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: Modularity of trianguline Galois representations Abstract: The Fontaine-Mazur conjecture (proved by Kisin and Emerton) says that (under certain technical hypotheses) a Galois representation rho: Gal_Q -> GL2(Qp) is modular if it is unramified outside finitely many places and de Rham at p. I will talk about what this means, and I will discuss an […]