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On the topology of Hitchin fibrations

Date: Thursday, June 18, 2020 14:00 - 16:00
Speaker: Junliang Shen (Massachusetts Institute of Technology)
Location: https://mathseminars.org/seminar/AGNTISTA
Series: Mathematics and CS Seminar
Host: Tamas Hausel

The topology of the Hitchin fibrations plays crucial role in geometry, math physics, and representation theory. In this talk, we will discuss two questions arised naturally in the study of Hitchin fibrations in view of the P=W conjecture: (a) How to locate the tautological classes in the perverse filtration? (b) Is the perverse filtration multiplicative for Hitchin fibrations? 
I will explain how connnections to the geometry of some special algebraic varieties (Hilbert schemes, abelian surfaces, hyper-Kahler manifolds)  lead to progress to answering these questions.

Based on joint work with Mark de Cataldo, Davesh Maulik, Qizheng Yin, Zili Zhang.

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