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: 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: Torsion vanishing for some Shimura varietiesAbstract: We will discuss joint work with Linus Hamann on generalizing the torsion-vanishing results of Caraiani-Scholze and Koshikawa for the cohomology of Shimura varieties. We do this by applying various geometric methods to understand sheaves on Bun_G, the moduli stack of G-bundles on the Fargues-Fontaine curve. Our method showcases that […]

Title: Twisted Gan-Gross-Prasad conjecture and arithmetic fundamental lemma Abstract: The twisted Gan-Gross-Prasad (GGP) conjecture opens a way of studying (a twist of) central Asai L-values via descents and period integrals. Firstly, I will prove new cases of twisted GGP conjecture (joint work with Weixiao Lu and Danielle Wang), based on the relative trace formula approach […]

Title: On an application of the residue method. Abstract: When a period integral of an automorphic form converges and is not zero it is often related to a special value of an L-function and indicates that the automorphic form is a functorial transfer. When convergence fails it is still interesting to make sense of the […]