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SUMMARY:Claire Burrin (ETH Zurich)
DTSTART:20210505T150000Z
DTEND:20210505T160000Z
DTSTAMP:20260423T021433Z
UID:hnts/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/hnts/30/">A 
 sparse equidistribution problem for expanding horocycles on the modular su
 rface</a>\nby Claire Burrin (ETH Zurich) as part of Heilbronn number theor
 y seminar\n\n\nAbstract\nThe orbits of the horocycle flow on hyperbolic su
 rfaces (or orbifolds) are classified: each orbit is either dense or a clos
 ed horocycle around a cusp. Expanding closed horocycles are themselves asy
 mptotically dense\, and in fact become equidistributed on the surface. The
  precise rate of equidistribution is of interest\; on the modular surface\
 , Zagier observed that a particular rate is equivalent to the Riemann hypo
 thesis being true. In this talk\, I will discuss the asymptotic behavior o
 f evenly spaced points along an expanding closed horocycle on the modular 
 surface. In this problem\, the number of points depends on the expansion r
 ate of the horocycle\, and the difficulty is that these points are no more
  invariant under the horocycle flow. This is based on joint work with Uri 
 Shapira and Shucheng Yu.\n
LOCATION:https://researchseminars.org/talk/hnts/30/
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