Speaker: Xiyan Zhong
University of Notre Dame
Will give a Graduate Student Geometry Seminar entitled:
Prym representations and twisted cohomology of the mapping class group with level structures.
Abstract: For a finite cyclic cover Sp of a non-closed surface S of finite type, the whole mapping class group of S does not lift to the cover Sp. However, there is a finite-index subgroup which does lift to the cover and act on the first rational cohomology group of Sp, and this is called a Prym representation. We computed the twisted cohomology of this subgroup in coefficients r-tensor powers of H1(Sp;Q), which turns out to be unstable with respect to the genus of the surface when r2, contrasting to the stability of cohomology of the whole mapping class groups. As a corollary, we also know the Prym representations of finite abelian covers are locally rigid. Arxiv: http://arxiv.org/abs/2401.13869
Date: 02-27-2024
Time: 4:00 pm
Location: 258 Hurley Bldg