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# Dr. Junliang Shen, Yale – The P=W conjecture for GL_n

## October 28, 2022 @ 4:00 pm - 5:00 pm

Mode: In-person

Title: The P=W conjecture for GL_n

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.*