GT seminar: Lagrangian capacity and chain-level string topology

Abstract: In this talk, I will describe several conjectures concerning the Lagrangian capacity and report on the progress we have made so far. In particular, I will explain that the Lagrangian capacity of any convex or concave toric domain, in arbitrary dimension, is equal to its diagonal. This confirms a conjecture of Cieliebak–Mohnke on the Lagrangian capacities of ellipsoids. If time permits, I will also explain that any extremal Lagrangian torus in an ellipsoid, in arbitrary dimension, must lie on the boundary. Our proof is based on an S¹-equivariant variation of techniques developed by Fukaya and Irie, and avoids the use of holomorphic curves with local tangency constraints. This is ongoing joint work with Yin Li.

This is a talk in our Geometry and Topology Seminar Series.