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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:On frame flow ergodicity - Thibault Lefeuvre (Sorb
onne)
DTSTART;TZID=Europe/London:20230125T160000
DTEND;TZID=Europe/London:20230125T170000
UID:TALK193978AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/193978
DESCRIPTION:The frame flow over negatively-curved Riemannian m
anifolds is\na historical example of a partially h
yperbolic dynamical system. Excluding some obvious
counterexamples such as Kähler manifolds\, its er
godicity was conjectured by Brin in the 70s. While
it has been since Brin-Gromov (1980) that it is e
rgodic on odd-dimensional manifolds (and dimension
not equal to 7)\, the even-dimensional case is st
ill open. In this talk\, I will explain recent pro
gress towards this conjecture: I will show that in
dimensions 4k+2 the frame flow is ergodic if the
Riemannian manifold is 0.27 pinched (i.e.\, the se
ctional curvature is between -1 and -0.27)\, and i
n dimensions 4k if it is 0.55 pinched. This proble
m turns out to be surprisingly rich and at the int
erplay of different fields: (partially) hyperbolic
dynamical systems\, algebraic topology (classific
ation of topological structures over spheres)\, Ri
emannian geometry and harmonic analysis (Pestov id
entity and microlocal analysis). Joint work with M
ihajlo Cekić\, Andrei Moroianu\, Uwe Semmelmann.\n
LOCATION:MR13
CONTACT:Oscar Randal-Williams
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