Title: Speculations on Computations with the Relative Trace Formula. Abstract: This is a continuation of the talk from 9/15. I will discuss how many statistics of automorphic representations have been computed previously using "explicit" forms of Arthur's trace formula. I will then present a very speculative plan to develop similar "explicit" versions of relative trace […]
Title: Kapustin-Witten (KW) and Kapustin-Rozanksy-Witten (KRS) theory path to knot homologyAbstract: My talk is based on the joint project with Lev Rozansky. As a motivation, I will interpret KRS theory as KW theory with defects. Then I will explain how we rigorously construct 3D TQFT, which is a KRS theory with targets Hilbert scheme of […]
Title: Why you should take Differential EquationsAbstract: A first encounter with differential equations often leaves the impression that differential equation is just integrating with extra steps. In this talk we'll show that what it means to "solve" a differential equation is more subtle (and mathematically interesting) than it initially appears. We'll also describe how these different types of "solutions" contribute to the […]
Title: Minimal model program for algebraically integrable foliations and generalized pairs.Abstract: In this talk, I will discuss my recent research that establishes the minimal model program for Q-factorial foliated dlt algebraically integrable foliations and log canonical generalized pairs. This is joint work with G. Chen, J. Han, and L. Xie.
Title: Root Number Correlation Bias of Fourier Coefficients of Modular FormsAbstract: In a recent machine learning based study, He, Lee, Oliver, and Pozdnyakov observed a striking oscillating pattern in the average value of the P-th Frobenius trace of elliptic curves of prescribed rank and conductor in an interval range. Sutherland discovered that this bias extends to […]
Title: Well-Posedness of the 3D Peskin ProblemAbstract: This work introduces the 3D Peskin problem: a two-dimensional elastic membrane immersed in a three-dimensional steady Stokes flow. We obtain the equations that model this free boundary problem and we show that these equations admit a boundary integral reduction. This provides an evolution equation for the elastic interface. We also […]
Title: Spherical functions on spherical varieties I. Abstract: I will introduce the Gross-Prasad conjecture and its enhanced form- Ichino-Ikeda conjecture. I will then introduce the general period conjecture made by Sakellaridis-Venkatesh, we will see that the unramified Plancherel formula proved by Sakellaridis plays an important role in the formulation of the conjecture, which is a consequence of his study […]
Title: Bulk-edge correspondence and an alternative proof of Bott periodicity theorem via Quot schemesAbstract: The study of topological matter is one example of the application of algebraic topology in physics. The bulk-edge correspondence, which asserts that the bulk index of a topological matter coincides with its edge index, has been formulated mathematically in various forms […]
Title: Condensed abelian groups II Abstract: In the previous talk, we learned about how k-Condensed Abelian Groups are abelian categories of an especially nice sort. In this talk, I will discuss how this fixes issues in some of our motivating problems and endows additional structure on the category that we will use later. Time permitting, […]
Title: Rigid-analytic analogue of Artin-Grothendieck vanishing Abstract: The classical theorem of Andreotti and Frankel says that any Stein complex manifold has homotopy type of a CW complex of real dimension ≤ dimX. In particular, this implies that the cohomology groups H^i(X, A) vanish for any abelian group A and any i > dimX. This vanishing […]