Time：16:30, Wednesday, December 20 2023
Venue: E4-233 & ZOOM
ZOOM ID: 961 6546 1795
PASSCODE: 341574
Speaker：Andrei Moroianu, CNRS
Biography: Andrei Moroianu is a senior researcher at CNRS. He obtained his PhD degree at École Polytechnique in 1996. From 2004 to 2016, he was a professor at École Polytechnique. He has been the research director at CNRS since 2012. He is a member of editorial committees of: Manuscript mathematica, SIGMA SIGMA and Collectanea Mathematica.
Title：On the ergodicity of the frame flow
Abstract:
The geodesic flow of compact Riemannian manifolds with negative sectional curvature is ergodic with respect to the Liouville measure on the unit tangent bundle. Its natural lift to the orthonormal frame bundle, called the frame flow, is only partially hyperbolic, and is not always ergodic, e.g. when the manifold is Kähler. In the 80's, Brin and Gromov proved the ergodicity of the frame flow when the dimension $n$ of the manifold is odd and different from 7, and conjectured that ergodicity should hold whenever the sectional curvature is at least 0,25 pinched. Some partial results were obtained by Brin-Karcher ('84) and Burns-Pollicott ('03), under quite strong pinching assumptions of the order of 0,86 and 0,98. In this talk I will report on some recent developments towards the Brin-Gromov conjecture, where the required pinching is approximately 0,27 - 0,29 for $n=4k+2$ and 0,57 - 0,6 for $n=4k$. The talk is based on joint work with Mihajlo Cekic (ETH, Zürich), Thibault Lefeuvre (Sorbonne Université) and Uwe Semmelman (Stuttgart University).
