Séminaires : Séminaire Géométrie et Topologie

Equipe(s) : aa, acg,
Responsables :B. Petri, A. Sambarino, S. Seyfaddini et M. Zavidovique
Email des responsables :
Salle : 15-25-502
Adresse :Campus Pierre et Marie Curie
Description

Ce séminaire s’adresse aux géomètres, topologues et dynamiciens au sens large. Il est rattaché aux équipes Analyse Algébrique et Analyse Complexe et Géométrie. Les exposés seront accessibles à une audience large, doctorants inclus. Il se tiendra à Jussieu, le jeudi à 11h, en salle 15-25 502. Le séminaire a l'agenda google suivante: https://calendar.google.com/calendar/b/0?cid=dDgzNTJoczNmdDhlMm5nb2IzMXJwaWpsdHNAZ3JvdXAuY2FsZW5kYXIuZ29vZ2xlLmNvbQ


Orateur(s) Mihajlo Cekić - ,
Titre Ergodicity of frame flows on even-dimensional manifolds
Date06/10/2022
Horaire11:00 à 12:00
Diffusion
Résume

Flows of frames over negatively curved Riemannian manifolds (M, g) are one of the oldest examples of partially hyperbolic dynamics. It is well known that frame flows of hyperbolic manifolds are ergodic, while Kahler manifolds never have an ergodic frame flow; Brin conjectured in the 70's that all manifolds with sectional curvature between -1 and -0.25 (i.e. curvature is 0.25-pinched) have ergodic frame flows. In this talk I will explain recent progress on this conjecture: we show that in dimensions 4k+2 the frame flow is ergodic if (M, g) is ~0.27 pinched, and in dimensions 4k if it is ~0.55 pinched. Our new method uses techniques in hyperbolic dynamics (transitivity group, Parry's representation), topology of structure groups of spheres, and Fourier analysis in the vertical fibre of the unit sphere bundle (based on Pestov identity). This is joint work with Lefeuvre, Moroianu, and Semmelmann.

Salle15-25-502
AdresseCampus Pierre et Marie Curie
© IMJ-PRG