Conformal actions of semi-simple Lie groups on compact Lorentz manifolds.
Event details
| Date | 09.12.2015 |
| Hour | 16:30 › 17:30 |
| Speaker | Vincent Pécastaing |
| Location |
CM010
|
| Category | Conferences - Seminars |
A result of R. Zimmer going back to the 1980's asserts that up to local isomorphism, PSL(2,R) is the only non-compact simple Lie group that can act by isometries on a Lorentz manifold of finite volume. He presented it as a corollary of another strong result, known as "Zimmer's embedding theorem". The latter, based on ergodic theory, gives strong algebraic constrainst on Lie groups acting on a G-structure by preserving a finite measure and is well adapted to the study of isometric actions in any signature (they preserve the volume form).
If we relax the assumption and only consider conformal dynamics of Lie groups, we lose the existence of an invariant finite measure, even when the manifold is compact. However, conformal structures are rigid in dimension at least 3 and it seems possible to describe conformal Lie group actions.
I will present a result that extends Zimmer's theorem and classifies semi-simple Lie groups without compact factors acting by conformal transformations on a compact Lorentz manifolds. This work is in the continuation of a result of U. Bader and A. Nevo (2002). I will also discuss the local conformal geometry of the Lorentz manifolds where such dynamics occur, especially when the group that acts is locally isomorphic to PSL(2,R).
If we relax the assumption and only consider conformal dynamics of Lie groups, we lose the existence of an invariant finite measure, even when the manifold is compact. However, conformal structures are rigid in dimension at least 3 and it seems possible to describe conformal Lie group actions.
I will present a result that extends Zimmer's theorem and classifies semi-simple Lie groups without compact factors acting by conformal transformations on a compact Lorentz manifolds. This work is in the continuation of a result of U. Bader and A. Nevo (2002). I will also discuss the local conformal geometry of the Lorentz manifolds where such dynamics occur, especially when the group that acts is locally isomorphic to PSL(2,R).
Practical information
- Informed public
- Free
Organizer
- Louis Merlin