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Mathematics and Machine Learning Program Dates: September 3 - November 1, 2024 Location: Harvard CMSA, 20 Garden Street, Cambridge, MA 0213 Machine 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 […] 
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Mathematics and Machine Learning Closing Workshop Dates: October 28 - Oct. 30, 2024 Location: Room G10, CMSA, 20 Garden Street, Cambridge MA 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. We will devote one day to frontier […] Foundation Seminar (Joint Seminar with BHI) Location: BHI Title: Singularity Theorems, Part II Journal Club Discussion |
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General Relativity Seminar Speaker: Xuantao Chen, Johns Hopkins University Title: Formation of Trapped Surfaces in Geodesic Foliation Abstract: We reprove the formation of trapped surfaces for the Einstein vacuum equation using the incoming geodesic foliation. All previous results, starting with the seminal work of Christodoulou, make use of the double null foliation. In the new […]
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Geometry and Quantum Theory Seminar Speaker: Ben Gammage, Harvard University Title: Boundaries and duality for 3d gauge theories Abstract: 3d N=4 supersymmetric gauge theory has a pair of topological twists, the A-model and B-model, the latter of which is also known as Rozansky-Witten theory. Conjecturally, boundary conditions for these TFTs ought to admit descriptions in […] |
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CMSA Q&A Seminar Speaker: Michael Freedman, Harvard CMSA Topic: Broad perspective on manifolds: all dimensions, all structures, classification and dynamics |
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Mathematical Physics and Algebraic Geometry Seminar Speaker: Ju Tan (Boston University) Title: Mirror Construction for Nakajima Quiver Varieties Abstract: Quiver possesses a rich representation theory. On the one hand, it exhibits a deep connection with instantons and coherent sheaves as illuminated by the ADHM construction and the works of many others. On the other hand, […] |
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Foundation Seminar (Joint Seminar with BHI) Location: BHI Speaker: Christoph Kehle (MIT) Title: On the cosmic censorship conjectures Abstract: I will present the modern formulations of the weak and strong cosmic censorship conjectures and discuss some recent developments in the context of gravitational collapse.
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Colloquium Speaker: Martin Nowak (Harvard) Title: The mathematics of evolution Abstract: All living systems are guided by evolutionary dynamics. Evolution is a search process which occurs in populations of reproducing individuals. The three fundamental forces of evolution are mutation, selection and cooperation. I will present basic ideas in the mathematical description of evolutionary dynamics, including quasi-species theory, evolutionary […] |
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Geometry and Quantum Theory Seminar Speaker: Dan Freed, Harvard University Title: Introduction to Factorization algebras |
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CMSA Q&A Seminar Speaker: Michael Douglas, Harvard CMSA Topic: What is Argyres-Douglas theory?
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https://youtu.be/KOgh-FFDlvg New Technologies in Mathematics Seminar Speaker: Dylan Foster, Microsoft Research Title: Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning Abstract: Imitation learning (IL) aims to mimic the behavior of an expert in a sequential decision making task by learning from demonstrations, and has been widely applied to robotics, autonomous driving, and autoregressive language […] |
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Mathematical Physics and Algebraic Geometry Seminar Speaker: Fabian Ruehle (Northeastern University) Title: Bounds and Dualities of Type II Little String Theories Abstract: The goal of this seminar is to introduce Type II Little String Theories (LSTs), which are six-dimensional supersymmetric QFTs. We explore how to geometrically engineer these theories within the context of M-/F-theory (top-down) as well […] |
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Quantum Field Theory and Physical Mathematics Seminar Speaker: Victor Kac (MIT) Title: Representations of minimal W-algebras: unitarity and modular invariance Abstract: The minimal W-algebras, obtained by quantum Hamiltonian reduction from affina vertex algebras, form the most interesting class of vertex algebras, which includes all superconformal algebras: Virasoro, Neveu-Scharz, N=2, 3, 4, and big N=4. I will […]
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Member Seminar Speaker: Vasily Krylov, CMSA Title: ADHM spaces and their quantizations Abstract: In their paper “Construction of Instantons,” Atiyah, Drinfeld, Hitchin, and Manin introduced an algebraic construction of the moduli space of instantons on R^4, now also known as the "ADHM space." This is a Poisson complex variety; it has been actively studied by both […] |
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General Relativity Seminar Speaker: Ahmed Seta, Harvard University Title: pp Waves: Quasinormal Modes & Hidden Symmetries of Black Holes Abstract: The spectrum of quasinormal modes of 4D flat space black holes is not analytically tractable, but there are two asymptotic limits where the QNM spectrum is under control: weak damping and strong damping. In this talk, I […] |
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https://youtu.be/qC60ZgsIFvk New Technologies in Mathematics Seminar Speaker: Huajian Xin, DeepSeek Title: Frontier of Formal Theorem Proving with Large Language Models: Insights from the DeepSeek-Prover Series Abstract: Recent advances in large language models have markedly influenced mathematical reasoning and automated theorem proving within artificial intelligence. Yet, despite their success in natural language tasks, these models face notable obstacles […] |
