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Logic Seminar

Wednesday, July 29, 2020
12:00pm to 1:00pm
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Two applications of Arens-Eells spaces to geometric group theory and abstract harmonic analysis
Christian Rosendal, Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago,

Arens-Eells spaces (aka Lipschitz free spaces or transportation cost spaces) give rise to interesting examples of Banach spaces and provide analytic techniques within Banach space geometry. But they are also of importance as a tool for analysing objects outside Banach space theory using functional analytical techniques. I will present two such uses. The first is to abstract harmonic analysis where Arens-Eells spaces can be used to provide a very simple conceptual proof of a recent characterisation of amenability of topological groups due to F. M. Schneider and A. Thom. The second application is to the geometric study of topological groups, namely, to establish the Gromov correspondence between coarse equivalence and topological couplings in the widest possible setting.

For more information, please contact Math Department by phone at 626-395-4335 or by email at mathinfo@caltech.edu.