KASS seminar

Abstract:  In the late 80's, motivated by questions of Hamiltonian dynamics, Floer used the theory of pseudo-holomorphic curves in order to define a chain complex associated to a pair of Lagrangian submanifolds in a compact symplectic manifold. This led later to the definition of the Fukaya category of a symplectic manifold: an A-infinity category whose objects are Lagrangians and morphisms spaces are given in terms of Floer complexes. These categories are extremely studied because their derived versions appear for example in one "side" of the homological mirror symmetry conjecture.

In this talk, I will give some ideas about how to define such a Fukaya category for a non-compact symplectic manifolds with "nice" boundary, i.e. contact type boundary. The objects of this category are Lagrangian cobordisms between Legendrian submanifolds (living in the boundary). There will be more pictures than formulas!