Colloquium - Nicholas Ramsey - Model theory and Paradoxical Decompositions


Speaker: Nicholas Ramsey (Notre Dame)

Title:  Model theory and Paradoxical Decompositions

Abstract:  The Banach-Tarski paradox says that you can take a ball in 3-dimensional space, partition it into finitely many pieces, and rearrange those pieces in such a way that you obtain two balls of equal volume as the first.  This leads naturally to the question of how complicated these pieces need to be.  A version of this question arose recently in model theory, where it was asked if all groups definable in combinatorially simple mathematical structures must necessarily be definably amenable or, in other words, must carry an invariant probability measure on their definable subsets. In recent work, joint with several authors, we answered this in the negative, producing simple structures which carry a paradoxical decomposition.  We will describe this work and, along theway, we will explain the basic framework of model theory and the fundamental tool of Keisler measures.

Location: Hamilton Hall 305

Coffee and Cookies will be served in Hamilton Hall 305 at 3:00 pm. Everyone is welcome.
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