Joint IAS/Princeton University Number Theory Seminar

I will present asymptotic upper and lower bounds for the supremum norms of Maass forms of growing Laplace eigenvalue on a wide class of semisimple groups. I will also present a general lower bound in the level aspect that improves over the trivial bound one gets from the growing multiplicity of the space of forms. I will describe the connections between these results and topics such as the theta lift, period integral formulae, and the work of Sakellaridis-Venkatesh on the spectra of spherical varieties. The lower bounds I will present are joint work with Farrell Brumley.