学术报告(沈俊亮 11.2)

Topology of Hitchin systems: old and new

发布人:杨晓静 发布日期:2022-10-28
主题
Topology of Hitchin systems: old and new
活动时间
-
活动地址
Zoom :971 1062 5774
主讲人
沈俊亮 助理教授 耶鲁大学数学系
主持人
李长征

Abstract:
Hitchin’s integrable systems lie in the crossroads of geometry,representation theory, and mathematical physics. I will discuss two central conjectures raised in the last two decades which greatly influenced the development for the algebraic geometry of Hitchin moduli spaces. The first is the P=W conjecture, which concerns the interaction of the topology of the Hitchin system and the non-abelian Hodge correspondence. The second is the topological mirror symmetry conjecture which connects the Langlands duality of groups and the mirror symmetry for Hitchin systems. I will explain that both conjectures can be proved in a uniform way, via
vanishing cycles techniques and support theorem. Based on joint work with Davesh Maulik.