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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260506T140000
DTEND;TZID=America/New_York:20260506T150000
DTSTAMP:20260508T152445
CREATED:20260421T144955Z
LAST-MODIFIED:20260421T150144Z
UID:10003935-1778076000-1778079600@cmsa.fas.harvard.edu
SUMMARY:New directions in synthetic data
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Tatsunori Hashimoto\, Stanford \nTitle: New directions in synthetic data \nAbstract: Synthetic data has been an effective\, if boring set of techniques: prompt some language model to restructure your corpus to match some downstream task\, with occasionally some distillation. In this talk\, we will take a more expansive view of synthetic data as a general algorithmic tool for generative modeling\, arguing that the design space and possibilities of synthetic data are much bigger than it might seem. Through a few recent works\, we will show that synthetic data has major benefits beyond transforming the data – improving in-domain perplexities\, and enabling unique algorithmic primitives\, such as neighborhood smoothing and concatenated ‘mega’ documents. With this broader view\, we will point towards a nascent but interesting possibility of treating data itself as an algorithmic object to be engineered and optimized end-to-end. \n 
URL:https://cmsa.fas.harvard.edu/event/newtech_5626/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-5.6.2026.docx.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260424T140000
DTEND;TZID=America/New_York:20260424T163000
DTSTAMP:20260508T152445
CREATED:20260413T211415Z
LAST-MODIFIED:20260414T140519Z
UID:10003934-1777039200-1777048200@cmsa.fas.harvard.edu
SUMMARY:Compression Is All You Need: Modeling Mathematics
DESCRIPTION:Freedman Seminar \nSpeaker: Mike Freedman\, Harvard CMSA \nTitle: Compression Is All You Need: Modeling Mathematics \nAbstract: The talk will exposit a recent eponymous arXiv posting with coauthors Vitaly Aksenov\, Eve Bodnia\, and Mike Mulligan. The approach is to think like a physicist and model a seemingly complex bit of reality: mathematics\, by a simple toy model where exact computations can be carried out and then compared with observation.  The models are finitely generated monoids and the data is derived from MathLib a large Lean-based repository. The hierarchical nature of definitions and lemmas in math is modeled by adding redundant generators to the monoids – think of the powers of 10 within the natural numbers which support place notation. Place notation confers an exponential compression of how we describe numbers; exploration of MathLib shows that this theme persists to (human) mathematics writ large. We hope that the observables we describe will help our agents navigate to interesting mathematical destinations. \n 
URL:https://cmsa.fas.harvard.edu/event/freedman_42426/
LOCATION:Virtual
CATEGORIES:Freedman Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Freedman-Seminar-4.24.26.docx.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260327T150000
DTEND;TZID=America/New_York:20260327T171500
DTSTAMP:20260508T152445
CREATED:20260323T145751Z
LAST-MODIFIED:20260323T194752Z
UID:10003922-1774623600-1774631700@cmsa.fas.harvard.edu
SUMMARY:Exotic R^4's are unclassifiable
DESCRIPTION:Freedman Seminar \nSpeaker: Robert Gompf\, UT Austin \nTitle: Exotic R^4’s are unclassifiable \nAbstract: We will use descriptive set theory to show that there is a precise sense in which exotic R^4’s are unclassifiable. For other open manifolds\, we can reach a much higher level of unclassifiability. This is work in progress with Aristotelis Panagiotopoulos.
URL:https://cmsa.fas.harvard.edu/event/freedman_32726/
LOCATION:Virtual
CATEGORIES:Freedman Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Freedman-Seminar-3.27.26-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260318T140000
DTEND;TZID=America/New_York:20260318T150000
DTSTAMP:20260508T152445
CREATED:20260309T145907Z
LAST-MODIFIED:20260311T161332Z
UID:10003916-1773842400-1773846000@cmsa.fas.harvard.edu
SUMMARY:Dynamic reasoning
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Emmanuel Abbé\, EPFL\, Institute of Mathematics and School of Computer and Communication Sciences & Apple \nTitle: Dynamic reasoning \nAbstract: In the current AI landscape\, reasoning is frequently equated with the generation of intermediate “thinking traces”. However\, these traces are merely a mechanism\, not the ultimate objective.\nRelying solely on the presence of a trace can be deceptive\, as models often learn to mimic the format of reasoning while effectively overfitting to specific training distributions.\nTo build more robust and versatile reasoners\, we shift our focus to more specific structural properties of the thinking process\, in particular compositionality (inductive CoT\, AdaBack) and abstraction (AbstRaL).
