The theory of automorphic forms and the Langlands program are fundamental subjects of modern number theory with Langlands’ principle of functoriality and reciprocity being central pillars of this area. However, despite the many results achieved in more than 40 years of intense efforts, its most deepest parts still remain elusive. Since the beginning, the Arthur-Selberg trace formula has played a key-role in the development of the subject. It is the stabilized twisted version of this formula that allows, together with the fundamental lemma proved by Ngô, the greatest number of applications. The Arthur-Selberg trace formula is a powerful tool towards establishing cases of Langlands functoriality/reciprocity : by comparing two trace formulas (e.g. the classification of the automorphic spectrum of classical groups by Arthur) ; to study the cohomology of Shimura varieties, by combining it with a Grothendieck-Lefschetz trace formula ; etc. Altough the trace formula made it possible to obtain remarkable results, new techniques and ideas have started to emerge that may renew our vision on the whole subject. The main aim of this conference will be to discuss current progress at the forefront of Langlands functoriality and the theory of trace formulas (in all its forms). This should in particular include :

– The “relative Langlands program” with the important progress made on the Gan-Gross-Prasad conjectures. As for the usual Langlands program, the relative trace formula (introduced by Jacquet) is a central tool whose reach and theoretical context remain to be fully investigated.

– Recent spectacular progess on the Langlands local correspondence with the work of Genestier-(V.)Lafforgue for function fields and Fargues-Scholze for number fields. This also includes recent impressive series of works towards establishing explicit local Langlands correspondences for supercuspidal representations by Kaletha et al and relations to the theory of endoscopy.

– Ways of going “beyond endoscopy” and proving new cases of functoriality. This includes Langlands original ideas but also the Braverman-Kazhdan approach through non-standard Poisson summation formulas and the new methods developped by Sakellaridis in the relative setting.

– New applications or extensions of the trace formula and the theory of endoscopy such as to the cohomology of arithmetic groups/Shimura varieties or in the context of covering groups.