Time：14:00-15:00, Wednesday, October 18 2023
Venue：E4-233 & ZOOM
ZOOM ID:921 6725 8223
Passcode：064984
Speaker：Zili Zhang, Tongji University
Title：Simpson's correspondence and the P=W conjecture
Abstract：For a complex projective curve C and a reductive group G, the character variety M_B and the moduli of Higgs bundles M_Dol are canonically homeomorphic via the non-abelian Hodge correspondence and hence the cohomology groups of them are naturally identified. The geometric structures of the moduli spaces induce various filtrations in the cohomology groups. De Cataldo-Hausel-Migliorini conjectured in 2012 that the Perverse filtration (P) of M_Dol is identical to the Hodge-theoretic Weight filtration (W) of M_B; the P=W conjecture. We will introduce the background recent progress of the P=W conjecture.