URL:https://cmsa.fas.harvard.edu/event/newtech_31826-2/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-3.18.2026.docx-1-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260211T140000
DTEND;TZID=America/New_York:20260211T150000
DTSTAMP:20260508T152445
CREATED:20260126T152202Z
LAST-MODIFIED:20260126T212834Z
UID:10003878-1770818400-1770822000@cmsa.fas.harvard.edu
SUMMARY:ReLU and Softplus neural nets as zero-sum\, turn-based\, stopping games
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Yiannis Vlassopoulos\, Athena Research Center \nTitle: ReLU and Softplus neural nets as zero-sum\, turn-based\, stopping games \nAbstract: Neural networks are for the most part treated as black boxes. In an effort to begin elucidating the mathematical structure they encode\, we will explain how ReLU neural nets can be interpreted as zero-sum turn-based\, stopping games. The game runs in the opposite direction to the net. The input to the net is the terminal reward of the game\, the output of the net is the value of the game at its initial states. The bias at each neuron is used to define the reward and the weights are used to define state-transition probabilities. One player –Max– is trying to maximize reward and the other –Min-\, to minimize it. Every neuron gives rise to two game states\, one where Max plays and one where Min plays. In fact running the ReLU net is equivalent to the Shapley-Bellman backward recursion for the value of the game. As a corollary of this construction we get a path integral expression for the output of the net\, given input. Moreover using the fact that the Shapley operator is monotonic (with respect to the coordinate-wise order) we get bounds for the output of the net\, given bounds for the input. Adding an entropic regularization to the ReLU net game allows us to interpret Softplus neural nets as games in an analogous fashion.\nThis is joint work with Stéphane Gaubert. \n 
URL:https://cmsa.fas.harvard.edu/event/newtech_21126/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-2.11.2026.docx-1-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251203T140000
DTEND;TZID=America/New_York:20251203T150000
DTSTAMP:20260508T152445
CREATED:20251110T191407Z
LAST-MODIFIED:20251110T225824Z
UID:10003833-1764770400-1764774000@cmsa.fas.harvard.edu
SUMMARY:Machine learning tools for mathematical discovery
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Adam Zsolt Wagner\, Google DeepMind \nTitle: Machine learning tools for mathematical discovery \nAbstract: I will discuss various ML tools we can use today to try to find interesting constructions to various mathematical problems. I will briefly mention simple reinforcement learning setups and PatternBoost\, but the talk will mainly focus on LLM-based tools such as FunSearch and AlphaEvolve. We will discuss the pros and cons of several of these methods\, and try to figure out which one is best for the problems we care about.\nJoint work with François Charton\, Jordan Ellenberg\, Bogdan Georgiev\, Javier Gómez-Serrano\, Terence Tao\, and Geordie Williamson.
URL:https://cmsa.fas.harvard.edu/event/newtech_12325/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-12.3.2025-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251120T160000
DTEND;TZID=America/New_York:20251120T170000
DTSTAMP:20260508T152445
CREATED:20250904T163048Z
LAST-MODIFIED:20251117T220513Z
UID:10003785-1763654400-1763658000@cmsa.fas.harvard.edu
SUMMARY:Tropical-Topological(Tropological) Sigma Models
DESCRIPTION:Differential Geometry and Physics Seminar  \nSpeaker: Andrés Franco Valiente\, UC Berkeley \nTitle: Tropical-Topological (Tropological) Sigma Models \nAbstract: Tropical geometry provides a powerful bridge between complex and combinatorial worlds\, allowing certain curve-counting invariants to be computed in a piecewise-linear “tropical” limit. Building on Mikhalkin’s insight that Gromov–Witten invariants can be recovered from tropical curves\, this talk revisits Mikhalkin’s result from the viewpoint of topological field theory and functional integration.  I will first review the topological sigma model and explain how the localization equations admit a natural notion of tropicalization which allows us to reproduce the Gromov-Witten invariants using standard cohomological BRST methods without having to reformulate the functional integral in terms of the tropical semifield. We find that the relevant geometries associated to the tropical limit of the topological sigma models no longer require a complex structure but they are instead based on nilpotent structures on singular foliated manifolds. We close with a discussion on recent progress on how the tropological sigma model has a close connection to Hořava’s topologicial quantum gravity for Ricci Flow in a joint work with Emil Albrychiewicz and Viola Zixin Zhao. \n  \n  \n 
URL:https://cmsa.fas.harvard.edu/event/dgphys_112025/
LOCATION:Virtual
CATEGORIES:Differential Geometry and Physics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/DG-Physics-Seminar-11.20.2025.docx-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251114T130000
DTEND;TZID=America/New_York:20251114T160000
DTSTAMP:20260508T152445
CREATED:20251104T215810Z
LAST-MODIFIED:20251105T144505Z
UID:10003832-1763125200-1763136000@cmsa.fas.harvard.edu
SUMMARY:Freedman Seminar: Michael Freedman\, CMSA & Bowen Yang\, CMSA
DESCRIPTION:Freedman Seminar \nSpeaker: Michael Freedman\, Harvard CMSA \nTitle: Sullivan’s work on Lipschitz structures Part II (but self-contained) \n  \nSpeaker: Bowen Yang\, CMSA \nTitle: Deligne and Sullivan’s work on complex bundles with discrete structure group \n 
