The purpose of this seminar is to study basic notions of contact geometry and contact Hamiltonian systems.  Hamilton's equations are more known in the context of symplectic geometry, where they model conservative mechanical systems. Through contact geometry, we will see how to account for systems interacting with the environment. 

We will study the relation between contact and symplectic manifolds, and how contact manifolds provide a good framework for an Hamiltonian formulation of time-dependant and dissipative systems. Further topics may include Jacobi manifolds, their relation to Poisson manifolds, Hamiltonian systems on them, and modern approaches to contact Hamilton-Jacobi theory.

The first sessions are scheduled for April 4 and 11. The following sessions, and their topics, will be scheduled together by the participants.