Explore symplectomorphism invariants of open domains in this 1-hour 4-minute lecture by Michael Hutchings at ICBS2024. Delve into methods for determining symplectomorphism between open sets in ${\mathbb R}^{2n}$. Examine the use of zeta functions describing Reeb dynamics on boundaries and bar codes associated with equivariant symplectic homology as tools for creating symplectomorphism invariants. Learn how these invariants can be applied to distinguish certain families of open toric domains, providing valuable insights into the field of symplectic geometry.