A topological group is extremely amenable if it has a fixed

point under every continuous action on a compact Hausdorff space. The

group of measure preserving transformations of the standard

probability space is extremely amenable by a result of Giordano and

Pestov applying analytical techniques. This in turn implies that the

class of finite measure algebras posseses the approximate Ramsey

property. Via discretization, Giordano and Pestov's result would

follow from (an exact) Ramsey property for finite measure algebras

where all atoms have equal measure as shown by Kechris, Sokic, and

Todorcevic. However, this problem resists a variety of attempts of

applying different Ramsey theoretic techniques.

Friday, April 19, 2019 - 11:00 to 11:45

Thackeray 427