# GAN

## Seminar

### On the Greenfield-Wallach and Katok conjectures

Flaminio, L (Université Lille 1)
Tuesday 01 July 2014, 13:30-14:20

Seminar Room 1, Newton Institute

#### 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.

#### Video

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