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Texas A&M University
Mathematics

Groups and Dynamics Seminar

Date: November 14, 2018

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Anton Bernshteyn, CMU

  

Title: Is multiplication of weak equivalence classes continuous?

Abstract: The relations of weak containment and weak equivalence were introduced by Kechris in order to provide a convenient framework for describing global properties of p.m.p. actions of countable groups. Weak equivalence is a rather coarse relation, which makes it relatively well-behaved; in particular, the set of all weak equivalence classes of p.m.p. actions of a given countable group $\Gamma$ carries a natural compact metrizable topology. Nevertheless, a lot of useful information about an action (such as its cost, type, etc.) can be recovered from its weak equivalence class. In addition to the topology, the space of weak equivalence classes is equipped with a multiplication operation, induced by taking products of actions, and it is natural to wonder whether this multiplication operation is continuous. The answer is positive for amenable groups, as was shown by Burton, Kechris, and Tamuz. In this talk, we will explore what happens in the nonamenable case. Number theory will make an appearance.