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Colloquium talk, Timothy Rainone, Arizona State University

Date: Tuesday, September 26, 2017

Location: Rocky 300

Time: 12:30

Title:Paradoxical decompositions and finite/infinite dichotomies in operator algebras.

Abstract: Notions of paradoxical decompositions appear in the work of Hausdorff, Banach, and Tarski, and some may argue go as far back as Galileo who noted that an infinite set X can be partitioned into two disjoint subsets; each having the same cardinality as X. In this talk we will explore such decompositions as they pertain to groups and group actions, and subsequently tie paradoxical phenomena to ideas of infiniteness in the realm of operator algebras. We will introduce the theory of bounded operators on Hilbert space and study various examples of concrete C*-algebras, emphasizing the finite/infinite nature of each example. We will end our discussion by studying the stably finite/purely infinite divide for certain C*-algebras that arise from dynamical systems. This talk is aimed at a general math audience.