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Geometry and Quantum Theory Seminar Speaker: Daniel Spiegel, Harvard Title: The Quasi-Adiabatic Theorem and All That Abstract: Yosuke Kubota has recently made progress on understanding Kitaev's conjecture by constructing a loop spectrum consisting of spaces of quantum spin systems, indexed by spatial dimension of the lattice (arXiv: 2503.12618). After a brief reminder on the C*-algebraic […] |
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CMSA Spring Welcome Back Event Date: Jan 28, 2026 Time: 4:00 pm Location: CMSA Common Room, 20 Garden Street, Cambridge MA All CMSA and Math affiliates are invited. |
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Differential Geometry and Physics Seminar Speaker: Tristan Collins, University of Toronto Title: Complete Calabi-Yau Metrics and Optimal Transport Abstract: I will discuss the connection between optimal transport and the existence of complete Calabi-Yau metrics on log Calabi-Yau varieties. I will explain how the geometric problem of constructing complete Calabi-Yau metrics gives rise to problems in the boundary […] |
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Member Seminar Speaker: Stephen Landsittel Title: Some results about saturation Abstract: Given a local ring R we can ask when saturation of ideals in R commutes with other operations on ideals (such as extension to a ring containing R). We show that the condition that extension of ideals along a ring map R \to S […]
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Freedman Seminar Speakers: Michael Freedman, CMSA and Slava Krushkal, University of Virginia (2-3 pm and 3:15-4:15 pm) Title: Formulating 4D surgery for AI agents Abstract: The topological category surgery exact sequence is still open for free groups (and most groups of exponential growth). The lack of knowledge is about both surgery and s-cobordism; and the […] |
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Quantum Field Theory and Physical Mathematics Seminar Speaker: Pierre Vanhove (Institute of Theoretical Physics - Saclay) Title: Reflexive Polytopes and the Convergence of Feynman Integrals Abstract: In the parametric representation, Feynman integrals can be viewed as Euler integrals defined by the Symanzik polynomials of a graph. The convergence properties of these integrals are intimately tied […]
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Colloquium Speaker: Olivier Bernardi, Brandeis University Title: Bijections for hyperplane arrangements of Coxeter type Abstract: This talk is about real hyperplane arrangements whose hyperplanes are of the form {xi −xj = s} or {xi +xj = s}. We describe a bijective framework for a large family of such arrangements which we call transitive. For each transitive arrangement A, […] |
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Geometry and Quantum Theory Seminar Speakers: Dan Freed and Bowen Yang, Harvard CMSA Title: More on Kubota's spectrum of invertible states Abstract: Bowen will explain a construction aptly dubbed “Kitaev’s pump” in Kubota’s paper. Time permitting, Bowen will demonstrate its ubiquity throughout the study of topological phases, where it appears under various guises. In the second hour, […] |
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https://youtu.be/14-9iCoclFE Date: February 4, 2026 Time: 5:00–6:00 pm Location: Harvard Science Center Hall C, 1 Oxford St., Cambridge MA Speaker: Barry Mazur, Harvard University Title: About the Birch and Swinnerton–Dyer Conjecture Abstract: In the 1950s Bryan Birch and Peter Swinnerton–Dyer made computations that suggested a striking connection between a basic global invariant of an elliptic […] 
CMSA Q&A Seminar Speaker: Ludmil Katzarkov, University of Miami Title: New Birational Invariants Abstract: We will introduce the origins of the main ideas of the theory of atoms. Applications follow. Equivariant and mixed atoms will be considered.
