Seminario Teoría de Números
On the Endoscopic Classification of Representations of Classical Groups
Ponente: Alberto Minguez (Universidad de Sevilla - Universidad de Viena)Fecha: viernes 08 de mayo de 2026 - 12:30Lugar: Aula Naranja, ICMAT
Resumen:
The so-called endoscopic classification of representations of classical groups (symplectic, orthogonal, and quasi-split unitary groups) is a fundamental result due to James Arthur. It is the culmination of several decades of effort, including monumental achievements such as the stabilization of the (twisted) trace formula and the proof of the fundamental lemma. This breakthrough has had a profound impact on both representation theory and number theory. Essentially, it provides a precise description of the irreducible representations of these groups over local fields, as well as of the discrete automorphic representations over number fields, organizing them into what are known as A-packets.
For many years, the validity of this result depended on several unproven technical conjectures related to the construction and identification of these A-packets in the non-Archimedean case. However, in recent joint work with Atobe, Gan, Ichino, Kaletha, and Shin, we have completed these missing pieces. Thus, Arthur’s result now depends only on a single remaining unresolved aspect: the so-called weighted fundamental lemma.
In this talk, I will present the main ideas behind Arthur’s classification and explain the obstacles that have been resolved.
