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 […]