P=W conjecture for GL_n

Appears in collection : 2023 - T2 - WS2 - Higher structures in enumerative geometry

The P=W conjecture, 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).