Joint IAS/PU Number Theory

In this talk, I will focus on simultaneous non-vanishing results for Dirichlet L-functions at the central point 1/2. Specifically, I will describe non-vanishing results (conditional on GRH) for two L-functions associated to Dirichlet characters in the same Galois orbit, and simultaneous non-vanishing of four L-functions as we vary over characters \chi modulo q, conditional on GRH and the Ramanujan-Petterson conjecture. This is based on joint works with Bui-Ngo and Bui-Milinovich.