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SUMMARY:Ramin Takloo-Bighash (Department of Math\, Stat\, and Computer Sci
 ence\, UIC Chicago\, IL)
DTSTART:20210928T150000Z
DTEND:20210928T170000Z
DTSTAMP:20260424T095004Z
UID:FGC-IPM/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FGC-IPM/1/">
 The distribution of rational points on some spherical varieties.</a>\nby R
 amin Takloo-Bighash (Department of Math\, Stat\, and Computer Science\, UI
 C Chicago\, IL) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstrac
 t\nIn this talk I will discuss a work in progress in which\, together with
  Sho Tanimoto and Yuri Tschinkel\, we study the distribution of rational p
 oints on some anisotropic spherical varieties of rank 1 over an arbitrary 
 number field. Our work is the non-split analogue of the results of Valenti
 n Blomer\, Jörg Brüdern\, Ulrich Derenthal\, and Giuliano Gagliardi wher
 e they consider split spherical varieties of rank 1 over the rational numb
 ers\, though our methods are completely different. In our proof we use the
  theory of automorphic forms\, especially Waldspurger's celebrated theorem
  on toric periods\, to analyse the height zeta function. Once this analysi
 s is done\, the result on the distribution of rational points follows from
  a standard Tauberian theorem. We hope to address split spherical varietie
 s of rank 1 over an arbitrary number field using similar methods in a futu
 re work.\n\nMeeting ID: 908 611 6889\nPasscode: ''the order of the symmetr
 ic group on 9 elements (type the 6-digit number)''\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/1/
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