On a geometric realization of the center of the small quantum group

• 主讲人：Prof. Peng Shan (Yau Mathematical Sciences Center)
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2022-06-02 20:00 - 2022-06-02 21:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/F98451EB7316CD31517990FA148AC092
Valid Until: 2026-07-31 23:59

 

Abstract: In Lie theory, the center of many important representation categories admits geometrical interpretations as singular cohomology of certain algebraic varieties. We will explain a new realization of this type, relating the center of the small quantum group to the cohomology of certain affine Springer fibres. As an application, we obtain a conjectural formula for the dimension of the center of the small quantum group. This is based on a joint work with R. Bezrukavnikov, P. Boixeda-Alvarez, and E. Vasserot.

 

Bio: Peng Shan is currently a Professor at Yau Mathematical Sciences Center, Tsinghua University. Her research interests lie in Geometric Representation Theory. In 2011, she received her Ph.D. from Paris Diderot University. After graduation, Peng Shan worked at MIT as C. L. E. Moore instructor. From 2011 to 2017, she was an associate researcher at the French National Center for Scientific Research. Also, she carried out research at the University of Caen-Normandie and Paris-Sud University. She is also the invited speaker at the ICM (2022). Prof. Shan Peng is on the editorial board of "J. Algebra" and has published many papers in top mathematics journals such as J. Amer. Math. Soc., Invent. Math., Duke Math. J. and Adv. Math.