Time：14:00-15:45, Wednesday, March 12 2025
Venue: E10-312
Speaker：Cheng Shu, ITS
Title: Singularities of character varieties
Abstract: For any complex reductive group $G$ and any compact Riemann surface with genus $g>0$, we show that every connected component of the associated character variety is $\mathbb{Q}$-factorial and has symplectic singularities. We classify the connected components which have each of the following properties: being factorial, having terminal singularities, and admitting symplectic resolutions. The main results for $g>1$ were obtained by Herbig-Schwarz-Seaton via a different approach, while we use elliptic endoscopy to control the singularities caused by irreducible local systems with automorphism groups larger than the centre of $G$. Our treatment of the case $g=1$ is based on the results of Borel-Friedman-Morgan and Li-Nadler-Yun.
