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Texas A&M University

Events for 03/04/2020 from all calendars

Graduate Student Organization Seminar

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Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: James O'Quinn

Title: Topological Dynamics and Entropy

Abstract: Topological dynamics is the study of the asymptotic and perturbative properties of continuous group actions on topological spaces. The subject has its roots in the development of the qualitative theory of differential equations by Poincaré, and became a formal discipline in the 1920s and 30s. Today, research in topological dynamics is flourishing with broad applications to fields like operator algebras, group theory, number theory, differential geometry, and computer science. Despite the age of the field, many topics in the field are still in their infancy. During this talk, I will introduce some of the core concepts and examples in this area. I will also introduce amenable topological entropy which is the premier numerical invariant for topological dynamical systems. Roughly speaking, entropy measures the exponential growth of the number of distinguishable finite orbits under the dynamics. I will then show how entropy can be used to distinguish a large class of dynamical systems. Time permitting, I will introduce some current directions of research in the subject.