In this talk, I will state a conjecture giving a formula for the Lagrangian capacity of a convex or concave toric domain. First, I will explain a proof of the conjecture in the case where the toric domain is convex and 4-dimensional, using the Gutt-Hutchings capacities as well as the McDuff-Siegel capacities. Second, I will explain a proof of the conjecture in full generality, but assuming the existence of a suitable virtual perturbation scheme which defines the curve counts of linearized contact homology. This second proof makes use of Siegel’s higher symplectic capacities.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
