Organisers: Ioan Marcut (Radboud University), Oliver Fabert (Vrije Universiteit Amsterdam)
Marco Zambon (KU Leuven, Belgium)
Foliations, regular and singular
A regular foliation gives a partition of a space (manifold) into smooth subspaces (leaves), all of which have the same dimension. A regular foliation carries a rich geometry structure: for instance, as I will discuss, it comes with a certain dynamics, which can be used to provide a normal form nearby a given leaf and also to attach a group-like structure (a Lie groupoid) to the regular foliation.
If one allows the leaves to vary dimension, it turns out that it is a good idea to prescribe vector fields (necessarily with singularities) giving rise to the partition. One then obtains a rich geometry, and results analogous to those of the regular case.
Fabian Ziltener (Utrecht University)
Hamiltonian Lie group actions: examples and a classification result
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 discuss some examples of such actions and present some joint work with Yael Karshon, in which we classify Hamiltonian actions of compact Lie groups on exact symplectic manifolds with proper momentum maps.