Title	Measurable realizations of abstract systems of congruence
Creator	Marks, Andrew
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2019-10-02T11:12
Description	An abstract system of congruences describes a way of partitioning a space into finitely many pieces satisfying certain congruence relations. Examples of abstract systems of congruences include paradoxical decompositions and $n$-divisibility of actions. We consider the general question of when there are realizations of abstract systems of congruences satisfying various measurability constraints. We completely characterize which abstract systems of congruences can be realized by nonmeager Baire measurable pieces of the sphere under the action of rotations on the 2-sphere. This answers a question of Wagon. We also construct Borel realizations of abstract systems of congruences for the action of $PSL_2(\mathbb Z)$ on $P^1( \mathbb R)$.
Extent	26.0 minutes
Subject	Mathematics; Functional analysis; Dynamical systems and ergodic theory
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: University of California Los Angeles
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2020-03-31
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0389695
URI	http://hdl.handle.net/2429/73863
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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Measurable realizations of abstract systems of congruence Marks, Andrew

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