Title: Canonical representations of surface groups.Abstract: For $Sigma_{g,n}$ a genus $g$ surface with $n$ punctures, we study the character variety parameterizing representations of $pi_1(Sigma_{g,n})$. This character variety has a natural action of the fundamental group of the moduli space of curves. In joint work with Josh Lam and Daniel Litt, we aim to describe the points with […]
Title: Twisted GGP conjecture for unramified quadratic extensions Abstract: The twisted Gan--Gross--Prasad conjectures consider the restriction of representations from GL_n to a unitary group over a quadratic extension E/F. In this talk, I will explain the relative trace formula approach to the global twisted GGP conjecture. In particular, I will discuss some differences between the […]
Title: Introduction to the trace formula. (Cont.)Abstract: In the first talk I presented some useful notions and translations in the theory of automorphic representations (Hecke operators and p-adic groups, locally symmetric spaces and adelic quotients, etc.). In this talk, I will give a general introduction to trace formulas, and some of the questions that we […]