Topology and MHSs of Representation and Character Varieties of Abelian and Nilpotent groups
Ponente: Carlos Florentino (Universidade de Lisboa)Fecha: miércoles 18 de enero de 2023 - 11:30Lugar: Aula Naranja, ICMAT
Let R be the connected component of the identity of the variety of representations of a finitely generated nilpotent group into a connected reductive complex affine algebraic group G. Neither R nor the character variety R//G are smooth or projective, in general. Nevertheless, we were able to explicitly determine (via closed and recursive formulae) the Poincaré polynomials and the mixed Hodge structures of R and R//G. This is the culmination of several works on these varieties over the last 10 years, done in collaboration with S. Lawton, A. Nozad, J. Silva and A. Zamora, and also inspired by other recent articles on the geometric approach to E-polynomials of character varieties, by V. Muñoz, Á. González-Prieto, M. Logares and collaborators.