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SUMMARY:Thibault Leveufre (Université Paris-Sud)
DTSTART:20200922T140000Z
DTEND:20200922T150000Z
DTSTAMP:20260423T035410Z
UID:Geometry/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Geometry/11/
 ">Marked length spectrum\, geodesic stretch and pressure metric</a>\nby Th
 ibault Leveufre (Université Paris-Sud) as part of Pangolin seminar\n\n\nA
 bstract\nThe marked length spectrum of a negatively-curved manifold is t
 he data of all the lengths of closed geodesics\, marked by the free homoto
 py of the manifold. The marked length spectrum conjecture (also known as t
 he Burns-Katok conjecture\, 1985) asserts that two negatively-curved manif
 olds with same marked length spectrum should be isometric. This conjecture
  was proved on surfaces (Croke '90\, Otal '90) but remains open in higher 
 dimensions. I will present a proof of a local version of this conjecture\,
  based on the notions of geodesic stretch and pressure metric (a gener
 alization of the Weil-Petersson metric to the context of variable curvatur
 e). Some elements of the theory of Pollicott-Ruelle resonances and anisotr
 opic spaces will also be needed (I will recall everything). Joint work wit
 h C. Guillarmou and G. Knieper.\n
LOCATION:https://researchseminars.org/talk/Geometry/11/
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