Introduction to P=W and Mirror symmetry

Описание: Tamas Hausel

Abstract:
Motivated by topological mirror symmetry for Langlands dual Higgs bundle moduli spaces, one can study the arithmetic of the corresponding character varieties to gain information on the weight filtration on their cohomology. In turn this lead to the P=W conjecture which identifies the weight filtration on the cohomology of the character variety with the perverse filtration of the Hitchin system on the cohomology of the Higgs moduli space.