Principal Investigator: Paul Seidel
The main aim of the project is to harness the power of Fukaya categories for use in symplectic topology. This includes developing computational tools, building a repertoire of nontrivial examples, and also studying the relationship between Fukaya categories and Gromov-Witten invariants. Concrete examples that will be looked at include: Fukaya categories of Riemann surfaces; Lagrangian submanifolds in cotangent bundles; and the symplectic geometry of Khovanov's link invariants. Various aspects of mirror symmetry will be important sources of intuition, and the experience gained in this way should ultimately feed back into a better understanding of mirror symmetry itself, especially its homological aspects.
From a wider perspective, the project is part of the reaction of the scientific community to recent advances in theoretical physics. The contribution that mathematics can make is to verify the soundness and consistency of physical intuition, and to prepare the general ground on which further development can occur. This is particularly important in those situations where developments in physics suggest the presence of deep and complex structures, which are difficult to detect by direct experiment. A nice aspect is that the same circle of ideas allows one to answer some purely mathematical (geometric) questions inspired by the "old" physics of classical mechanics.
