Month: June 2020

Global rigidity of some partially hyperbolic abelian actions

Abstract: We consider abelian actions with sufficiently many partially hyperbolic elements and compact center foliation with trivial holonomy and leaves of dimension ≤ 2. Under some extra conditions we obtain that the action is essentially a product over affine Anosov action or even essentially algebraic. I will explain in the talk all these notions and some of the mechanisms in the proof. This is joint work with Amie Wilkinson and Disheng Xu.

Slides

On the unitary dual of higher rank semi-simple lattices

Abstract: In this talk, based on joint work with Cyril Houdayer, I
will present a curious property of the unitary representations of
lattices in semi-simple higher rank Lie groups: either they contain a
finite dimensional invariant subspace or they are factorizations of
the regular representation, in a strong sense. I will explain how this
result generalizes and unifies recent advances in operator algebras.
Our approach relies on ergodic theory and stationary dynamical
systems.

Slides

A D’Ambra Theorem in conformal Lorentzian geometry

Abstract: D’Ambra proved in 1988 that the isometry group of a compact, simply connected, real-analytic Lorentzian manifold must be compact. I will discuss my recent theorem that the conformal group of such a manifold must also be compact, and how it relates to the Lorentzian Lichnerowicz Conjecture.

Geodesic planes in hyperbolic 3-manifolds