The asymptotic behavior of sup norms of Maass forms

The asymptotic behavior of sup norms of Maass forms

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Simon Marshall, University of Wisconsin-Madison
Fine Hall 314

Please note special day, time and location.   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.