Cohomology rings of character varieties

2025/07/16 by Mellit, Anton
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2507.12454

Abstract

In this talk I give an introduction and present some recent progress towards understanding the cohomology rings of character varieties of Riemann surfaces, such as the proof of the P=W conjecture and the computation of the zero-dimensional COHA. In the case of punctured sphere I present an explicit description relating the cohomology rings to the Hilbert scheme of ℂ², refining conjectures of Hausel-Letellier-Rodriguez-Villegas and Chuang-Diaconescu-Donagi-Pantev. I explain how the general case should be related to the symplectic geometry of the Hilbert scheme.

Related

• Ideals of the cohomology rings of Hilbert schemes and their applications
• Twisted cohomology of the Hilbert schemes of points on surfaces
• Generators for the cohomology ring of Hilbert schemes of points on surfaces
• Intersection cohomology of rank two character varieties of surface\n groups
• On the cohomology rings of Grassmann varieties and Hilbert schemes