Number Theory

Title: Sup-norms of automorphic forms
Speaker: Nicolas Templier
Speaker Info: Princeton
Brief Description:
Special Note:

If f is a cuspidal automorphic forms on a reductive group G it is classical to study its value distribution and in particular its sup-norm, that is the maximum of |f(g)|. We will survey recent results on the problem of bounding the sup-norm, focusing on the GL(2) case which includes Hecke--Maass cusp forms, holomorphic and Hilbert modular forms and automorphic forms on quaternion algebras. There are interesting connections with local harmonic analysis (archimedean and non-archimedean), quantum chaos, integers represented by quadratic forms. Then we will explain an approach to lower bounds via unipotent periods with a new formula for non-archimedean Whittaker functions.
Date: Monday, December 03, 2012
Time: 5:00PM
Where: Lunt 107
Contact Person: Simon Marshall
Contact email: slm@math.northwestern.edu
Contact Phone: 847-467-0715
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