URL:https://cmsa.fas.harvard.edu/event/freedman_111425/
LOCATION:Virtual
CATEGORIES:Freedman Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Freedman-Seminar-11.14.25.docx-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251022T140000
DTEND;TZID=America/New_York:20251022T150000
DTSTAMP:20260508T152445
CREATED:20251008T132005Z
LAST-MODIFIED:20251008T133142Z
UID:10003808-1761141600-1761145200@cmsa.fas.harvard.edu
SUMMARY:The Carleson project: A collaborative formalization
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: María Inés de Frutos Fernández\, Mathematical Institute\, University of Bonn \nTitle: The Carleson project: A collaborative formalization \nAbstract: A well-known result in Fourier analysis establishes that the partial Fourier sums of a smooth periodic function $f$ converge uniformly to $f$\, but the situation is a lot more subtle for e.g. continuous functions. However\, in 1966 Carleson proved that they do converge at almost all points for $L^2$ periodic functions on the real line. Carleson’s proof is famously hard to read\, and there are no known easy proofs of this theorem. As a large collaborative project\, we have formalized in Lean a generalization of Carleson’s theorem in the setting of doubling metric measure spaces (proven in 2023)\, and Carleson’s original result as a corollary. In this talk I will give an overview of the project\, with a focus on how the collaboration was organized. \n 
URL:https://cmsa.fas.harvard.edu/event/newtech_102225/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-10.22.2025-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251017T130000
DTEND;TZID=America/New_York:20251017T160000
DTSTAMP:20260508T152445
CREATED:20250930T134721Z
LAST-MODIFIED:20251014T133421Z
UID:10003800-1760706000-1760716800@cmsa.fas.harvard.edu
SUMMARY:Freedman Seminar: Michael Freedman\, CMSA & Bowen Yang\, CMSA
DESCRIPTION:Freedman Seminar \nSpeaker: Michael Freedman\, Harvard CMSA \nTitle: Sullivan’s work on Lipschitz structures \nAbstract: I’ll begin with an elementary\, but now little known\, piece of PL topology: engulfing. John Stalling used it to give an alternative proof of the high dimensional Poincare conjecture. Then I’ll explain Dennis Sullivan’s enhancement of Kirby’s torus trick (which relies on engulfing.) I’ll note an open question regarding Lipschitz structures on 4-manifolds. \n  \nSpeaker: Bowen Yang\, CMSA \nTitle: Quantum Cellular Automata and Algebraic L-Theory \nAbstract: Quantum cellular automata (QCAs) are models of reversible quantum dynamics that preserve locality; they can be thought of as quantum analogues of classical cellular automata\, but with much richer structure. I will describe a classification of the Clifford subclass of QCAs using methods from algebraic L-theory. The main result identifies the group of Clifford QCAs\, up to natural equivalences\, with L-theory homology of the underlying space. This gives a conceptual explanation of previously observed periodic patterns in lattice models and extends the picture to more general spaces. I will outline the ideas behind the construction and indicate how the framework connects topology\, operator algebras\, and quantum information. If time permits\, I will also comment on what is known — and unknown — about the general (non-Clifford) case.
URL:https://cmsa.fas.harvard.edu/event/freedman_101725/
LOCATION:Virtual
CATEGORIES:Freedman Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Freedman-Seminar-10.17.25.docx-1-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251016T140000
DTEND;TZID=America/New_York:20251016T150000
DTSTAMP:20260508T152445
CREATED:20250911T184527Z
LAST-MODIFIED:20251006T162709Z
UID:10003790-1760623200-1760626800@cmsa.fas.harvard.edu
SUMMARY:Lech's inequality and stability of local rings
DESCRIPTION:Algebra Seminar \nSpeaker: Linquan Ma (Purdue University) \nTitle: Lech’s inequality and stability of local rings \nAbstract: We explore Lech’s inequality relating the colength and multiplicity of m-primary ideals in a Noetherian local ring (R\,m). We introduce a natural invariant that measures the sharpness of Lech’s inequality and show its connections with singularities of asymptotically semistable varieties and singularities arising from the MMP. We compute this invariant in various examples. This is joint work with Ilya Smirnov. \n 
URL:https://cmsa.fas.harvard.edu/event/algebra-seminar_101625/
LOCATION:Virtual
CATEGORIES:Algebra Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebra-Seminar-10.16.25.docx-1-1-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251006T150000
DTEND;TZID=America/New_York:20251006T160000
DTSTAMP:20260508T152445
CREATED:20250924T182709Z
LAST-MODIFIED:20251006T144221Z
UID:10003796-1759762800-1759766400@cmsa.fas.harvard.edu
SUMMARY:Non-perturbative aspects of self-dual gauge theory
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \nSpeaker: Kevin Costello (Perimeter Institute)\n\nTitle: Non-perturbative aspects of self-dual gauge theory\n\nAbstract: Self-dual gauge theory is conformal in perturbation theory\, but has a non-trivial beta-function when instanton effects are included. I will give two computations of this beta-function\, one based on the Grothendieck-Riemann-Roch formula and one using holography in the topological string.   This leads to two new ways to compute the standard QCD beta-function at one loop\, without using Feynman diagrams.  If time permits\, I will also discuss how instantons effect scattering amplitudes.\n\n 
