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Symplectic Geometry Seminar

Topological entropy, barcodes and Floer theory

Basak Gurel (University of Central Florida)

Location:  Hill 705
Date & time: Thursday, 29 February 2024 at 1:30PM - 2:30PM

Abstract: Topological entropy is one of the fundamental invariants of a dynamical system, measuring the orbit complexity. In this talk, we discuss a connection between the topological entropy of compactly supported Hamiltonian diffeomorphisms and Floer theory. Namely, we introduce a new invariant associated with the Floer complexes of the iterates of such a diffeomorphism, which we call barcode entropy. We show that barcode entropy is closely related to topological entropy and that these invariants are equal in dimension two. We also touch upon applications of the methods to some other questions in symplectic topology. The talk is based on joint work with Erman Cineli and Viktor Ginzburg.