Fabio Gironella
Summary: Symplectic geometry is a branch of differential geometry and topology that studies manifolds with a symplectic structure, i.e. with a closed, nondegenerate differential 2-form. This field has seen an explosion in interest over the last few decades, mainly because it is characterized by a very interesting interplay between geometric phenomena, also called "rigid", and topological phenomena, also called "flexible". Topological techniques are particularly effective for studying this interaction, which sometimes leads to the field being referred to as "symplectic topology".
The main aim of the course is to give an introduction to one of the main tools used to study rigidity, namely pseudo-holomorphic curves introduced by Gromov. This will be done specifically in the case of spheres, and the main aim is to prove a famous theorem due to Eliashberg-Floer-McDuff theorem on the classification up to diffeomorphism of exact symplectic fillings of the standard contact sphere in all odd dimensions.