URL:https://cmsa.fas.harvard.edu/event/qft_100625/
LOCATION:Virtual
CATEGORIES:Quantum Field Theory and Physical Mathematics
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QFT-and-Physical-Mathematics-10.6.25-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251001T140000
DTEND;TZID=America/New_York:20251001T150000
DTSTAMP:20260508T152445
CREATED:20250128T214901Z
LAST-MODIFIED:20251002T140605Z
UID:10003710-1759327200-1759330800@cmsa.fas.harvard.edu
SUMMARY:Tropicalized quantum field theory
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Michael Borinsky\, Perimeter Institute  \nTitle: Tropicalized quantum field theory \nAbstract: Quantum field theory (QFT) is one of the most accurate methods for making phenomenological predictions in physics\, but it has a significant drawback: obtaining concrete predictions from it is computationally very demanding. The standard perturbative approach expands an interacting QFT around a free QFT\, using Feynman diagrams. However\, the number of these diagrams grows superexponentially\, making the approach quickly infeasible. \nI will talk about arXiv:2508.14263\, which introduces an intermediate layer between free and interacting field theories: a tropicalized QFT. Often\, this tropicalized QFT can be solved exactly. The exact solution manifests as a non-linear recursion equation fulfilled by the expansion coefficients of the quantum effective action. Geometrically\, this recursion computes volumes of moduli spaces of metric graphs and is thereby analogous to Mirzakhani’s volume recursions on the moduli space of curves. Building on this exact solution\, an algorithm can be constructed that samples points from the moduli space of graphs approximately proportional to their perturbative contribution. Via a standard Monte Carlo approach we can evaluate the original QFT using this algorithm. Remarkably\, this algorithm requires only polynomial time and memory\, suggesting that perturbative quantum field theory computations actually lie in the polynomial-time complexity class\, while all known algorithms for evaluating individual Feynman integrals are at least exponential in time and memory. The (potential) capabilities of this approach are remarkable: For instance\, we can compute perturbative expansions of massive scalar D=3 phi^3 and D=4 phi^4 quantum field theories up to loop orders between 20 and 50 using a basic proof-of-concept implementation. These perturbative orders are completely inaccessible using a naive approach.
URL:https://cmsa.fas.harvard.edu/event/newtech_10125/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-10.1.2025.docx-1-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250522T100000
DTEND;TZID=America/New_York:20250522T110000
DTSTAMP:20260508T152445
CREATED:20250417T165226Z
LAST-MODIFIED:20250519T144738Z
UID:10003742-1747908000-1747911600@cmsa.fas.harvard.edu
SUMMARY:Higher Gauge Theory and Integrability
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Joaquin Liniado\, Instituto de Física La Plata \nTitle: Higher Gauge Theory and Integrability \nAbstract: Integrable field theories are remarkable for possessing an infinite number of conserved quantities\, which often allow for their exact solvability. In two dimensions\, this structure is elegantly captured by the existence of a Lax connection\, whose path ordered exponential allows for the systematic construction of an infinite number of conserved quantities. In 2019\, Costello\, Witten and Yamazaki introduced a four-dimensional holomorphic extension of Chern-Simons theory that provides the first attempt at explaining the appearance of the Lax connection\, whose origin had remained somewhat mysterious until then. \nIn this talk\, we present a generalization of these ideas to three-dimensional field theories\, guided by the so-called “categorical ladder = dimensional ladder” principle. The central idea is that conserved quantities arise from surface-ordered exponentials of higher-rank tensors\, defining a higher categorical notion of the Lax connection. We show that such a structure naturally emerges from a five-dimensional holomorphic extension of higher Chern-Simons theory. This work\, carried out in collaboration with Hank Chen\, provides a framework that enables the systematic construction of integrable field theories in three dimensions. \n  \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_52225/
LOCATION:Virtual
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-5.22.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250508T100000
DTEND;TZID=America/New_York:20250508T110000
DTSTAMP:20260508T152445
CREATED:20250312T185317Z
LAST-MODIFIED:20250501T191129Z
UID:10003728-1746698400-1746702000@cmsa.fas.harvard.edu
SUMMARY:Residues and homotopy Lie algebras
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Zhenping Gui\, Shanghai Institute for Mathematics and Interdisciplinary Sciences \nTitle: Residues and homotopy Lie algebras \nAbstract: I will introduce the notion of a chiral operad for any compact Riemann surface. This operad consists of compositions of residue operations\, which give rise to the Chevalley-Cousin complex and lead to the definition of chiral homology (derived conformal blocks). I will explain how to use this machinery to rigorously define certain Feynman integrals in 2D chiral CFTs. Subsequently\, I will present a polysimplicial construction of a series of chain models for the configuration space of points in an affine space and study residue operations. These residue operations can be described by a homotopy Lie algebra structure\, and the latter defines a higher-dimensional analog of the Chevalley-Cousin complex. This is based on joint work in progress with Charles Young and Laura Felder. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_5825/
