(26 september 2024/September 26, 2024) Colloque des sciences mathématiques du Québec/CSMQ. https://www.crmath.ca/en/activities/#...

Su Gao (Nankai University): Extremely amenable automorphism groups of countable structures

Abstract: Extreme amenability is a remarkable property for a topological group to have. Ever since the first example of such groups was constructed in 1975, many groups have been shown to be extremely amenable. In this talk I will address the question: How many pairwise non-isomorphic extremely amenable groups are there? We demonstrate that there are continuum many pairwise non-isomorphic extremely amenable groups which are automorphism groups of countable structures, and in particular Polish. I will also talk about some related results from the point of view of descriptive set theory. This is joint work with Mahmood Etedadialiabadi and Feng Li.