colloquium Mathematics, Dr. Fabian Ziltener (Utrecht University)

Title:

Hamiltonian group actions on exact symplectic manifolds with proper momentum maps are standard.

Abstract:

Symplectic geometry originated from classical mechanics.
Hamiltonian Lie group actions correspond to symmetries in mechanics.
They can be used to reduce the number of degrees of freedom of a mechanical system.

I will completely characterize Hamiltonian actions of compact Lie groups on exact symplectic manifolds with proper momentum maps. I will deduce that every Hamiltonian action of a compact Lie group on a contractible symplectic manifold with a proper momentum map is globally linearizable.

(This is joint work with Yael Karshon.)