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SUMMARY:Pratyush Sarkar (ETHZ)
DTSTART:20251021T164500Z
DTEND:20251021T174500Z
DTSTAMP:20260423T021830Z
UID:NEDNT/93
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/93/">E
 ffective equidistribution of translates of tori in arithmetic homogeneous 
 spaces and applications</a>\nby Pratyush Sarkar (ETHZ) as part of New Engl
 and Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstr
 act\nA celebrated theorem of Eskin–Mozes–Shah gives an asymptotic coun
 ting formula for the number of integral (n x n)-matrices with a prescribed
  irreducible (over the integers/rationals) integral characteristic polynom
 ial. We obtain a power saving error term for the counting problem for (3 x
  3)-matrices. We do this by using the connection to homogeneous dynamics a
 nd proving effective equidistribution of translates of tori in SL_3(R)/SL_
 3(Z). A key tool is that the limiting Lie algebra corresponding to the tra
 nslates of tori is a certain nilpotent Lie algebra. This allows us to use 
 the recent breakthrough work of Lindenstrauss–Mohammadi–Wang–Yang on
  effective versions of Shah’s/Ratner’s theorems. We actually study the
  phenomenon more generally for any semisimple Lie group which we may discu
 ss if time permits.\n
LOCATION:https://researchseminars.org/talk/NEDNT/93/
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