Abstract: Lagrangian submanifolds appear naturally in symplectic geometry from different angles: real algebraic geometry, dynamics and integrable systems are just a few sources to mention. In fact, once the concept is introduced many symplectic phenomena can be rephrased in a Lagrangian language, as a famous citation of A. Weinstein goes "Everything is Lagrangian".

I will survey the development of Lagrangian topology, which is a theory that mixes topological and symplectic invariants associated to Lagrangian submanifolds. I will explain how these can be applied to solve various problems in symplectic geometry. I will then move on to newer developments that have to do with the algebraic structure of the totality of these invariants, such as the Donaldson and Fukaya categories. If time permits I will outline a new and more geometric approach to study these categories.

No apriori knowledge of symplectic geometry is needed.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006