LOCATION:Virtual
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-5.8.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250425T030000
DTEND;TZID=America/New_York:20250425T160000
DTSTAMP:20260508T152445
CREATED:20250422T134510Z
LAST-MODIFIED:20250422T140503Z
UID:10003713-1745550000-1745596800@cmsa.fas.harvard.edu
SUMMARY:Adversarial KA
DESCRIPTION:Freedman CMSA Seminar \nSpeaker: Slava Dzhenzher\, MIPT \nTitle: Adversarial KA \nAbstract: Regarding the representation theorem of Kolmogorov and Arnold (KA) as an algorithm for representing or «expressing» functions\, we test its robustness by analyzing its ability to withstand adversarial attacks. We find KA to be robust to countable collections of continuous adversaries\, but unearth a question about the equi-continuity of the outer functions that\, so far\, obstructs taking limits and defeating continuous groups of adversaries. This question on the regularity of the outer functions is relevant to the debate over the applicability of KA to the general theory of NNs. Based on  https://arxiv.org/abs/2504.05255 \n  \n 
URL:https://cmsa.fas.harvard.edu/event/freedman_42525/
LOCATION:Virtual
CATEGORIES:Freedman Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Freedman-Seminar-4.25.25.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250410T100000
DTEND;TZID=America/New_York:20250410T110000
DTSTAMP:20260508T152445
CREATED:20250128T191238Z
LAST-MODIFIED:20250404T155809Z
UID:10003684-1744279200-1744282800@cmsa.fas.harvard.edu
SUMMARY:3d Mirror Symmetry is 2d Mirror Symmetry
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Ki Fung Chan (Chinese University of Hong Kong) \nTitle: 3d Mirror Symmetry is 2d Mirror Symmetry \nAbstract: We introduce an approach to studying 3d mirror symmetry via 2d mirror symmetry. The main observations are: (1) 3d brane transforms are given by SYZ-type transforms; (2) the exchange of symplectic and complex structures in 2d mirror symmetry induces the exchange of Kähler and equivariant parameters in 3d mirror symmetry; and (3) the functionalities of 2d mirror symmetry control the gluing of 3d mirrors. If time permits\, we will also discuss some applications to 2d mirror symmetry at the end of the talk. Joint works with Naichung Conan Leung. \n  \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_41025/
LOCATION:Virtual
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-4.10.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250401T110000
DTEND;TZID=America/New_York:20250401T120000
DTSTAMP:20260508T152445
CREATED:20250128T213541Z
LAST-MODIFIED:20250331T195936Z
UID:10003702-1743505200-1743508800@cmsa.fas.harvard.edu
SUMMARY:Low-regularity Local Well-posedness of the Elastic Wave System
DESCRIPTION:General Relativity Seminar \nSpeaker: Sifan Yu\, National University of Singapore \nTitle: Low-regularity Local Well-posedness of the Elastic Wave System \nAbstract: In this talk\, I will present a recent work on the elastic wave system in three spatial dimensions. For admissible harmonic elastic materials\, we prove a low-regularity local well-posedness result for the corresponding elastic wave equations. For such materials\, we can split the dynamics into the “divergence-part” and the “curl-part\,” and each part satisfies a distinct coupled quasilinear wave system with respect to different acoustical metrics. Our main result is that the Sobolev norm H^{3+} of the “divergence-part” (the “faster-wave part”) and the H^{4+} of the “curl-part” (the “slower-wave part”) can be controlled in terms of initial data for short times. We note that the Sobolev norm assumption H^{3+} is optimal for the “divergence-part.” This is a joint work with Xinliang An and Haoyang Chen.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-4125/
LOCATION:Virtual
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-4.1.2025.docx_11-am.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250327T100000
DTEND;TZID=America/New_York:20250327T110000
DTSTAMP:20260508T152445
CREATED:20250128T214249Z
LAST-MODIFIED:20250327T192309Z
UID:10003666-1743069600-1743073200@cmsa.fas.harvard.edu
SUMMARY:AlphaProof: when reinforcement learning meets formal mathematics
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Thomas Hubert (Google DeepMind) \nTitle: AlphaProof: when reinforcement learning meets formal mathematics \nAbstract: Galileo\, the renowned Italian astronomer\, physicist\, and mathematician\, famously described mathematics as the language of the universe. Progress since only confirmed his intuition as the world we live in can be described with extreme precision with just a few mathematical equations.\nIn the last 70 years\, the rise of computers has also enriched our understanding of and revolutionized the world we live in. Mathematics tremendously benefited from this digital revolution as well: while Gauss had to compute primes by hand\, computers and computation are now routinely used in research mathematics and contribute to grand problems like the Birch and Swinnerton-Dyer conjecture\, one of the Millennium Prize Problems.\nToday\, computers are entering a new age\, one in which computation can be transformed into reasoning. In this talk\, I would like to discuss two such developments that will undoubtedly have an integral role to play in the future of mathematics: the concurrent rise of formal mathematics and of machine intelligence.
