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UID:20260711T045702EDT-1736MNIV0K@132.216.98.100
DTSTAMP:20260711T085702Z
DESCRIPTION:Title: Measurable solutions to abstract systems of congruence.
 \n\nAbstract: An abstract system of congruences describes a way of partiti
 oning a space into finitely many pieces satisfying certain congruence rela
 tions. Examples of abstract systems of congruences include paradoxical dec
 ompositions and partitioning a set into n congruent pieces. We consider th
 e general question of when there are realizations of abstract systems of c
 ongruences satisfying various measurability constraints. We completely cha
 racterize which abstract systems of congruences can be realized by nonmeag
 er Baire measurable pieces of the sphere under the action of rotations on 
 the 2-sphere. We also construct Borel realizations of abstract systems of 
 congruences for the action of PSL2(Z) on the projective line. The combinat
 orial underpinnings of our proof are certain types of decomposition of Bor
 el graphs into paths\n
DTSTART:20190321T183000Z
DTEND:20190321T193000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Andrew Marks (UCLA) 
URL:https://www.mcgill.ca/mathstat/channels/event/andrew-marks-ucla-295465
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