Local-global principles for periods of automorphic forms

BIMSA-YMSC Tsinghua Number Theory Seminar

Organizers：

Hansheng Diao, Heng Du, Yueke Hu, Bin Xu, Yihang Zhu

Speaker：

Nadir Matringe (NYU Shanghai)

Time：

Mon., 10:00-11:00 am, Dec. 1, 2025

Venue：

B627, Shuangqing Complex Building A

Title:

Local-global principles for periods of automorphic forms

Abstract:

In a famous paper, Waldspurger proved a local-global principle for a cuspidal automorphic representation of an inner form of GL(2), to support a non-vanishing toric period integral. This was generalized in two directions. The first direction is the famous global Gan-Gross-Prasad conjectures, proven in many cases, but maybe not yet for special orthogonal groups. The second, which is in a sense more natural, leads to the so-called Guo-Jacquet conjecture for automorphic representations of inner forms of GL(n), so far proven under local restrictions. I will present a local-global principle for non-vanishing of period integrals attached to several symmetric subgroups of inner forms of GL(n), in particular generalizing that of Waldspurger. This in particular gives a complete proof of the direct implication of the Guo-Jacquet conjecture. This work is a collaboration with Omer Offen and Chang Yang.