## MAIN CONFERENCE

Relative Trace Formula, Periods, L-Functions and Harmonic Analysis (1351)

**Dates: 23-27 May 2016 at CIRM (Marseille Luminy, France)**

DescriptionAutomorphic 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. |
## Scientific committee
- Hervé Jacquet (Columbia University)
- Jean-Pierre Labesse (Prof. Emeritus, Aix-Marseille)
- Colette Moeglin (IMJ-PRG Paris)
## Organizing committee
- Pierre-Henri Chaudouard (Université Paris Diderot)
- Volker Heiermann (Aix-Marseille Université)
- Dipendra Prasad (TIFR Mumbai)
- Yiannis Sakellaridis (Rutgers University Newark & National Technical University of Athens)
## Speakers
- James Arthur (University of Toronto)
*-***VIDEO**
Beyond Endoscopy and elliptic terms in the trace formula - Raphaël Beuzart-Plessis (CNRS, National University of Singapore)
The local Gan-Gross-Prasad conjecture for unitary groups - VIDEO- Masaaki Furusawa (Osaka City University)
On special Bessel periods and the Gross-Prasad conjec- ture for SO(2n + 1) × SO(2) - Wee Teck Gan (National University of Singapore) -
**VIDEO**
Theta lifts of tempered representations and Langlands parameters- Nadia Gurevic (Ben Gurion University)
Poles of the standard L-function for G2 and the image of functorial lifts- Jeffrey Hakim (American University Washington DC)
Constructing Tame Supercuspidal Representations- Michael Harris (IMJ-PRG Paris)
Special values of Rankin-Selberg L-functions and automorphic periods- Atsushi Ichino (Kyoto University)
The automorphic discrete spectrum of Mp(2n)- Dihua Jiang (University of Minnesota)
On the Central Value of Tensor Product L-functions and the Langlands Functoriality- Wen-Wei Li (Chinese Academy of Science)
Prehomogeneous zeta integrals with generalized coefficients- Nadir Matringe (Université de Poitiers)
Distinction of the Steinberg representation for GL(n) and its inner forms- Fiona Murnaghan (University of Toronto) -
**VIDEO**
Tame relatively supercuspidal representations- Omer Offen (Technion-Israel Institute of Technology)
On gamma factors, root numbers and distinction- Eric Opdam (University of Amsterdam)
On the spherical automorphic spectrum supported in the Borel subgroup- Jean-Loup Waldspurger (CNRS, IMJ-PRG Paris)
Caractères des représentations de niveau 0- Chen Wan (University of Minnesota)
Multiplicity one theorem for the Ginzburg-Rallis model- Hang Xue (Max Planck Institut)
Approximating smooth transfer in Jacquet--Rallis relative trace formulas- Shunsuke Yamana (Kyoto University)
On the lifting of Hilbert cusp forms to Hilbert-Siegel cusp forms- Shou-Wu Zhang (Princeton University) -
**VIDEO**
Congruent number problem and BSD conjecture- Wei Zhang (Columbia University)
Cycles on the moduli of Shtukas and Taylor coefficients of L-functions- Michal Zydor (Weizmann Institute of Science)
The Jacquet-Rallis trace formula |