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UID:20260602T200423EDT-599059EUzp@132.216.98.100
DTSTAMP:20260603T000423Z
DESCRIPTION:Title: Applications of the Endoscopic Classification to Statist
 ics of Cohomological Automorphic Representations on Unitary Groups.\n\nAbs
 tract: Consider the family of automorphic representations on some unitary 
 group with fixed (possibly non-tempered) cohomological representation $\pi
 _0$ at infinity and level dividing some finite upper bound. We compute sta
 tistics of this family as the level restriction goes to infinity. For unra
 mified unitary groups and a large class of $\pi_0$\, we are able to comput
 e the exact leading term for both counts of representations and averages o
 f Satake parameters. We get bounds on our error term similar to previous w
 ork by Shin-Templier that studied the case of discrete series at infinity.
  We also discuss corollaries related to the Sarnak-Xue density conjecture\
 , average Sato-Tate equidistribution in families\, and growth of cohomolog
 y for towers of locally symmetric spaces. The main technical tool is an ex
 tension of an inductive argument that was originally developed by Taïbi to
  count unramified representations on Sp and SO and used the endoscopic cla
 ssification of representations (which our case requires for non-quasisplit
  unitary groups). This is joint work with Mathilde Gerbelli-Gauthier.\n
DTSTART:20230223T153000Z
DTEND:20230223T163000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Rahul Dalal (Johns Hopkins University)
URL:/mathstat/channels/event/rahul-dalal-johns-hopkins
 -university-346314
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