Speaker: 邹佳良，中科院数学与系统科学研究院数学所

Inviter: 杨若涛

Title: Relative Langlands duality and Springer theory

Language: Chinese

Time & Venue: 2026.09.11 10:30-11:30 南楼N820

Abstract: Ben-Zvi, Sakellaridis, and Venkatesh (BZSV) proposed a relative Langlands duality relating certain hyperspherical varieties for a reductive group G to those for its Langlands dual group. A conjecture of Finkelberg, Ginzburg, and Travkin predicts that the top Borel–Moore homology groups of the associated Steinberg varieties are isomorphic as representations of the common Weyl group. This can be viewed as a representation-theoretic shadow of an expected Koszul duality. In this talk, I will discuss our ongoing work on verifying this conjecture for the dual pair of hyperspherical varieties underlying the theta correspondence and the Gan–Gross–Prasad branching problem. Our approach uses Springer theory to give geometric realizations of Weyl group representations arising from Hecke modules associated with these two problems over finite fields. This translates the conjecture into a comparison of the corresponding Hecke modules at q = 1. I will also explain how this picture suggests a categorical enhancement in the form of Koszul duality. This talk is based on joint work with Jiajun Ma and Zhiwei Yun.