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{\Large Department of Mathematics, BGU}

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{\Huge BGU Probability and Ergodic Theory  (PET) seminar}\\[0.2\baselineskip]

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\textbf{On} \emph{Thursday, January  7, 2021}
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\textbf{At} \emph{11:10 -- 12:00}
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\textbf{In} \emph{Online}

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{\large\scshape Guy Salomon 
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  (Weizmann Institute)
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will talk about
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{\Large\bfseries Amenability, proximality, and higher order syndeticity\par}
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\textsc{Abstract:}
An action of a discrete group G on a compact Hausdorff space X is called proximal if for every two points x and y of X there is a net g\_i in G such that lim(g\_i x)=lim(g\_i y), and strongly proximal if the action of G on the space Prob(X) of probability measures on X is proximal. The group G is called strongly amenable if all of its proximal actions have a fixed point and amenable if all of its strongly proximal actions have a fixed point.

In this talk, I will present a correspondence between (strongly) proximal actions of G and Boolean algebras of subsets of G consisting of certain kinds of “large” subsets. I will use these Boolean algebras to establish new characterizations of amenability and strong amenability. Furthermore, I will show how this machinery helps to characterize “dense orbit sets” answering a question of Glasner, Tsankov, Weiss, and Zucker.

This is joint work with Matthew Kennedy and Sven Raum.





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{\bfseries Please Note the Unusual Place!}
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