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
Title: Three theorems about asymptotic expansions of harmonic functions at the boundaryAbstract: Consider a harmonic function on a domain, vanishing along a part of its boundary, and a point on that part of the boundary which is asymptotically conical. I will explain that under a very mild notion of "asymptotically conical," the harmonic function has […]
Title: On the generalized Beauville decomposition.Abstract: Over 30 years ago, the work of Beauville and Deninger-Murre endowed the cohomology of an abelian scheme a (motivic) decomposition which splits the Leray filtration. This structure, now known as the Beauville decomposition, is induced by algebraic cycles obtained from the Fourier-Mukai coherent duality. In recent years, the study of Hitchin […]