A proof of P=W conjecture


Event details

Date 24.11.2022 10:1511:45  
Speaker Sasha Minets (University of Edinburgh)
Category Conferences - Seminars
Event Language English

Let C be a smooth projective curve. The non-abelian Hodge theory (NAHT) 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) under NAHT. In this talk, I will explain a recent proof of this conjecture, which crucially uses the action of Hecke correspondences on H^*(M_D). This is a joint work with T. Hausel, A. Mellit, O. Schiffmann.

Practical information

  • Informed public
  • Free


  • Dimitri Wyss


  • Monique Kiener (if you want to attend to the seminar by zoom, please contact me, and I'll give you the link)

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