P=W conjecture for GL_n

Abstract: The P=W conjecture, first proposed by de Cataldo-Hausel-Migliorini in 2010, gives a link between the topology of the moduli space of Higgs bundles on a curve and the Hodge theory of the corresponding character variety, using non-abelian Hodge theory. In this talk, I will explain this circle of ideas and discuss a recent proof of the conjecture for GL_n (joint with Junliang Shen).

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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