Title: Stability for Vlasov and Hartree equations Abstract: I focus on presenting the survival threshold of wave numbers found in mean field equations such as Vlasov and Hartree equations, which completely characterizes the large time behavior of linearized equations near non-trivial backgrounds into plasma oscillations, Landau damping, and phase mixing regime. I shall also mention progress […]
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, […]