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SUMMARY:Yaiza Canzani (University of North Carolina at Chapel Hill)
DTSTART:20230117T160000Z
DTEND:20230117T170000Z
DTSTAMP:20260423T022719Z
UID:Geolis/109
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Geolis/109/"
 >Counting closed geodesics and improving Weyl’s law for predominant sets
  of metrics</a>\nby Yaiza Canzani (University of North Carolina at Chapel 
 Hill) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nWe discuss the t
 ypical behavior of two important quantities on compact manifolds with a Ri
 emannian metric g: the number\, c(T\, g)\, of primitive closed geodesics o
 f length smaller than T\, and the error\, E(L\, g)\, in the Weyl law for c
 ounting the number of Laplace eigenvalues that are smaller than L. For Bai
 re generic metrics\, the qualitative behavior of both of these quantities 
 has been understood since the 1970’s and 1980’s. In terms of quantitat
 ive behavior\, the only available result is due to Contreras and it says t
 hat an exponential lower bound on c(T\, g) holds for g in a Baire-generic 
 set. Until now\, no upper bounds on c(T\, g) or quantitative improvements 
 on E(L\, g) were known to hold for most metrics\, not even for a dense set
  of metrics. In this talk\, we will introduce the concept of predominance 
 in the space of Riemannian metrics. This is a notion that is analogous to 
 having full Lebesgue measure in finite dimensions\, and which\, in particu
 lar\, implies density. We will then give stretched exponential upper bound
 s for c(T\, g) and logarithmic improvements for E(L\, g) that hold for a p
 redominant set of metrics. This is based on joint work with J. Galkowski.\
 n
LOCATION:https://researchseminars.org/talk/Geolis/109/
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