Barcode Entropy and Relative Symplectic Cohomology

Uploaded March 2026 | Updated September 2026, 3 weeks ago

IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar
9:15am|Remote Access
Topic: Barcode Entropy and Relative Symplectic Cohomology
Speaker: Jonghyeon Ahn
Affiliation: IBS Center for Geometry and Physics (IBS-CGP)
Date: March 06, 2026

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.

Barcode Entropy and Relative Symplectic Cohomology - Jonghyeon Ahn

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