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SUMMARY:Sasha Minets (The University of Edinburgh)
DTSTART:20230510T030000Z
DTEND:20230510T043000Z
DTSTAMP:20260422T161057Z
UID:HKUST-AG/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HKUST-AG/10/
 ">A proof of $P=W$ conjecture</a>\nby Sasha Minets (The University of Edin
 burgh) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in 
 5564.\n\nAbstract\nLet $C$ be a smooth projective curve. The non-abelian H
 odge 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 $C$. Sin
 ce this diffeomorphism is not algebraic\, it induces an isomorphism of coh
 omology rings\, but does not preserve finer information\, such as the weig
 ht filtration. Based on computations in small rank\, de Cataldo-Hausel-Mig
 liorini 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 cruci
 ally uses the action of Hecke correspondences on $H^*(M_D)$. Based on join
 t work with T. Hausel\, A. Mellit\, O. Schiffmann.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/10/
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