Junliang Shen : The P=W conjecture for GL_n

Posted by Izzet Coskun , part of the Algebraic Geometry Seminar.

At

Nov. 14, 2022, 3 p.m.

In

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Abstract

In 2010, de Cataldo-Hausel-Migliorini proposed a conjecture connecting topology of the Hitchin system and Hodge theory of the corresponding character variety via the non-abelian Hodge theory. This conjecture is now referred to as the P=W conjecture. The purpose of this talk is to explain a recent proof of this conjecture (for GL_n) in joint work with Davesh Maulik for any rank and genus, where we combine tools from algebraic geometry and representation theory.