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Relative Trace Formula, Periods, L-Functions, Harmonic Analysis, and Langlands Functoriality (1351)
Formule des traces relatives, Périodes, Fonctions L, analyse harmonique et fonctorialité de Langlands

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 cross-roads of number theory, representation theory, 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).


Beyond endoscopy and elliptic terms in the trace formula 

The local Gan-Gross-Prasad conjecture for unitary groups 

On special Bessel periods and the Gross-Prasad conjecture forSO(2n + 1) × SO(2)

Theta lifts of tempered representations and Langlands parameters

Poles of the standard L-function for G2 and the image of functorial lifts

Constructing Tame Supercuspidal Representation

Special values of Rankin-Selberg L-functions and automorphic periods

The automorphic discrete spectrum of Mp(2n)

On the Central Value of Tensor Product L-functions and the Langlands Functoriality

Prehomogeneous zeta integrals with generalized coefficients

  • Nadir Matringe (Université de Poitiers)

Distinction of the Steinberg representation for GL(n) and its inner forms

Tame relatively supercuspidal representations

  • Omer Offen (Technion-Israel Institute of Technology)

On gamma factors, root numbers and distinction

On the spherical automorphic spectrum supported in the Borel subgroup

Caractères des représentations de niveau 0

Multiplicity one theorem for the Ginzburg-Rallis model

Approximating smooth transfer in Jacquet-Rallis relative trace formulas

On the lifting of Hilbert cusp forms to Hilbert-Siegel cusp forms

Congruent number problem and BSD conjecture

Cycles on the moduli of Shtukas and Taylor coefficients of L-functions

The Jacquet-Rallis trace formula