Intersection cohomology of character varieties for punctured Riemann surfaces
Ponente: Mathieu Ballandras (ICMAT)Fecha: miércoles 01 de febrero de 2023 - 11:30Lugar: Aula Naranja, ICMAT
The character varieties we are interested in classify representations of the fundamental group of a punctured Riemann surface. The monodromy around each puncture is prescribed to be in the closure of a conjugacy class in GL_n. These varieties are usually singular and we compute their Poincaré polynomial for intersection cohomology. The proof relies on a result from Mellit for smooth character varieties and on Grothendieck—Springer resolution of singularities. I will recall some background about local systems and Springer theory before applying it to compute the intersection cohomology of character varieties.