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Mathematics and Biology I: Morphometry, Morphogenesis and Mathematics Dates: February 23–March 11, 2026 Location: Harvard CMSA, Room G10, 20 Garden Street, Cambridge MA Mathematics, Morphometry and Morphogenesis is a 3-week program at the Harvard CMSA, which will bring together researchers from a few different communities with a common aim—to understand shape and its development and evolution in […] |
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Geometry and Quantum Theory Seminar Speakers: Max Hübner, CMSA Title: Bi-HKT Manifolds, Sigma Models, Large N=4 and their String Constructions Abstract: We continue our review of Witten's paper "Instantons and the Large N=4 Algebra". We discuss the realization of large N=4 supersymmetry in the context of supersymmetric sigma-models, and discuss and motivate string theoretic duals […] |
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New Technologies in Mathematics Seminar Speaker: Courtney Paquette, McGill University Title:Â Scaling Stochastic Momentum from Theory to LLMs Abstract:Â Given the massive scale of modern ML models, we now often get only a single shot to train them effectively. This limits our ability to sweep architectures and hyperparameters, making it essential to understand how learning algorithms scale […] |
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Differential Geometry and Physics Seminar Speaker: Mirjam Cvetic, University of Pennsylvania Title:Â Higher Symmetries, Eta Invariants and Anomaly Theories Abstract:Â In recent years, much progress has been made in understanding the extra-dimensional origin of higher symmetry structures of many quantum field theories (QFTs) obtained via geometric engineering. Among others, our understanding of anomaly structures in QFTs has […] |
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Member Seminar Speaker: Saman Habibi Esfahani, CMSA Title: Gauge theory, from low dimensions to higher dimensions and back Abstract: Almost thirty years ago, Donaldson and Thomas proposed extending powerful ideas from gauge theory, which had transformed the study of three- and four-dimensional manifolds, to higher dimensions, with the goal of defining new invariants of special […] |
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Colloquium Speaker: L. Mahadevan, Harvard Title: Inverse problems in soft and active matter Abstract: How can one grow a face or a flower from a flat sheet? Fold a sheet into an origami pattern? Control phase separation? Transport a drop of active matter? Steer an ant swarm? I will discuss potential answers to some of […] |
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Geometry and Quantum Theory Seminar Speaker: Sanjay Raman, Harvard Title: Solitonic Symmetry: Cohomology with TFT Coefficients Abstract: We review the formalism of https://arxiv.org/pdf/2307.00939, which develops the theory of solitonic symmetry in quantum field theory. The algebraic structure of solitonic symmetry is determined by the fusion of topological functionals in a given path-integral formulation of topological field theory, and […] |
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https://youtu.be/gXiVVZypHJg 2026 Ding Shum Lecture Date: March 4, 2026 Time: 4:00 pm Location: Harvard Science Center Hall D & via Zoom Webinar Speaker: Sanjeev Arora, Princeton Title: How could a Superhuman AI mathematician come about? Abstract: Can AI systems exceed the capabilities of the human experts who provided their training data? The talk will examine […] |
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Differential Geometry and Physics Seminar Speaker: Vivek Shende (Syddansk Universitet & UC Berkeley) Title: Fukaya categories and higher representation theory Abstract: I will explain how Lagrangian Floer homology in certain monopole moduli spaces recovers the Khovanov homology and its relatives, by a description strikingly similar to the Oszvath-Szabo Heegard-Floer theory. I will also explain how the […] |
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Freedman Seminar Speakers: Mattie Ji (Penn) and Jeongwan Haah (Stanford) Mattie Ji Title: Quantum Cellular Automata via Algebraic K-Theory Abstract:Â Algebraic K-theory, on a very high level, is the study of how to break apart and assemble objects linearly, which makes the field amenable to classification questions. In this work, we apply this methodology to study […] |
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Quantum Field Theory and Physical Mathematics Seminar Speaker: Davide Gaiotto (Perimeter Institute) |
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https://youtu.be/V6uVihYhSEM CMSA/Tsinghua Math-Science Literature Lecture Date: March 10, 2026 Time: 8:45 - 10:15 am ET Location: Harvard Science Center Hall A, 1 Oxford Street, Cambridge MA &Â via Zoom Webinar Speaker: Martin Bridson FRS is the Whitehead Professor of Pure Mathematics at Oxford and President of the Clay Mathematics Institute. Title: Profinite rigidity: Chasing finite […]
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Joint Math/CMSA Geometry and Quantum Theory Seminar Speaker: Lorenzo Riva, Harvard CMSA Title: TQFTs do not detect the Milnor sphere Abstract: I will talk about the recent paper of Gripaios and Randall-Williams with that title, where they prove that a functorial TQFT (i.e. a symmetric monoidal functor from the n-dimensional bordism category into a suitably […] |
