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YMSC Topology Seminar | Dickson Invariants and Chern Classes of the Conjugation Representations

来源: 06-04

时间:Monday, 16:00-17:00 June 3, 2024

地点:Zoom meeting ID: 405 416 0815 Password: 111111;C654, Shuangqing Complex Building A 清华大学双清综合楼A座 C654报告厅

组织者:陈伟彦、高鸿灏、黄意、林剑锋

主讲人:Xing GU 古星 (Westlake)

Abstract:

The theory of characteristic classes of the projective unitary group PU(n) is fundamental yet very mysterious as of today. We will review recent progresses on the study on this topic, and consider the Chern classes γi of the conjugation representation of the projective unitary group PU(p^l), where p is an odd prime. We show that the restriction of γi on a maximal elementary abelian p subgroup are expressed as Dickson invariants, a collection of purely algebraically defined elements in the polynomial ring Fp[x1, · · · , xn]. Furthermore, we present some relations in the cohomology algebra H∗(BPU(p^2); Fp) involving the classes γi.

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