Almost Toric Fibrations and Lagrangian Poincaré non-recurrence

Abstract

Almost Toric Fibrations (ATFs) are a certain type of integrable system and provide a useful tool to study symplectic four-manifolds, allowing for various explicit constructions of Lagrangian torus knots and interesting symplectomorphisms. The latter gives a counterexample to the Lagrangian Poincaré recurrence conjecture. This talk will give a "users manual" to ATFs, outlining the tools used to manipulate them.