走向现代数学学术报告 -古星助理教授（No. 674）

题目：Dickson invariants and Chern classes of the conjugation representations

报告人：古星 助理教授（西湖大学）

时间：2023年12月12日 14:00

地点：东校区D209

摘要：The theory of characteristic classes of the projective unitary group $PU(n)$ is fundamental yet very mysterious as of today. In this talk, we consider the Chern classes $\gamma_i$ of the conjugation representation of the projective unitary group $\pu{l}$, where $p$ is an odd prime. We show that the restriction of $\gamma_i$ on a maximal elementary abelian $p$ subgroup are expressed as Dickson invariants, a collection of purely algebraically defined elements in the polynomial ring $\F_p[x_1,\cdots,x_n]$. Furthermore, we present some relations in the cohomology algebra $H^*(B\pu{2};\F_p)$ involving the classes $\gamma_i$.

报告人简介：Xing Gu completed his doctorate degree at the University of Illinois at Chicago in 2017. He subsequently conducted postdoctoral research works at the University of Melbourne and the Max Planck Institute for Mathematics at Bonn. He has been an assistant professor at the Institute of Theoretical sciences, Westlake University since 2022. His main research interests is algebraic topology, with applications in algebraic geometry. His current research work concerns the characteristic theory of projective unitary groups.