Universal flows for closed subgroups of the permutation group of the integers
Speaker:
Lionel Nguyen Van Thé, Aix-Marseille University
Date and Time:
Thursday, October 14, 2010 - 11:00am to 11:50am
Abstract:
In their 2005 paper, Kechris, Pestov and Todorcevic showed that in order to compute the universal minimal flow of some closed subgroups of the permutation group of the integers, two combinatorial properties are relevant. Those are respectively called ”Ramsey property” and ”ordering property” (or more generally, ”expansion property”). They proved that the expansion property is equivalent to minimality of a certain flow, while the conjunction of the Ramsey and the expansion property is equivalent to minimality and universality of this same flow. A natural question is therefore: Is Ramsey property alone equivalent to universality? The purpose of this talk is to give an answer to this question