Time：December 30, Monday, 16:00-17:00  

Venue: Lecture Hall

Title: Theta correspondence and Springer correspondence

Speaker: Jialiang Zou 邹佳良 (University of Michigan)

Abstract: Let V and W be an orthogonal and a symplectic space, respectively. The action of G=O(V)\times Sp(W) on V\otimes W provides an example of G-hyperspherical varieties introduced by D. Ben-Zvi, Y. Sakellaridis, and A. Venkatesh (BZSV for short). It is the classical limit of theta correspondence from the perspective of quantization.. I will explain a geometric construction motivated by theta correspondence over finite fields, which describes how principal series representations behave under theta correspondence using Springer correspondence. 

BZSV proposed a relative Langlands duality linking certain G-hyperspherical varieties M with their dual G^\vee-hyperspherical varieties M^\vee. A remarkable instance of this duality is that the hyperspherical variety underlying theta correspondence is dual to the hyperspherical variety  underlying the branching problem in the Gan-Gross-Prasad conjecture. I will discuss how these results fit into the broader framework of this relative Langlands duality. This is an ongoing  joint work with Jiajun Ma, Congling Qiu, and Zhiwei Yun.