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New Technologies in Mathematics Seminar Speaker: George Tsoukalas, UT Austin Dept. of Computer Science and Google DeepMind. Title: Automated Theory Formation and Interestingness in Mathematics Abstract: Advances in modern learning systems are beginning to demonstrate utility for select problems in research mathematics. A broader challenge is that of developing new theories automatically. This area has a rich […] |
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Differential Geometry and Physics Seminar Speaker: Monica Jinwoo Kang, Texas A&M University Title: Index from a point Abstract: We argue that protected data of 4d N=2 SCFTs admits a purely algebro-geometric characterization. We conjecture that both the Macdonald index (and hence the Schur index) and the Higgs branch are encoded by a bifiltered affine scheme determined by […]
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Differential Geometry and Physics Seminar Speaker: Yinan Wang, Peking University Title: On E7+1/2 gauge theory Abstract: We propose that an exotic gauge theory based on the intermediate Lie algebra E7+1/2 naturally appears in the landscape of 6d F-theory. We give strong evidence of this proposal with 6d anomaly cancellation, dual M-theory geometry and elliptic genus of the single-string […] |
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Member Seminar Speaker: Ahsan Khan, Harvard CMSA Title: Lie algebra cohomology and Seiberg-Witten theory Abstract: I will discuss how a certain (relative) Lie algebra cochain complex categorifies the Schur index of N=2 supersymmetric gauge theory. For the special case of Seiberg-Witten theory I will provide a conjectured description of this cohomology. |
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Quantum Field Theory and Physical Mathematics Seminar Speaker: Shaoyun Bai (MIT) Title: On the p-curvature of quantum connections of CY threefolds Abstract: The small quantum connection of Calabi-Yau varieties has integral coefficients, thus admits reduction mod a prime number p. A fundamental invariant associated with flat connections over characteristic p is the p-curvature, which lies […]
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Colloquium Speaker: Pankaj Metha, Boston University Title: Phase Transition to Chaos in Complex Ecosystems with Non-reciprocal Interactions Abstract: Nonreciprocal interactions between microscopic constituents can profoundly shape the large-scale properties of complex systems. In this pedagogical chalk talk, I will discuss recent work from our group on phase transitions and chaos in high-dimensional ecosystems with non-reciprocal […] |
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CMSA Q&A Seminar Speaker: James Eldred Pascoe, Drexel University Title: (What is) The tracial fundamental group and free universal monodromy? Abstract: We introduce the tracial fundamental group to classify the analytic continuation of functions that are locally behave like the trace of natural matrix valued functions. While globally defined natural matrix-valued functions (known as free […]
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New Technologies in Mathematics Seminar Speaker: Yiannis Vlassopoulos, Athena Research Center Title: ReLU and Softplus neural nets as zero-sum, turn-based, stopping games Abstract: 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 […] |
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Differential Geometry and Physics Seminar Speaker: Gabor Szekelyhidi, Northwestern University Title: Gromov-Hausdorff limits of collapsing Calabi-Yau fibrations Abstract: A well studied problem is the metric behavior of Calabi-Yau metrics on a fibration in a family of Kahler classes that collapses the fibers. I will discuss recent progress showing that the Gromov-Hausdorff limit can be identified […] |
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Member Seminar Speaker: Lorenzo Riva, Harvard CMSA Title: A leisurely stroll through the theory of adjunctions Abstract: Adjoint functors (and, more generally, adjunctions in a 2-category) are ubiquitous in algebra and topology. In this talk I will give an overview of the basics of adjunctions, with the ultimate goal being understanding the statement of the […] |
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Geometry and Quantum Theory Seminar Speaker: Saman Habibi Esfahani (CMSA) Title: Geometric structures on gauge theoretic moduli spaces Abstract: Motivated by Witten’s study of instantons on S3 x S1, we survey some classical and recent results, programs, and conjectures on geometric structures, such as symplectic and hyperkahler, on moduli spaces of instantons and monopoles on various […] |
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CMSA Q&A Seminar Speaker: Dan Freed, Harvard Topic: How does one navigate the job market as a postdoc in 2026? |
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Differential Geometry and Physics Seminar Speaker: Greg Moore, Rutgers University Title: Topics in the Relation of Four-Manifold Invariants and Supersymmetric Field Theory Abstract: We will begin with a review of topological twisting as a choice of background fields. We then review the standard paradigm for the formulation of Donaldson invariants as correlation functions in twisted supersymmetric […]
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Geometry and Quantum Theory Seminar Speaker: William Stewart Title: Constructing oriented TQFTs from twisted pivotal tensor categories Abstract: The cobordism hypothesis classifies n-dimensional oriented TQFTs in terms of SO(n) homotopy fixed point data. An SO(2) homotopy fixed point structure on a finite tensor category gives rise to a twisted pivotal structure (a more general notion […] |
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Member Seminar Speaker: Blake Bordelon, CMSA Title: Theory of Task-Adapted Dynamics in Large Recurrent Neural Networks Abstract: Recurrent neural networks (RNNs) encode expressive and flexible dynamical systems which can adapt to perform tasks by modifying the internal connections between neurons. In this work we analyze the structure of the dynamical systems encoded in RNNs after […] |
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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: Scaling Stochastic Momentum from Theory to LLMs Abstract: 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: Higher Symmetries, Eta Invariants and Anomaly Theories Abstract: 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 […] |