Por Azizeh Nozad (IPM, Iran).

With G a complex reductive group, let Xr(G) denote the G-character varieties of free group Fr, of rank r. In this talk we shall present a result showing that the mixed Hodge structures on the cohomology groups of Xr(SLn) and Xr(PGLn), and on the compactly supported cohomology groups of the irreducible loci are isomorphic, for any n,r ∈ N. In particular, this implies their Serre (also called E-) polynomials coincide, settling the question raised by Lawton-Muñoz. This is based on joint work with Carlos Florentino and Alfonso Zamora.