October 7: Marco Castronovo

Title: Lagrangian tori and cluster charts

Abstract:

I will describe a conjectural correspondence between Lagrangian tori in a real symplectic manifold and algebraic tori in a mirror variety. It is not clear what this mirror should be, but for coadjoint orbits work of Rietsch suggests a relation to Langlands duality. I will then explain how to partially verify this correspondence for Grassmannians. This point of view allows to answer purely dynamical questions about displaceability and abundance of Lagrangians. I will end with speculations on how symplectic topology might one day return the favor.