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Group actions, warped cones and expanders

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David Fisher (Indiana)

Abstract: The talk focuses on connections between basic questions is
two areas of mathematics. The first is the classification of group actions
up to conjugacy, a fundamental question in dynamics. The second is the
classification of metric spaces up to quasi-isometry, a fundamental
question in coarse geometry. Using John Roe's notion of a warped cone
over a group action, we show that for a certain class of group
actions/metric spaces, these questions are equivalent. I.e. from a
group action one can construct a metric space which is a complete
conjugacy invariant for a certain class of group actions. If time
permits, I will also describe some applications to the coarse geometry of
expanders and superexpanders and to the coarse Baum Connes conjecture.