Fabio Gironella (Humboldt-Universität zu Berlin)
Symplectic and contact geometry - from the origins in classical mechanics to some modern topological questions
The aim of the talk is to give a (non exhaustive panorama) of some aspects of symplectic and contact geometry, focusing on the many interactions between these two fields. Starting with a very concrete point of view, I will describe how these two geometries give a natural framework to generalize classical mechanics, respectively in the conservative and dissipative settings. I will then introduce the modern definitions of these structures and focus on some key topological problems, for instance tightness/overtwistedness of contact manifolds and their fillability by symplectic manifolds. In the last part of the talk, I will give an overview of some new results, from a joint work with Jonathan Bowden and Agustin Moreno, concerning these last two topological problems, and, time permitting, explain some ideas behind their proofs.