Konrad Królicki
Konrad Królicki: Nonsingular hyperfinite actions of groups
09/04/22 15:36
Tuesday, April 12, 2022 17:00
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Konrad Królicki (Hungarian Academy of Sciences)
Title: Nonsingular hyperfinite actions of groups
Abstract: Any action of a finitely generated group on a standard probability space induces a measurable Schreier graph.When the action is nonsingular, i.e. it preserves the measure class, the measurable graph is called a measured graphing. We say that a measured graphing is hyperfinite if for any \(\varepsilon >0\), one can remove a part of measure at most \(\varepsilon\) in such a way that the components of the remainder are finite. I will define the notion of local convergence for measured graphs, i.e. finite Schreier graphs with a probability measure on their vertices, and how their limits may be represented with nonsingular actions. The objective of the talk is to present one part of the nonsingular theorem of Schramm: if a sequence of measured graphs is hyperfinite, then the limit graphing is hyperfinite as well. Joint work with Gabor Elek.
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Konrad Królicki (Hungarian Academy of Sciences)
Title: Nonsingular hyperfinite actions of groups
Abstract: Any action of a finitely generated group on a standard probability space induces a measurable Schreier graph.When the action is nonsingular, i.e. it preserves the measure class, the measurable graph is called a measured graphing. We say that a measured graphing is hyperfinite if for any \(\varepsilon >0\), one can remove a part of measure at most \(\varepsilon\) in such a way that the components of the remainder are finite. I will define the notion of local convergence for measured graphs, i.e. finite Schreier graphs with a probability measure on their vertices, and how their limits may be represented with nonsingular actions. The objective of the talk is to present one part of the nonsingular theorem of Schramm: if a sequence of measured graphs is hyperfinite, then the limit graphing is hyperfinite as well. Joint work with Gabor Elek.