Room P3.10, Mathematics Building

Tudor Ratiu, Ecole Polytechnique Fédérale de Lausanne, Suiça
Convexity for symplectic actions

This talk is based on joint work with P. Birtea and J.-P. Ortega. If one has a proper symplectic Lie group action is there a convexity result associated to it? Since it is not assumed that this action admits a momentum map, even the question of what one means by convexity is open. It turns out that any such action admits a so-called cylinder valued momentum map and that this map has convexity properties in the metric category. The talk will explain how this map is constructed, why it is a genuine generalization of the momentum map, and what the associated convexity result is. In the process the key technical result of the topological proof of the convexity result for Hamiltonian actions will be generalized in various ways and one of the statements is useful for potential applications to infinite Banach weak symplectic manifolds.

Please note the exceptional date.