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SUMMARY:Ergodic theory in groups with a contracting element - Rémi Coulon
  (CNRS (Centre national de la recherche scientifique))
DTSTART:20250905T104500Z
DTEND:20250905T114500Z
UID:TALK233674@talks.cam.ac.uk
DESCRIPTION:Ergodic theory has proven to be a powerful tool for studying n
 egatively curved Riemannian manifolds and their fundamental groups. For in
 stance\, the seminal work of Margulis extracts from the mixing of the geod
 esic flow precise asymptotics for the number of closed geodesics of a give
 n length. This approach has been extended beyond the realm of manifolds\, 
 e.g.\, to CAT(-1) spaces and CAT(0) spaces with a rank-one element. This t
 alk will report on an ongoing project whose goal is to carry (some of) the
 se tools to the context of geometric group theory: given a general metric 
 space X with a weak form of negative curvature (captured by the existence 
 of a contracting element in its isometry group)\, we will explain how to b
 uild a geodesic flow on X and investigate its dynamical properties\, such 
 as ergodicity and mixing.\njoint work with Samuel Tapie
LOCATION:Seminar Room 1\, Newton Institute
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