11-28【Yuan Gao】Rabinowitz Floer theory and categorical formal completion

Rabinowitz Floer theory originates from the studies of dynamics on a contact-type hypersurface in an convex symplectic manifold, on which fruitful algebraic structures have been studied recently, which have intriguing relations to Fukaya categories and string topology. In this talk, I will discuss a generalization of these invariants to Liouville sectors, a certain class of exact symplectic manifolds with boundary introduced by Ganatra-Pardon-Shende with a full package of functoriality properties and computational tools. This new Floer-theoretic invariant naturally corresponds to a purely algebraic notion - the categorical formal completion arising from the similar notion from algebraic geometry and ring theory, and the whole picture matches with predications from mirror symmetry.