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SUMMARY:On frame flow ergodicity - Thibault Lefeuvre (Sorbonne)
DTSTART:20230125T160000Z
DTEND:20230125T170000Z
UID:TALK193978@talks.cam.ac.uk
CONTACT:Oscar Randal-Williams
DESCRIPTION:The frame flow over negatively-curved Riemannian manifolds is\
 na historical example of a partially hyperbolic dynamical system. Excludin
 g some obvious counterexamples such as Kähler manifolds\, its ergodicity 
 was conjectured by Brin in the 70s. While it has been since Brin-Gromov (1
 980) that it is ergodic on odd-dimensional manifolds (and dimension not eq
 ual to 7)\, the even-dimensional case is still open. In this talk\, I will
  explain recent progress towards this conjecture: I will show that in dime
 nsions 4k+2 the frame flow is ergodic if the Riemannian manifold is 0.27 p
 inched (i.e.\, the sectional curvature is between -1 and -0.27)\, and in d
 imensions 4k if it is 0.55 pinched. This problem turns out to be surprisin
 gly rich and at the interplay of different fields: (partially) hyperbolic 
 dynamical systems\, algebraic topology (classification of topological stru
 ctures over spheres)\, Riemannian geometry and harmonic analysis (Pestov i
 dentity and microlocal analysis). Joint work with Mihajlo Cekić\, Andrei 
 Moroianu\, Uwe Semmelmann.\n
LOCATION:MR13
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