# On the Greenfield-Wallach and Katok conjectures

Presented by:
L Flaminio Université Lille 1
Date:
Tuesday 1st July 2014 - 13:30 to 14:20
Venue:
INI Seminar Room 1
Abstract:
In the early 70's, Greenfield and Wallach studied fields globally hypo-elliptic vectors fields on compact manifolds and made the following conjecture : Let $G$ be a Lie group and let $H$ be a closed subgroup Such That $G/H$ is compact. Let $X ^ *$ be the vector field on $G / H$ determined by some element $X$ in the Lie algebra of $G$. Given by If $X ^ *$ is globally hypo-elliptic, then $G / H$ is a torus.'' In a work in collaboration with F.~Rodriguez-Hertz and G. Forni, we gave a positive solution to this problem. In this talk I will recall thistory of the problem, wxplain its relation with Katok's conjecture on cohomologically free vector fields and give some idea of the proof.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.