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https://youtu.be/3j1VW9REm7s Date: March 11, 2026 Time: 5:00–6:00 pm Location: Harvard Science Center Hall C, 1 Oxford St., Cambridge MA & via Zoom Webinar Speaker: Javier Gómez-Serrano, Brown University Title: Navier-Stokes Existence or Breakdown Abstract: The Navier-Stokes equations have been the cornerstone of fluid dynamics for over a century, accurately describing the motion of viscous fluids […] |
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Differential Geometry and Physics Seminar Speaker: Surena Hozoori (Brandeis) Title: Strongly adapted contact geometry of Anosov 3-flows Abstract: We will discuss some recent developments in the contact geometric theory of Anosov 3-flows, whose roots go back to the works of Mitsumatsu and Eliashberg-Thurston in the mid 1990s. In particular, we provide a contact geometric characterization […] |
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Quantum Field Theory and Physical Mathematics Seminar Speaker: Kasia Budzik (Harvard University) Title: Finite N indices from branes and negative branes Abstract: Finite-N effects in large-N gauge theories, such as trace relations, are expected to be holographically dual to non-perturbative phenomena in string theory, such as Giant Graviton branes. A convenient setting to study these […] |
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New Technologies in Mathematics Seminar Speaker: Emmanuel Abbé, EPFL, Institute of Mathematics and School of Computer and Communication Sciences & Apple Title: Dynamic reasoning Abstract: 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. Relying solely on the presence of […] |
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Algebra Seminar Speaker: Dawei Chen, Boston College Title: Moduli of subcanonical points Abstract: Subcanonical points are special Weierstrass points on smooth algebraic curves whose semigroups are symmetric. In this talk, I will explain the rich geometry of the moduli space of subcanonical points, with a focus on its connected components, birational geometry, topology, and the deformation theory […] |
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Joint Math/CMSA Geometry and Quantum Theory Seminar Speaker: Keyou Zeng (CMSA) Title: Line operators in holomorphic QFT Abstract: We will discuss the recent work (arxiv:2508.11749), which defines the so called dg shifted Yangian. I will discuss their origin from the study of 3d holomorphic topological field theories, a variant of 3d TQFT. AÂ dg shifted Yangian […] |
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Differential Geometry and Physics Seminar Speaker. Emily Autumn Windes (New Uzbekistan University) Title: Gauge theory on Hyperkähler manifolds Abstract: In this talk, I describe various distinguished classes of connections on Hyperkähler manifolds and their dimensional reductions. Then, I describe a construction of new examples of Sp(2)-instantons, primitive HYM connections, and Spin(7)-instantons with symmetry on the manifold T*CP2. This talk […]
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Algebra Seminar Speaker: Matt Broe, Boston University Title: The Beilinson-Bloch conjecture for some non-isotrivial varieties over global function fields Abstract: The Beilinson-Bloch conjecture is a generalization of the Birch and Swinnerton-Dyer conjecture, which relates the ranks of Chow groups of smooth projective varieties over global fields to the order of vanishing of L-functions. We prove […] |
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Freedman Seminar Speaker: Robert Gompf, UT Austin Title: Exotic R^4's are unclassifiable Abstract:Â 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. |
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Quantum Field Theory and Physical Mathematics Seminar Speaker: Tianqin Zhu, Columbia University Title: K-theoretic stable envelopes, quantum loop groups and wall-crossings Abstract: The stable envelope is an important tool in both geometric representation theory and the enumerative geometry. One of the most important application is that it generates the geometric quantum loop group via the FRT […] |
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Joint Math/CMSA Geometry and Quantum Theory Seminar Speaker: Vasily Krylov, Harvard Title: 1-shifted Yangians from 1-shifted Lie bialgebras Abstract: In the previous talk, Keyou explained that the fusion of line defects in 3d holomorphic–topological field theories is expected to be governed by so-called DG-shifted Yangians. Following arXiv:2503.08770, I will present examples of such DG-shifted Yangians arising from […] |
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CMSA Q&A Seminar Speaker: Lauren Williams, Harvard Topic: The First Proof Project |
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Member Seminar Speaker: Elliott Gesteau, CMSA Title: Failures of Holographic Emergence Abstract: Recent developments have taught us that some semiclassical spacetimes, in particular those containing closed universe components, cannot emerge from a holographic correspondence. In this talk, I will explain how one can get to this conclusion by using either quantum information theory or properties of the large N limit of […] |
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