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.

Bio-Sketch: 

Gao Su received his undergraduate degree in Mathematics from Peking University and his Ph.D. from UCLA. He is currently a Chair Professor at Nankai University and has previously held positions as a Chancellor's Professor, Chair of the Mathematics Department, and Dean of the College of Sciences at the University of North Texas, USA. His primary research areas are mathematical logic, foundations of mathematics, and their applications in other branches of pure mathematics. Using descriptive set theory, he has investigated the complexity of classification problems across various fields in mathematics, solving several significant open problems. His achievements span multiple mathematical branches including algebra, geometry, topology, functional analysis, and dynamical systems, and have been published in top international mathematics journals such as Inventiones Mathematicae.