Speaker: Marco Castronovo (Columbia University)

Title: Liouville domains from Okounkov bodies

Abstract: Any smooth complex projective algebraic variety X can be made symplectic, by choosing an ample divisor D. A purely algebraic construction associates to D several convex polytopes, known as Okounkov bodies. I will report on work in progress, aimed at constructing a Liouville subdomain of X from each top-dimensional Okounkov body. The main feature is high control on the dynamics of the Reeb vector field defined on the boundary of each domain. This is part of a larger project to understand scattering diagram as in the Gross-Siebert program from the point of view of Symplectic Field Theory in the sense of Eliashberg-Givental-Hofer.