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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
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC


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.

28400?type=thumb Venkatesh Notes 2.08 MB application/pdf Download
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H.264 Video 12-Venkatesh.mp4 199 MB video/mp4 rtsp://videos.msri.org/data/000/028/326/original/12-Venkatesh.mp4 Download
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