Barcode Entropy and Relative Symplectic Cohomology

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 SHM(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 SHM(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.