URL:https://cmsa.fas.harvard.edu/event/newtech_32625/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-3.27.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250327T100000
DTEND;TZID=America/New_York:20250327T110000
DTSTAMP:20260508T152445
CREATED:20250128T172102Z
LAST-MODIFIED:20250324T152627Z
UID:10003682-1743069600-1743073200@cmsa.fas.harvard.edu
SUMMARY:From quantum difference equations to Maulik-Okounkov quantum affine algebra
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \n*via Zoom only* \nSpeaker: Tianqing Zhu (Tsinghua University) \nTitle: From quantum difference equations to Maulik-Okounkov quantum affine algebra \nAbstract: Capping operator is one the core subject in the K-theoretic quasimap counting to quiver varieties. It has been shown by Okounkov and Smirnov that it satisfies a system of q-difference equations governed by the MO quantum affine algebras. In this talk we will show how to construct the similar quantum difference equation via the shuffle algebras. Then we will show how to use the monodromy data of these quantum difference equations to prove the isomorphism of the positive half of the MO quantum affine algebras of affine type A and the positive half of the quantum toroidal algebras. If time permits\, I will also give a brief explanation on how to extend the proof to the general case. \n  \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_32725/
LOCATION:Virtual
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-3.27.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250325T160000
DTEND;TZID=America/New_York:20250325T170000
DTSTAMP:20260508T152445
CREATED:20250128T213506Z
LAST-MODIFIED:20250326T194012Z
UID:10003701-1742918400-1742922000@cmsa.fas.harvard.edu
SUMMARY:Unstable Fluids in Expanding Cosmologies
DESCRIPTION:General Relativity Seminar \nSpeaker: Elliot Marshal\, School of Mathematics at Monash University \nTitle: Unstable Fluids in Expanding Cosmologies \nAbstract: The FLRW solution is the simplest cosmological model in general relativity\, describing a fluid-filled\, spatially homogeneous universe. While there is extensive literature in the physics community on cosmological models with a linear equation of state \, rigorous stability results have\, until recently\, been limited to FLRW models with accelerated expansion and small sound speeds. In this talk\, I will discuss numerical work on two types of instabilities which can occur in non-linearly perturbed FLRW models outside of this regime. The first concerns a longstanding conjecture of Alan Rendall on FLRW models with positive cosmological constant and super-radiative (K>1/3) equations of state. Our numerical work\, in collaboration with F. Beyer and T.A. Oliynyk\, supports Rendall’s conjecture and highlights the underlying mechanism for the instability. In the second case\, I will discuss evidence that perturbations of slowly expanding (decelerated) FLRW models generically form shocks in finite time. This contrasts with known results for accelerated models where shock formation is suppressed for suitably small perturbations.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-32525/
LOCATION:Virtual
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-3.25.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250226T140000
DTEND;TZID=America/New_York:20250226T150000
DTSTAMP:20260508T152445
CREATED:20250124T154400Z
LAST-MODIFIED:20250623T124501Z
UID:10003663-1740578400-1740582000@cmsa.fas.harvard.edu
SUMMARY:Datasets for Math: From AIMO Competitions to Math Copilots for Research
DESCRIPTION:  \nNew Technologies in Mathematics Seminar \nSpeaker: Simon Frieder\, Oxford \nTitle: Datasets for Math: From AIMO Competitions to Math Copilots for Research \nAbstract: This talk begins with a brief exposition of the AI Mathematical Olympiad (AIMO) on Kaggle\, now in its second iteration\, outlining datasets and models available to contestants. Taking a broader perspective\, I then examine 1) the overarching issues the current datasets suffer from—such as binary evaluation or constrained sets of use cases— and 2) the trajectory they set for competition-style mathematical problem-solving\, which is different from mathematical research practice. I argue for a fundamental shift in dataset structure and composition\, both for training and evaluation\, and introduce the idea of mapping mathematical workflows to data\, a key example underscoring the need for this shift. I touch upon new thinking LLMs and their role in redefining LLM math evaluation\, highlighting their implications for dataset design. Finally\, I propose general improvements to the current state of mathematical datasets\, including mathematical adaptations of dataset documentation (e.g.\, datasheets). \n 
URL:https://cmsa.fas.harvard.edu/event/newtech_22625/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/1740494700974-e6086db9-08ab-4681-9ecd-580092fe27b62025-1_1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250220T100000
DTEND;TZID=America/New_York:20250220T110000
DTSTAMP:20260508T152445
CREATED:20250128T171842Z
LAST-MODIFIED:20250218T155455Z
UID:10003678-1740045600-1740049200@cmsa.fas.harvard.edu
SUMMARY:The geometry of pure spinor superfield formalism 
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Simone Noja (Heidelberg University) \nTitle: The geometry of pure spinor superfield formalism \nAbstract: In this talk I will present a mathematical perspective on the pure spinor superfield formalism. In particular\, I will discuss how field multiplets in supersymmetric theories can be constructed mathematically from geometric data associated with certain algebraic varieties—namely\, the nilpotence variety of the (super)symmetry algebra of the theory. After discussing key examples\, I will\, time permitting\, outline a possible generalization of the formalism within the framework of derived geometry.
