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SUMMARY:Osama Khalil (University of Utah)
DTSTART:20201204T171500Z
DTEND:20201204T183000Z
DTSTAMP:20260423T053046Z
UID:NEDNT/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/13/">L
 arge centralizers and counting integral points on affine varieties</a>\nby
  Osama Khalil (University of Utah) as part of New England Dynamics and Num
 ber Theory Seminar\n\nLecture held in Online.\n\nAbstract\nDuke-Rudnick-Sa
 rnak and Eskin-McMullen initiated the use of ergodic methods to count inte
 gral points on affine homogeneous varieties. They reduced the problem to o
 ne of studying limiting distributions of translates of periods of reductiv
 e groups on homogeneous spaces. The breakthrough of Eskin\, Mozes and Shah
  provided a rather complete understanding of this question in the case the
  reductive group has a “small centralizer” inside the ambient group. I
 n this talk\, we describe work in progress giving new results on the equid
 istribution of generic translates of closed orbits of semisimple groups wi
 th “large centralizers”. The key new ingredient is an algebraic descri
 ption of a partial compactification (for lack of a better word) of the set
  of intermediate groups which act as obstructions to equidistribution. Thi
 s allows us to employ tools from geometric invariant theory to study the a
 voidance problem.\n
LOCATION:https://researchseminars.org/talk/NEDNT/13/
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