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SUMMARY:Mikey Chow (Mikey Chow)
DTSTART:20231116T171500Z
DTEND:20231116T183000Z
DTSTAMP:20260423T022035Z
UID:NEDNT/66
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/66/">J
 ordan and Cartan spectra in higher rank with applications to correlations<
 /a>\nby Mikey Chow (Mikey Chow) as part of New England Dynamics and Number
  Theory Seminar\n\nLecture held in Online.\n\nAbstract\nThe celebrated pri
 me geodesic theorem for a closed hyperbolic surface says that the number o
 f closed geodesics of length at most t is asymptotically e^t/t. For a clos
 ed surface equipped with two different hyperbolic structures\, Schwartz an
 d Sharp (’93) showed that the number of free homotopy classes of length 
 about t in both hyperbolic structures is asymptotically a constant multipl
 e of e^{ct} /t^{3/2} for some 0<c<1. \nWe will discuss the asymptotic corr
 elations of the length spectra of convex cocompact manifolds\, generalizin
 g Schwartz-Sharp’s results. Surprisingly\, it is helpful for us to relat
 e this problem with understanding the Jordan spectrum of a discrete subgro
 up in higher rank. In particular\, we will explain the source of the expon
 ential and polynomial factors in Schwartz-Sharp’s asymptotics from a hig
 her rank viewpoint. \nWe will also discuss the asymptotic correlations of 
 the displacement spectra and the ratio law between the asymptotic correlat
 ions of the length and displacement spectra.   \nThis is joint work with H
 ee Oh.\n
LOCATION:https://researchseminars.org/talk/NEDNT/66/
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