Arithmetic Study Group: Representation growth of special linear groups
16 January 2018 14:00 in CM219
One way of studying the complex representations of the special linear groups over the integers is to determine the convergence of its representation zeta function.
Recently Avni and Aizenbud have given a method that relates special values of the zeta function at even integers $2g - 2$ with the singularities of the representation variety of the fundamental group of a Riemann surface of genus $g$ into the special linear group. This way, Avni and Aizenbud determine that the degree of polynomial representation growth of the special linear group over the integers is smaller than $22$. In this talk I shall report on a recent result obtained in collaboration with N. Budur pushing down this bound to $2$.