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SUMMARY:Claire Burrin (ETH Zurich)
DTSTART:20201120T170000Z
DTEND:20201120T180000Z
DTSTAMP:20260423T024551Z
UID:SOQUAGAT/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SOQUAGAT/2/"
 >Expanding horocycles on the modular surface and some deep open problems i
 n analytic number theory</a>\nby Claire Burrin (ETH Zurich) as part of Ser
 ies on open questions in Arithmetic\, Geometry and Topology\n\n\nAbstract\
 nThe orbits of the horocycle flow on surfaces are classified: each orbit i
 s either dense or a closed horocycle around a cusp. Expanding closed horoc
 ycles are asymptotically dense\, and in fact become equidistributed on the
  surface. The precise rate of equidistribution is of interest\; on the mod
 ular surface\, Zagier observed that a particular rate is equivalent to the
  Riemann hypothesis being true. In a recent preprint with Uri Shapira and 
 Shucheng Yu\, we explored the asymptotic behavior of evenly spaced points 
 along an expanding closed horocycle on the modular surface. In this proble
 m\, the number of sparse points is made to depend on the expansion rate\, 
 and the difficulty is that these points are no more invariant under the ho
 rocycle flow: Ratner’s theory does not apply. In this talk\, I will sket
 ch how this problem involves the theory of Diophantine approximation\, and
  estimates towards the Ramanujan conjecture for Hecke-Maass forms. The goa
 l is for this talk to be accessible for topologists\; no prior background 
 in analytic number theory will be assumed.\n
LOCATION:https://researchseminars.org/talk/SOQUAGAT/2/
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