Gergely Harcos: On the non-spherical sup-norm problem

A central problem in analytic number theory is to estimate the sup-norm of cusp forms on various Lie groups. It is natural to consider the Lie group $GL(n,\mathbb{R})$, but for $n>2$, the results so far were confined to cusp forms that are right-invariant under the maximal compact subgrop $O(n)$. I will explain how to deal with more general cusp forms on $GL(n,\mathbb{R})$. A key ingredient is a new uniform decay bound for generalized spherical functions. Based on recent joint work with Valentin Blomer, Péter Maga, and Djordje Milićević.