Time: 16:00-17:00, Thursday, August 22, 2024

Venue: Lecture Hall

Speaker: Cheng Chen  (Institut de Mathématiques de Jussieu-Paris Rive Gauche)

Abstact: The classical branching problem investigates the spectrum of the restriction of an irreducible representation of a compact group. The work of Gross-Prasad and Gan-Gross-Prasad expanded this framework into a conjecture for classical groups over local fields of characteristic zero. The first major breakthrough came from Waldspurger in the non-Archimedean special orthogonal cases. Since then, various approaches have been developed, leading to the conjecture being fully proven in all cases. In this talk, I will introduce an approach that applies uniformly to both Archimedean and non-Archimedean unitary and non-unitary Bessel and Fourier-Jacobi cases. This approach is grounded in the foundational works of Waldspurger, Moeglin-Waldspurger, and Gan-Ichino. The development of this approach includes some of my own work, as well as joint work with Luo, joint work with Chen and Zou, and joint work with Jiang, Liu, and Zhang.