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Mathematical Physics and Algebraic Geometry Seminar Speaker: Tom Scanlon, UC Berkeley Title: (Un)likely intersections Abstract: The Zilber-Pink conjectures predicts that for an ambient special variety (such as an abelian variety or a Shimura variety), if is an irreducible algebraic subvariety which is not contained a proper special subvariety of (e.g. a proper algebraic subgroup in the abelian variety case […] |
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Member Seminar Speaker: Uri Kol Title: Quantum Criticality in Black Hole Scattering Abstract: Perturbation theory around rotating black holes captures a few important effects in the physics of gravitational waves emitted from binary mergers. Despite a long and rich history, developing a qualitative understanding of the system remains a challenging problem. In this talk I […]
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Freedman CMSA Seminar *Note: via Zoom only* 2:00-3:30 pm ET Speaker: Michael Freedman, Harvard CMSA Title: Some questions and theorems about closed 3 manifolds embedded in S^4 Abstract: Much is unknown about smooth embeddings of 3-manifolds in S^4; the Schoenflies problem (Is there only one smoothly embedded 3-sphere in S^4 up to isotopy?) is […] |
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Quantum Field Theory and Physical Mathematics Seminar Speaker: Shani Nadir Meynet (Uppsala) Title: Emergent Non-Invertible Symmetries — The Adjoint QCD Example Abstract: After reviewing some general properties of generalized symmetries and the renormalization group (RG) flow for quantum field theories (QFT), I'll describe how the recently discovered non-invertible symmetries can be used to study theories […] |
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General Relativity Seminar Speaker: Marcelo Disconzi, Vanderbilt University Title: The Einstein-Euler system with a physical vacuum boundary in spherical symmetry Abstract: We establish local well-posedness for the Einstein-Euler system with a physical vacuum boundary in spherical symmetry. Our proof relies on a new way of thinking about Einstein’s equations in spherical symmetry that is well-adapted […]
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Geometry and Quantum Theory Seminar Speakers: Mayuko Yamashita, Kyoto University Title: Factorization algebras in TQFT Abstract: This is the first in the series of our working seminars on factorization algebras/homologies. This talk focuses on locally constant factorization algebras, which correspond to Topological QFTs. I first explain they are equivalent to algebras over E_n operads and […] |
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New Technologies in Mathematics Seminar Speaker: Gail Weiss, EPFL Title: Thinking Like Transformers - A Practical Session Abstract: With the help of the RASP programming language, we can better imagine how transformers---the powerful attention based sequence processing architecture---solve certain tasks. Some tasks, such as simply repeating or reversing an input sequence, have reasonably straightforward solutions, […] 
CMSA Q&A Seminar Speaker: Anurag Anshu, Harvard University Topic: What is quantum complexity theory? 
Mathematical Physics and Algebraic Geometry Seminar Speaker: Qianyu Hao, University of Geneva Title: A new construction of c = 1 conformal blocks Abstract: The Virasoro conformal blocks are very interesting since they have many connections to other areas of math and physics. For example, when c = 1, they are related to tau functions of Painlevé equations. I will first explain what […] |
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https://youtu.be/HcKVfUcffUo CMSA/Tsinghua Math-Science Literature Lecture Date: November 21, 2024 Time: 9:00 - 10:30 am ET Location: CMSA G10, 20 Garden Street, Cambridge MA & via Zoom Speaker: Bjorn Poonen, MIT Title: Ranks of elliptic curves Abstract: Elliptic curves are simplest varieties whose rational points are not fully understood, and they are the simplest projective varieties […] 
Mathematical Physics and Algebraic Geometry Seminar Speaker: Tobias Ekholm, Uppsala University Title: Skein valued curve counts for the topological vertex and knot conormals Abstract: Combining the invariance of holomorphic curve counts in the skein module with a study of holomorphic curves at infinity of the vertex we find three simple skein operator polynomials that annihilates […] |
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Member Seminar Speaker: Alejandro Poveda Title: Identity crises phenomena in the large cardinal hierarchy Abstract: It is well-known that certain mathematical questions cannot be answered on the grounds of the standard foundation of mathematics. Large cardinal axioms constitute a series of postulates about the higher infinite which permit to classify these undecidable problems in a coherent hierarchy way. […] |
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Foundation Seminar (Joint Seminar with BHI) Title: Searching for Dark Matter in the Sky Abstract: Astrophysical and cosmological observations have allowed us to measure the abundance of dark matter and have provided important information on its properties. I will discuss past, present and future efforts to map the gravitational footprint of dark matter throughout the […]
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Colloquium Speaker: Anastasia Volovich, Brown University Title: Mathematical Structures of Scattering Amplitudes Abstract: Planar N=4 Yang-Mills scattering amplitudes have been computed to very high loop order. They have many remarkable properties that have sparked interest from mathematicians working on combinatorics, algebraic geometry, and number theory. At the same time, several methods that have been developed […] |
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