Relative Trace Formula, Periods, L-Functions and Harmonic Analysis (1351)
Dates: 23-27 May 2016 at CIRM (Marseille Luminy, France)
Automorphic forms and Langlands fonctoriality is a very active area of contemporary international mathematical research at the crossroads of number theory, representation theory and arithmetic and algebraic geometry .
Endoscopy, a technique that allows to study certain instances of functoriality, was initiated by Langlands and Shelstad almost forty years ago, and is now at a mature state. Endoscopic functorialities are determined by character identities that are dual to transfer of conjugacy classes. Endoscopy is fundamental as it puts a structure (L-packet and A-packet) on "the set" of automorphic representations. The most recent highlight of the theory is the classification of the automorphic spectrum of orthogonal, symplectic (Arthur) and unitary groups (Mok) in terms of the automorphic spectrum of GL(n). The proof relies on highly sophisticated tools such as the stable version of the twisted Arthur-Selberg trace formula. lt depends also on deep results on local harmonic analysis such as: transfer of orbital integrals (Waldspurger) and the famous fundamental Iemma (whose most general statement was proved by Ngô by powerful geometric methods).
New techniques and methods are needed for further study of fonctoriality that complements or goes beyond endoscopy. The common motivation for the conference "Relative Trace Formula, Periods and L-Functions and Harmonic Analysis" is to study the "periods " of automorphic forms. The non-vanishing of certain periods should be characterized by functoriality. Moreover, special values of L-functions should be related to periods (a paradigm is on old result on Waldspurger of the relation between toric periods and central values of L-function of automorphic forms; a broad generalization is the so-called global Gross-Prasad conjecture).
The aim of the conference is to bring together people from different areas and places working on these or related questions to get some kind of state-of-the-art and merge to further results.
SO(2n + 1) × SO(2)