12. The orbit method and analysis of automorphic forms - Akshay Venkatesh [2017]

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The orbit method and analysis of automorphic forms
Recent Developments In Analytic Number Theory May 01, 2017 - May 05, 2017
May 04, 2017 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Akshay Venkatesh (Stanford University)
Location: MSRI: Simons Auditorium
Abstract:
In the analytic theory of automorphic forms, especially in higher rank, one encounters complicated integrals over Lie groups which must be either evaluated or estimated. I will discuss how Kirillov's orbit method allows one to do this, at least heuristically. These ideas can often be made rigorous; I will apply it to evaluate the average value of L-functions over certain (Gross-Prasad) families, in any rank. This evaluation also uses Ratner's theorem on measure rigidity. Joint work with Paul Nelson.
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