Organizers: Lin Chen, Will Donovan, Penghui Li, Peng Shan, Changjian Su, Wenbin Yan

Time: 10:30 am-11:30 am, Friday

Place: B627, Shuangqing Complex Building（双清综合楼B627教室), Yau Mathematical Sciences Center,  Tsinghua University

双清综合楼地址：北京市海淀区逸清南路西延6号院1号，双清公寓马路对面、清华附小（双清校区）西侧。

official seminar webpage,  which contains the zoom information for online talks

• 09/19 Sergey Oblezin (BIMSA)

Whittaker functions in representation theory, geometry and number theory

In my talk I report on an ongoing research project have been running jointly with A. Gerasimov and D. Lebedev. I present the key results and constructions restricting myself to the special case of GL(2,R). I start with introducing GL(2,R)-Whittaker function associated with a spherical principal series representation. Then I explain its role in the local Langlands correspondence and its geometric interpretation in terms of quantum cohomology of complex projective line. In the second part of my talk, I introduce the Hecke-Baxter for spherical principal series representations and its global extension for the GL(2)-Eisenstein series.

• 09/26 Hyun Kyu Kim (KIAS)

Frobenius homomorphisms for SL_n-skein algebras of surfaces

The $SL_n$-skein algebra $\mathscr{S}_q(S)$ of an oriented surface $S$ is a quantization of the $SL_n$-character variety of $S$. It is spanned by isotopy classes of framed links in the thickened surface $S \times (-1,1)$. When the quantum parameter $q$ is specialized at a root of unity $\omega$ (with some condition), there is a so-called Frobenius homomorphism $\mathscr{S}_1(S) \to \mathscr{S}_\omega(S)$, which can be viewed as a generalization of the Frobenius maps for quantum groups. We review its recent developments, and discuss some future directions. The talk is partially based on the joint work (arXiv:2504.08657) with Thang Lê and Zhihao Wang.

• 10/10 Yongchang Zhu (YMSC)

• 10/17 Liang Xiao (PKU)

• 10/24 Yun Gao (York University)

• 10/31 Gaston Burrull (BICMR)

• 11/07 Aron Heleodoro (SIMIS)

• 11/14

• 11/21

• 11/28 Xuanzhong Dai (RIMS)

• 12/05

• 12/12 Sian Nie (AMSS, CAS)

• 12/19

• 12/26

• 01/02

seminar arxiv: 2025 Spring, 2024 Fall, 2024 Spring, 2023 Fall, 2023 Spring, 2022 Fall, official page