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.
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 […]
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 […]
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 […]
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 […]
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 […]
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 […]
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 […]
CMSA Q&A Seminar Speaker: Dan Freed, Harvard Topic: How does one navigate the job market as a postdoc in 2026?
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 […]
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 […]
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 […]