Motivated by ideas in quantum chaos, there has been a lot of work studying sup-norms of automorphic forms. In this talk we will focus on Hecke-Maass forms on certain locally symmetric spaces of SL(n). I will present some new upper bounds on the sup-norms of such forms that are uniform in the volume of the space (or the level). Part of the work involves understanding Hecke congruence subgroups in higher rank and developing a version of reduction theory, in the sense of the geometry of numbers, with level structure.