Counting Representations of Fuchsian Groups Over Finite Fields

Explore advanced mathematical concepts in this seminar talk focusing on the asymptotic growth of n-dimensional representations of Fuchsian groups over finite fields. Delve into character bounds for groups of Lie type and their applications in determining dimensions of complex representation varieties. Learn about the existence of strongly Zariski-dense Fuchsian subgroups in classical groups of high rank, drawing from the work of Breuillard-Green-Guralnick-Tao. Examine how recent mathematical progress enables the analysis of representation counting when q is fixed and n approaches infinity, presented by Indiana University's Michael Larsen at the Institute for Advanced Study's Special Groups and Dynamics Seminar.