics of Language Models: Knowledge Storage\, Extraction\, and Manipulation \nAbstract: Large language models (LLMs) can memorize a massive amount of knowledge during pre-training\, but can they effectively use this knowledge at inference time? In this work\, we show several striking results about this question. Using a synthetic biography dataset\, we first show that even if an LLM achieves zero training loss when pretraining on the biography dataset\, it sometimes can not be finetuned to answer questions as simple as “What is the birthday of XXX” at all. We show that sufficient data augmentation during pre-training\, such as rewriting the same biography multiple times or simply using the person’s full name in every sentence\, can mitigate this issue. Using linear probing\, we unravel that such augmentation forces the model to store knowledge about a person in the token embeddings of their name rather than other locations. \nWe then show that LLMs are very bad at manipulating knowledge they learn during pre-training unless a chain of thought is used at inference time. We pretrained an LLM on the synthetic biography dataset\, so that it could answer “What is the birthday of XXX” with 100% accuracy.  Even so\, it could not be further fine-tuned to answer questions like “Is the birthday of XXX even or odd?” directly.  Even using Chain of Thought training data only helps the model answer such questions in a CoT manner\, not directly. \nWe will also discuss preliminary progress on understanding the scaling law of how large a language model needs to be to store X pieces of knowledge and extract them efficiently. For example\, is a 1B parameter language model enough to store all the knowledge of a middle school student? \n  \n 
URL:https://cmsa.fas.harvard.edu/event/nt-101823/
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/NTM-10.18.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231020T120000
DTEND;TZID=America/New_York:20231020T130000
DTSTAMP:20240223T110405Z
CREATED:20240223T110405Z
LAST-MODIFIED:20240223T110405Z
UID:10002856-1697803200-1697806800@cmsa.fas.harvard.edu
SUMMARY:Black Holes as Quantum Systems
DESCRIPTION:Member Seminar \nSpeaker: Daniel Kapec (CMSA) \nTitle: Black Holes as Quantum Systems \nAbstract: To an outside observer\, a black hole appears to be an ordinary quantum mechanical system with finite entropy and highly chaotic internal dynamics. Nevertheless\, the low-temperature thermodynamics of the Kerr black hole presents several puzzles. For instance\, the leading order semiclassical approximation to the black hole density of states predicts a surprisingly large ground state degeneracy\, while poorly understood quantum corrections are known to become increasingly important at low temperatures. I will review the modern picture of black holes as quantum systems and then discuss a recent result on the leading correction to the low-temperature thermodynamics of the Kerr black hole that resolves many of the old puzzles. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-102023/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231023T163000
DTEND;TZID=America/New_York:20231023T173000
DTSTAMP:20240223T092904Z
CREATED:20240223T092904Z
LAST-MODIFIED:20240223T092904Z
UID:10002843-1698078600-1698082200@cmsa.fas.harvard.edu
SUMMARY: On Provable Copyright Protection for Generative Model
DESCRIPTION:Speaker: Boaz Barak (Harvard) \nTitle: On Provable Copyright Protection for Generative Model \nAbstract: There is a growing concern that learned conditional generative models may output samples that are substantially similar to some copyrighted data C that was in their training set. We give a formal definition of near access-freeness (NAF) and prove bounds on the probability that a model satisfying this definition outputs a sample similar to C\, even if C is included in its training set. \nRoughly speaking\, a generative model p is k-NAF if for every potentially copyrighted data C\, the output of p diverges by at most k-bits from the output of a model q that did not access C at all. We also give generative model learning algorithms\, which efficiently modify the original generative model learning algorithm in a black box manner\, that output generative models with strong bounds on the probability of sampling protected content. Furthermore\, we provide promising experiments for both language (transformers) and image (diffusion) generative models\, showing minimal degradation in output quality while ensuring strong protections against sampling protected content. \nJoint work with Nikhil Vyas and Sham Kakade. Paper appeared in ICML 2023 and is on https://arxiv.org/abs/2302.10870
URL:https://cmsa.fas.harvard.edu/event/colloquium-102323/
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-10.23.2023.png
END:VEVENT
END:VCALENDAR