Title: Fourier Interpolation and the Weil Representation Abstract: In 2017, Radchenko-Viazovska proved a remarkable interpolation result for even Schwartz functions on the real line: such a function is entirely determined by its values and those of its Fourier transform at square roots of integers. We give a new proof of this result, exploiting the fact […]

Title: Kudla-Rapoport conjecture at bad reduction primes Abstract: The Kudla-Rapoport conjecture is a local analogue of arithmetic Siegel-Weil formula which relates arithmetic intersections of special cycles with derivatives of local densities. The original conjecture is formulated when the underlying Rapoport-Zink space has good reduction and proved by Chao Li and Wei Zhang. However, it is […]

Title: Laumon sheaf and the mod p Langlands program for GL_2 of a finite degree extension of Qp Abstract: Let E be a finite degree extension of Qp. Given a mod p representation of the absolute Galois group of E we construct a sheaf on a punctured absolute Banach-Colmez space that should give the first […]

Title: On the vanishing of Selmer groups for odd orthogonal Galois representations Abstract: Let $pi$ be a cuspidal automorphic representation of $Sp_2n$ over $mathbb{Q}$ which is holomorphic discrete series at infinity, and $chi$ a Dirichlet character. Then one can attach to $pi$ an orthogonal $p$-adic Galois representation $rho$ of dimension $2n+1$. Assume $rho$ is irreducible, […]

Title: Automorphic forms, motives and periods Abstract: I shall try to give an overview of parts of the Langlands program in a way that suggests future directions and applications. Among these are motivic periods, which I will discuss in general terms. Then, time permitting, I will discuss a conjectural construction of the automorphic and motivic […]

Title: Analytic de Rham stack Abstract: In this talk I will present a new geometric construction in analytic geometry that encodes different theories of analytic D-modules, analogous to the classical algebraic de Rham stack of Simpson.  I will explain some of their main features such as theories of six functors, the relation with more classical theories […]