动力系统讨论班    

题目：The Automorphism Equivariant Hitchin Index

报告人： William Elbæk Mistegård教授（南丹麦大学）    

摘要：Let T be the one-dimensional complex torus. We consider the action of an automorphism f of a Riemann surface X on the cohomology of the T-equivariant determinant line bundle over the moduli space M of rank two Higgs bundles on X with fixed determinant of odd degree. We define and study the automorphism equivariant Hitchin index. We prove a formula for it in terms of cohomological pairings of canonical T-equivariant classes of certain moduli spaces of parabolic Higgs bundles over the quotient Riemann surface.

The study of the automorphism equivariant Hitchin index is motivated by complex quantum Chern-Simons theory and non-abelian Hodge theory. Further, this index is a generalization of the Witten-Reshetikhin-Turaev quantum invariant of the three-manifold Y obtained as the mapping torus of the automorphism f. This project is based on joint work with J. E. Andersen and G. Ayuso.    

报告时间：2025年4月24日（周四）上午10:30-11:30

报告地点：教二楼201

联系人：孙善忠