Lin Weng, Kyushu U.

Mar. 16 in MS 6221

Title: Stability and Arithmetic

Abstract: In this talk, we will explain the key role played by stability in arithmetic. There are two parts: Globally, we talk about how stability leads to non-abelian zetas for number fields and certain abelian zetas for (reductive group, maximal parabolic)s, which exposes a hidden role played by Symmetry in the Riemann Hypothesis; Locally, we talk about how stability of filtered (phi,N;omega)-modules leads to a conjectural Micro Reciprocity Law, characterizing de Rham representation, as a central part of our Tannakian category approach to a general non-abelian CFT for p-adic number fields.