Leírás
Abstract: A hybrid bound for the sup-norm of automorphic forms is a bound uniform in the eigenvalue and the volume aspect simultaneously. In this talk, I will discuss a method of proving hybrid bounds for Hecke-Maass forms on compact quotients $\Gamma \backslash \mathrm{SL}_n(\mathbb{R}) / \mathrm{SO}_n(\mathbb{R})$, where $\Gamma$ is the unit group of an order in a central simple division algebra over $\mathbb{Q}$, and $n$ is prime. The bounds feature uniformity in the full covolume of $\Gamma$ and an explicit power-saving over what is considered the local bound. By restricting to a certain family of orders (of Eichler type), we also obtain partial results when $n$ is an arbitrary odd number.
The link for the talk is https://zoom.us/j/94752830725, the password is the order of $\mathrm{SL}_2(\mathbb{F}_{97})$.