Geometry and Topology Seminar: "Naive symplectic capacities"

Speaker: Kyler Siegel, USC

Abstract: A central challenge in symplectic geometry is to understand in what ways a Hamiltonian flow can "squeeze" a domain. Despite some remarkable progress, especially in dimension four, the high dimensional situation is still largely open and extremely subtle. The main tools are symplectic capacities, i.e. real-valued invariants of domains which are monotone under symplectic embeddings. In recent years a number of sophisticated symplectic capacities have been defined using Floer theory, embedded contact homology, symplectic field theory, and so on. These frameworks typically require delicate perturbations to achieve transversality, making the necessary counts involved rather inaccessible. In this talk I will describe a new perspective which directly constructs capacities of geometric significance, and I will explain how this opens up avenues for previously inaccessible computations and applications.

Host: Michael Landry