RTG Seminar on Number Theory Seminar

The goal of the S-V conjectures is to understand the relation between automorphic periods and L-values, as well as questions about distinction, both locally and globally. The motivating theorem is that of Tunnell-Saito-Waldspurger (T-S-W) for GL_2 and its inner forms, later generalized by the Gan-Gross-Prasad (G-G-P) and Ichino-Ikeda (I-I) conjectures. The SV conjectures are a further vast generalization of this circle of ideas to the setting of spherical varieties, though not yet formulated at the same level of precision. I will start by recalling the work of T-S-W, G-G-P and I-I to put things in context, then explain how the S-V conjectures generalize all of this. Speaker(s): Kartik Prasanna (UM)