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SUMMARY:Emilio Corso (ETH)
DTSTART:20220407T161500Z
DTEND:20220407T173000Z
DTSTAMP:20260423T021928Z
UID:NEDNT/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/46/">A
 symptotics of the equidistribution rate of expanding circles on compact hy
 perbolic quotients and applications</a>\nby Emilio Corso (ETH) as part of 
 New England Dynamics and Number Theory Seminar\n\nLecture held in Online.\
 n\nAbstract\nEquidistribution properties of translates of orbits for subgr
 oup actions on homogeneous spaces are intimately linked to the mixing feat
 ures of the global action of the ambient group. The connection appears alr
 eady in Margulis’ thesis (1969)\, displaying its full potential in the w
 ork of Eskin and McMullen during the nineties. On a quantitative level\, t
 he philosophy underpinning this linkage allows to transfer mixing rates to
  effective estimates for the rate of equidistribution\, albeit at the cost
  of a sizeable loss in the exponent. In joint work with Ravotti\, we inste
 ad resort to a spectral method\, pioneered by Ratner in her study of quant
 itative mixing of geodesic and horocycle flows\, in order to obtain the pr
 ecise asymptotic behaviour of averages of regular observables along expand
 ing circles on compact hyperbolic surfaces. The primary goal of the talk i
 s to outline the salient traits of this method\, illustrating how it leads
  to the relevant asymptotic expansion. In addition\, we shall also present
  applications of the main result to distributional limit theorems and to q
 uantitative error estimates on the corresponding hyperbolic lattice point 
 counting problem\, the latter having been examined\, to date\, only throug
 h number-theoretical methods in works of Selberg\, Lax-Phillips and Philli
 ps-Rudnick.\n
LOCATION:https://researchseminars.org/talk/NEDNT/46/
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