A proof of $P=W$ conjecture

Abstract: Let $C$ be a smooth projective curve. The non-abelian Hodge theory of Simpson is a diffeomorphism between the character variety $M_B$ of $C$ and the moduli of (semi)stable Higgs bundles $M_D$ on $C$. Since this diffeomorphism is not algebraic, it induces an isomorphism of cohomology rings, but does not preserve finer information, such as the weight filtration. Based on computations in small rank, de Cataldo-Hausel-Migliorini conjectured that the weight filtration on $H^*(M_B)$ gets sent to the perverse filtration on $H^*(M_D)$, associated to the Hitchin map. In this talk, I will explain a recent proof of this conjecture, which crucially uses the action of Hecke correspondences on $H^*(M_D)$. Based on joint work with T. Hausel, A. Mellit, O. Schiffmann.

algebraic geometryrepresentation theory

Audience: researchers in the topic

Algebra and Geometry Seminar @ HKUST

Series comments: Algebra and Geometry seminar at the Hong Kong University of Science and Technology (HKUST).

If the talk is online/mixed mode, Zoom info is available on researchseminars.org in the talk details. But if you would also like to be added to the mailing list to get notifications for upcoming talks, please email agseminar@ust.hk.