
Lagrangian Hofer-Zehnder Capacities and Energy-Capacity Inequalities
Symplectic geometer Sam Lisi, of the University of Mississippi, presents joint work with Antonio Rieser at the Joint IAS/Princeton Symplectic Geometry Seminar. The talk revisits a variation on the Hofer-Zehnder capacity that Lisi and Rieser previously defined relative to a coisotropic submanifold, now specialized to the case where that submanifold is Lagrangian. Using a persistent homology approach to filtered Floer theory, building on methods of Polterovich and Shelukhin, Lisi derives two energy-capacity inequalities, one local and one global. He shows that the global inequality fails without imposing topological conditions on the admissible Hamiltonians, and argues this points to a close relationship between their capacity and Barraud-Cornea's real Gromov radius. The talk assumes familiarity with Floer theory and symplectic capacities, and proceeds at the technical level expected of a research seminar, with Lisi working through the constructions and inequalities on the board for an audience of specialists.