IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

In this talk, I will discuss the barcode entropy—the exponential growth rate of the number of not-too-short bars—of the persistence module associated with the relative symplectic cohomology $SH_M(K)$ of a Liouville domain $K$ embedded in a symplectic manifold $M$. The main result establishes a quantitative link between this Floer-theoretic invariant and the dynamics of the Reeb flow on $∂K$. More precisely, I will explain that the barcode entropy of the relative symplectic cohomology $SH_M(K)$ is bounded above by a constant multiple of the topological entropy of the Reeb flow on the boundary of the domain, where the constant depends on the embedding of $K$ into $M$.