Our Colloquium series offers a diverse platform for research scholars, faculty, students, and industry experts to share and exchange ideas, fostering discussion and networking across mathematics, statistics, and data science.
Our own Professor Başak Gürel will speak at this week's colloquium on "Topological Entropy of Hamiltonian Systems and Persistence Modules."
Abstract: Topological entropy is a fundamental invariant of a dynamical system, measuring its complexity. In this talk, we discuss connections between the topological entropy of a Hamiltonian system, e.g., a geodesic flow, and the underlying filtered Morse or Floer homology viewed as a persistence module in the spirit of Topological Data Analysis. We introduce barcode entropy — a Morse/Floer theoretic counterpart of topological entropy — and show that barcode entropy is closely related to topological entropy and that, in low dimensions, these invariants agree. For instance, for a geodesic flow on any closed surface, the barcode entropy is equal to the topological entropy. The talk is based on joint work with Erman Cineli, Viktor Ginzburg, and Marco Mazzucchelli.
Speaker Bio: Başak Gürel is a professor in the Department of Mathematics at the University of Central Florida in Orlando. Her research lies at the interface of symplectic topology and Hamiltonian dynamical systems, with a particular focus on the investigation of various dynamical phenomena using symplectic techniques. She received her Ph.D. from the University of California, Santa Cruz, and has held postdoctoral positions at Stony Brook University and the University of Montréal. Her honors include an NSF CAREER Award, a UCF Rising Star Award, and a Concours Annuel Prize from the Royal Academy of Belgium.
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