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Logic Seminar

Wednesday, December 1, 2021
12:00pm to 1:00pm
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Online Event
On the universal minimal flow of the homeomorphism group of a Knaster continuum
Lauren Wickman, Department of Mathematics, University of Florida,

The correspondence between Ramsey theory, Fraïssé theory, and dynamics established in 2003 by Kechris, Pestov, and Todorčević has had far-reaching consequences in the study of automorphism groups of discrete first-order structures. The dual notion, projective Fraïssé theory (developed by Irwin and Solecki in 2006), considers classes of topological structures and in 2017, Panagiotopoulos proved that every compact, metrizable space can be obtained as a quotient of a projective Fraïssé limit. Therefore, projective Fraïssé theory provides an ideal framework to consider the homeomorphism groups of compact spaces. In this talk, for each Knaster continuum KK, we will give a projective Fraïssé class of finite objects that approximates KK (up to homeomorphism) and use the dual of the KPT correspondence (proved by Bartošová and Kwiatkowska, 2018) to determine if the homeomorphism group of KK is extremely amenable.

For more information, please email A. Kechris at [email protected].