IPM Calendar 
Monday 2 October 2023   Today  
Events for day: Tuesday 20 December 2022    
           14:30 - 16:00     Algebraic Geometry Webinar
Serre Polynomials and Geometry of Character Varieties


With G a complex reductive group, let XrG denote the G-character varieties of free group Fr, of rank r, andXirrG? XrGbe the locus of irreducible representation conjugacy classes. In this talk we shall present a result showingthat the mixed Hodge structures on the cohomology groups ofXrSLnand ofXrPGLn, and on thecompactly supported cohomology groups of the irreducible lociXirrSLnandXirrPGLn are isomorphic,for anyn,r?N. The proofuses a natural stratification ofXrGby polystable typecoming from affine GIT and the combinatorics of partitions. In particular, this result would imply their E-polynomialscoincide, settling the quest ...