Orateur
Description
The classical branching problem studies the restriction of an irreducible representation to a compact subgroup. The works of Gross-Prasad and Gan-Gross-Prasad generalized this framework into a conjecture for classical groups over local fields of characteristic zero. The first breakthrough was achieved by Waldspurger in the non-Archimedean special orthogonal cases. Since then, various approaches have been developed, leading to the complete proof of the conjecture in all cases.
In this presentation, I will introduce an approach that applies to both unitary and non-unitary cases, Archimedean and non-Archimedean, as well as Bessel and Fourier-Jacobi cases. This approach, based on the foundational works of Waldspurger, Mœglin-Waldspurger, and Gan-Ichino, utilizes the trace formula, endoscopy, the multiplicity formula, and the Theta correspondence. The development of this approach includes some of my work, as well as collaborative efforts with Luo, work in collaboration with Chen and Zou, and work in collaboration with Jiang, Liu, and Zhang.
