Lagrangian Capacity and Chain-Level String Topology

In this talk, I will present an upper bound for the Lagrangian capacity of a Liouville domain with finite Gutt–Hutchings capacities. We prove that the Lagrangian capacity of every convex or concave toric domain, in arbitrary dimension, equals its diagonal. In particular, this settles a conjecture of Cieliebak–Mohnke on the Lagrangian capacity of ellipsoids. I will also discuss a boundary rigidity result for extremal Lagrangians. Our proofs are based on a quantitative 𝑆1-equivariant version of the chain-level string topology methods developed by Fukaya and Irie. This is joint work with Yin Li.