| Thursday 26 December 2024 | |
| Events for day: Tuesday 20 December 2022 |
| 14:30 - 16:00 Algebraic Geometry Webinar Serre Polynomials and Geometry of Character Varieties School MATHEMATICS With G a complex reductive group, let XrG denote the G-character varieties of free group Fr, of rank r, and XirrG ? XrG be the locus of irreducible representation conjugacy classes. In this talk we shall present a result showing that the mixed Hodge structures on the cohomology groups of XrSLn and of XrPGLn, and on the compactly supported cohomology groups of the irreducible loci XirrSLn and XirrPGLn are isomorphic, for any n,r ? N. The proof uses a natural stratification of XrG by polystable type coming from affine GIT and the combinatorics of partitions. In particular, this result would imply their E-polynomials coincide, settling the quest ... |