Mathieu Ballandras:Intersection cohomology of character varieties for punctured Riemann surfaces

Abstract: Character varieties for punctured Riemann surfaces admit natural resolutions of singularities. Those resolutions are constructed thanks to Springer Theory and they carry a Weyl group action on their cohomology. This structure gives a relation between intersection cohomology of character varieties and cohomology of the resolutions. Thanks to a result from Mellit for smooth character varieties, previous relation allows to compute the Betti numbers for intersection cohomology.