Spectral capacities of submanifolds

Tsinghua-BIMSA symplectic geometry seminar

Organizers：

Kenji Fukaya, Honghao Gao, Hang Yuan(BIMSA)

Speaker：

Jun Zhang (USTC)

Time：

Wed., 14:00-15:00

Dec. 25, 2024

Venue：

C548, Shuangqing Complex Building A

Title:

Spectral capacities of submanifolds

Abstract：

In this talk, we will discuss how to measure the size of submanifolds in a symplectic manifold. This is based on symplectic invariants that are constructed from spectra extracted from (Hamiltonian) Floer theory. Moreover, these invariants are concrete examples of spectral capacities. We will use these capacities to demonstrate the fundamental differences between Lagrangian submanifolds and symplectic submanifolds (or more generally nowhere coisotropic submanifolds). Meanwhile, we will also prove a quantitative Lagrangian control estimate that intriguingly relates these invariants. This talk is based on joint work with Dylan Cant.