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 […]