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SUMMARY:Joint equidistribution of CM points
DTSTART:20180328T161500
DTEND:20180328T171500
DTSTAMP:20260510T230046Z
UID:f7614b9c0471244a1d859c74540495cf9f7199d7b6a4069cf98dcedf
CATEGORIES:Conferences - Seminars
DESCRIPTION:Ilya Khayutin (Princeton)\nDescription:Joint equidistribution 
 of CM points A celebrated theorem of Duke states that Picard/Galois orbits
  of CM points on a complex modular curve equidistribute in the limit when 
 the absolute value of the discriminant goes to infinity. The equidistribut
 ion of Picard and Galois orbits of special points in products of modular c
 urves was conjectured by Michel and Venkatesh and as part of the equidistr
 ibution strengthening of the André-Oort conjecture. I will explain the pr
 oof of a recent theorem making progress towards this conjecture.\n\nCurren
 tly\, this problem does not seem to be amenable to methods of automorphic 
 forms even assuming GRH. Nevertheless\, assuming a splitting condition at 
 two primes the joining rigidity theorem of Einsiedler and Lindenstrauss ap
 plies. As a result the obstacle to proving equidistribution is the potenti
 al concentration of mass on graphs of Hecke correspondences and translates
  thereof. I will present a method to discard this possibility using a geom
 etric expansion of a relative trace\, description of the relative orbital 
 integrals in terms of integral ideals and a sieve argument.
LOCATION:MA A3 30 https://plan.epfl.ch/?room=MAA330
STATUS:CONFIRMED
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