Definably amenable NIP groups – Pierre Simon (CNRS, Université Lyon)


Sala Seminari (Dip. Matematica).


A group is definably amenable if there is a translation-invariant measure on the algebra of definable sets. This notion is particularly fruitful in the NIP context, where definable amenability is equivalent to the existence of some kind of generic types. The theory is related to that of tame flows in topological dynamics. In this talk, I will survey what is known about definably amenable NIP groups, in particular results concerning the action of the group on its type space, minimal flows and the compact domination phenomenon.

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