Title: The Geometry of Theta Correspondence for Principal Series over Finite Fields Abstract: In this talk, we explore the finite field theta correspondence between principal series representations. We begin by categorifying the relevant Hecke algebra bimodules associated with this correspondence. Utilizing characteristic cycle maps, we provide a detailed description of the theta correspondence for principal […]
Title: From Instability to Singularity Formation in Incompressible FluidsAbstract: In this talk, I will first review the singularity formation problem in incompressible fluid dynamics, describing how particle transport poses the main challenge in constructing blow-up solutions for the 3d incompressible Euler equations. I will then outline a new mechanism that allows us to overcome the effects of […]
Title: ell-adic topological Jacquet-Langlands duality Abstract: I will describe the construction of an "ell-adic topological Jacquet-Langlands (TJL) dual" of each finite CW-complex. One effect of the TJL dual is that the representations of the Morava stabilizer group, which arise in the height n Morava E-theory of a finite spectrum X, get turned into continuous […]
Infinite dimensional representations of semisimple Lie algebras
Title: Mean curvature flow with multiplicity 2 convergence Abstract: Mean curvature flow (MCF) has been widely studied in recent decades, and higher multiplicity convergence is an important topic in the study of MCF. In this talk, we present two examples of immortal MCF in R^3 and S^n x , which converge to a plane and a […]
Title: The integral converse theorem and no-shadowing bounds for polynomials and L-functions Abstract: I will outline an alternative argument for the complex-analytic ingredient of the "unbounded denominators theorem" joint with Frank Calegari and Yunqing Tang, and then a refinement of the result as a converse theorem for Dirichlet series with almost-integer coefficients. This is followed […]
Title: On linear and non-linear stability of collisionless systems on black hole exteriors. Abstract: I will present upcoming linear and non-linear stability results for collisionless systems on spherically symmetric black holes. On the one hand, I will discuss the decay properties of massive Vlasov fields on the exterior of Schwarzschild spacetime. On the other hand, I will discuss […]
Title: Constructing (infinity,n)-categories with desired properties Abstract: In this talk I want to describe a specific example of a symmetric monoidal (infinity,3)-category of generalized spans with local systems (a la Haugseng) where the local systems compose with a push-pull formula similar to the Fourier-Mukai transform of algebraic geometry. The motivation comes from physics and functorial […]
Title: On a Mountain-pass Theorem in Hyperbolic Space and its Application
Plancherel formula 1