URL:https://cmsa.fas.harvard.edu/event/mathphys_22025/
LOCATION:Virtual
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-2.20.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250218T110000
DTEND;TZID=America/New_York:20250218T120000
DTSTAMP:20260508T152445
CREATED:20240903T191953Z
LAST-MODIFIED:20250219T144101Z
UID:10003426-1739876400-1739880000@cmsa.fas.harvard.edu
SUMMARY:General Relativity Seminar
DESCRIPTION:General Relativity Seminar \nSpeaker: Maximilian Ofner\, University of Vienna \nTitle: Stability and Instability of Relativistic Fluids in Slowly Expanding Spacetimes \nAbstract: Homogeneous and isotropic solutions to the relativistic Euler equations are known to be unstable on a Minkowski background. However\, for FLRW models with a fast expansion rate\, relativistic fluids stabilize. This scenario suggests a transition between stable and unstable behavior\, somewhere along a family of spacetimes parametrized by their expansion rate. In this talk we will discuss this phase transition for various equations of state\, focusing on the regime of linear and decelerated expansion. This is based on recent analytical results\, complemented by numerical analysis.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-21825/
LOCATION:Virtual
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-2.18.25.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250212T140000
DTEND;TZID=America/New_York:20250212T150000
DTSTAMP:20260508T152445
CREATED:20250123T194306Z
LAST-MODIFIED:20250228T212617Z
UID:10003661-1739368800-1739372400@cmsa.fas.harvard.edu
SUMMARY:Discovering Data Structures: Nearest Neighbor Search and Beyond
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Omar Salemohamed\, Mila \nTitle: Discovering Data Structures: Nearest Neighbor Search and Beyond \nAbstract: As neural networks learn increasingly sophisticated tasks—from image recognition to mastering the game of Go—we ask: can deep learning discover data structures entirely from scratch? We introduce a general framework for data structure discovery\, which adapts to the underlying data distribution and provides fine-grained control over query and space complexity. For nearest neighbor (NN) search\, our model (re)discovers classic algorithms like binary search in one dimension and learns structures reminiscent of k-d trees and locality-sensitive hashing in higher dimensions. Additionally\, the model learns useful representations of high-dimensional data such as images and exploits them to design effective data structures. Beyond NN search\, we believe the framework could be a powerful tool for data structure discovery for other problems and adapt our framework to the problem of estimating frequencies over a data stream. To encourage future work in this direction\, we conclude with a discussion on some of the opportunities and remaining challenges of learning data structures end-to-end.
URL:https://cmsa.fas.harvard.edu/event/newtech_21225/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-2.12.2025.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250210T110000
DTEND;TZID=America/New_York:20250210T120000
DTSTAMP:20260508T152445
CREATED:20250128T192122Z
LAST-MODIFIED:20250203T191001Z
UID:10003687-1739185200-1739188800@cmsa.fas.harvard.edu
SUMMARY:On 5d conformal matter
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \nSpeaker: Mario De Marco (UL Brussels) \nTitle: On 5d conformal matter \nAbstract: SCFTs with 8 supercharges lie at the sweet spot of the classification program of susy scale-invariant theories: with this amount of susy\, the classification is in principle achievable\, despite being non-trivial. In this talk\, I will present the geometric approach to the classification of 5d SCFTs\, based on geometric engineering on non-compact Calabi-Yau manifolds. The strategy is to imagine a 5d SCFT as a non-Lagrangian generalization of a quiver\, and to build this generalised quiver by gauging together indecomposable blocks\, called  “5d conformal matter theories”. In this talk\, I will start with a recap of the geometric construction of [2311.04984]. I will then present some forthcoming results\, concerning the (p\,q) web realization of 5d conformal matter theories\, their reduction to 4d\, their magnetic quiver\, and the discovery of exotic “trifundamental” and “quadrifundamental” 5d indecomposable blocks (with flavor group at least SO(4k+2)^3 or SO(4k)^4). \nIn collaboration with M. Del Zotto\, M. Graffeo\, J. Grimminger\, and A. Sangiovanni. \n 
URL:https://cmsa.fas.harvard.edu/event/qft_21025/
LOCATION:Virtual
CATEGORIES:Quantum Field Theory and Physical Mathematics
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QFT-and-Physical-Mathematics-2.10.25-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250207T140000
DTEND;TZID=America/New_York:20250207T154500
DTSTAMP:20260508T152445
CREATED:20250127T151529Z
LAST-MODIFIED:20250127T155730Z
UID:10003673-1738936800-1738943100@cmsa.fas.harvard.edu
SUMMARY:Is every knot isotopic to the unknot?
