BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nolan Wallach (UC San Diego) DTSTART:20230126T220000Z DTEND:20230126T230000Z DTSTAMP:20260423T024649Z UID:UCSD_NTS/82 DESCRIPTION:Title: The Whittaker Inversion Theorem and some applications\nby Nolan Wall ach (UC San Diego) as part of UCSD number theory seminar\n\nLecture held i n APM 6402 and online.\n\nAbstract\nThe Whittaker Plancherel theorem appea red as Chapter 15 in my two volume book\, Real Reductive Groups. It was me ant to be an application of Harish-Chandra’s Plancherel Theorem. As it turns out\, there are serious gaps in the proof given in the books. At the same time as I was doing my research on the subject\, Harish-Chandra was also working on it. His approach was very different from mine and appears as part of Volume 5 of his collected works\; which consists of three piece s of research by Harish-Chandra that were incomplete at his death and orga nized and edited by Gangolli and Varadarajan. Unfortunately\, it also doe s not contain a proof of the theorem. There was a complication in the proo f of this result that caused substantial difficulties which had to do with the image of the analog of Harish-Chandra’s method of descent. In this lecture I will explain how one can complete the proof using a recent resul t of Raphael Beuzzart-Plessis. I will also give an application of the resu lt to the Fourier transforms of automorphic functions at cusps.\n\n(This s eminar will be given remotely\, but there will still be a live audience in the lecture room.)\n\npre-talk at 1:20pm\n LOCATION:https://researchseminars.org/talk/UCSD_NTS/82/ END:VEVENT END:VCALENDAR