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Geometric Representation Theory Seminar

Organizers：

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

Speaker：

Hyun Kyu Kim (KIAS)

Time：

Fri., 10:30-11:30 am, Sept. 26, 2025

Venue：

B627, Shuangqing Complex Building A

Title:

Frobenius homomorphisms for SL_n-skein algebras of surfaces

Abstract:

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.