DESCRIPTION:Freedman CMSA Seminar \n*via Zoom* \nSpeaker: Sergey Melikhov\, Steklov Math Institute \nTitle: Is every knot isotopic to the unknot? \nAbstract: The following problem was stated by D. Rolfsen in his 1974 paper; according to R. Daverman it was being discussed since the mid-60s. Is every knot in $S^3$ isotopic (=homotopic through embeddings) to a PL knot — or\, equivalently\, to the unknot? In particular\, is the Bing sling isotopic to a PL knot? We show that the Bing sling $B$ is not isotopic to any PL knot by an isotopy which extends to an isotopy of any 2-component link obtained from $B$ by adding a disjoint component $Q$ such that $lk(B\,Q)=1$. Moreover\, the assertion remains true if the additional component is allowed to self-intersect\, and even to get replaced by a new one at any time instant $t$\, as long as it remains disjoint from the original component $K_t$ and represents the same conjugacy class as the old one in $G/[G’\,G”]$\, where $G=\pi_1(S^3\setminus K_t)$. The are examples showing that the latter result cannot be improved in certain ways. I plan to present a sketch of the proof\, modulo some ingredients. The details can be found in arXiv:2406.09365 and the main ingredients in arXiv:2406.09331 and arXiv:math/0312007v3. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/freedman_2725/
LOCATION:Virtual
CATEGORIES:Freedman Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Freedman-Seminar-2.7.25.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250206T100000
DTEND;TZID=America/New_York:20250206T110000
DTSTAMP:20260508T152445
CREATED:20241017T135403Z
LAST-MODIFIED:20250131T173042Z
UID:10003594-1738836000-1738839600@cmsa.fas.harvard.edu
SUMMARY:Quantum algebras and R-matrices from the equivariant affine Grassmannians
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Wenjun Niu\, Perimeter Institute \nTitle: Quantum algebras and R-matrices from the equivariant affine Grassmannians \nAbstract: In this talk\, I will explain my joint work with R. Abedin\, in which we construct\, for each Lie algebra g\, a Hopf algebra and a spectral R-matrix satisfying quantum Yang-Baxter equation. This Hopf algebra is a quantization of the Lie bi-algebra structure on T^*g[t] defined by Yang’s r-matrix\, and therefore we call it the Yangian of T^*g. The construction is based on the category of coherent sheaves on the equivariant affine Grassmannian associated to the formal group of g\, and is motivated by the study of the category of line defects in a 4 dimensional holomorphic-topological field theory. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_2625/
LOCATION:Virtual
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-2.6.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250204T110000
DTEND;TZID=America/New_York:20250204T120000
DTSTAMP:20260508T152445
CREATED:20240903T192049Z
LAST-MODIFIED:20250130T190257Z
UID:10003428-1738666800-1738670400@cmsa.fas.harvard.edu
SUMMARY:The mass angular momentum inequality
DESCRIPTION:General Relativity Seminar \nSpeaker: Gilbert Weinstein\, Ariel University \nTitle: The mass angular momentum inequality \nAbstract: We show that either there is a counterexample to black hole uniqueness\, in the form of a regular axisymmetric stationary vacuum spacetime with an asymptotically flat end and multiple degenerate horizons which is ‘ADM stable’\, or the following statement holds. Complete\, simply connected\, maximal initial data sets for the Einstein equations with multiple ends that are either asymptotically flat or asymptotically cylindrical\, admit an ADM mass lower bound given by the square root of total angular momentum\, under the assumption of nonnegative energy density and axisymmetry. Moreover\, equality is achieved bound only for a constant time slice of an extreme Kerr spacetime. The proof is based on a novel flow of singular harmonic maps with hyperbolic plane target\, under which the renormalized harmonic energy is monotonically nonincreasing. Relevant properties of the flow are achieved through a refined asymptotic analysis of solutions to the linearized harmonic map equations.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-2425/
LOCATION:Virtual
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-2.4.25.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241219T100000
DTEND;TZID=America/New_York:20241219T110000
DTSTAMP:20260508T152445
CREATED:20241203T214207Z
LAST-MODIFIED:20241219T193235Z
UID:10003600-1734602400-1734606000@cmsa.fas.harvard.edu
SUMMARY:Tyurin degenerations\, Relative Lagrangian foliations and categorification of DT invariants
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Artan Sheshmani (BIMSA) \nTitle: Tyurin degenerations\, Relative Lagrangian foliations and categorification of DT invariants \nAbstract: We discuss construction of a derived Lagrangian intersection theory of moduli spaces of perfect complexes\, with support on divisors on compact Calabi-Yau threefolds. Our goal is to compute deformation invariants associated to a fixed linear system of divisors in CY3. We apply a Tyurin degeneration of the CY3 into a normal-crossing singular variety composed of Fano threefolds meeting along their anti-canonical divisor. We show that the moduli space over the Fano 4 fold given by total space of degeneration family satisfies a relative Lagrangian foliation structure which leads to realizing the moduli space as derived critical locus of a global (-1)-shifted potential function. We construct a flat Gauss-Manin connection to relate the periodic cyclic homology induced by matrix factorization category of such function to the derived Lagrangian intersection of the corresponding “Fano moduli spaces”. The later provides one with categorification of DT invariants over the special fiber (of degenerating family). The alternating sum of dimensions of the categorical DT invariants of the special fiber induces numerical DT invariants. If there is time\, we show how in terms of “non-derived” virtual intersection theory\, these numerical DT invariants relate to counts of D4-D2-D0 branes which are expected to have modularity property by the S-duality conjecture. This talk is based on joint work with Ludmil Katzarkov\, Maxim Kontsevich\, recent work with Jacob Krykzca\, and former work with Vladimir Baranovsky. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_121924/
LOCATION:Virtual
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-12.19.2024.png
END:VEVENT
END:VCALENDAR