XVI International Luminy Workshop in Set Theory / XVI Atelier international de théorie des ensembles

Collection XVI International Luminy Workshop in Set Theory / XVI Atelier international de théorie des ensembles

Organizer(s) Fischer, Vera ; Velickovic, Boban ; Viale, Matteo

Date(s) 13/09/2021 - 17/09/2021

linked URL https://conferences.cirm-math.fr/2370.html

00:00:00 / 00:00:00

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Perfect matchings in hyperfinite graphings

By Marcin Sabok

We characterize hyperfinite bipartite graphings that admit measurable perfect matchings. In particular, we prove that every regular hyperfinite one-ended bipartite graphing admits a measurable perfect matching. We give several applications of this result. We extend the Lyons-Nazarov theorem by showing that a bipartite Cayley graph admits a factor of iid perfect matching if and only if the group is not iso-morphic to the semidirect product of Z and a finite group of odd order, answering a question of Kechris and Marks in the bipartite case. We also answer an open question of Bencs, Hruskova and Toth arising in the study of balanced orientations in graphings. Finally, we show how our results generalize and lead to a simple approach to recent results on measurable circle squaring.

Information about the video

Date of recording 16/09/2021
Date of publication 04/10/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19809703
Cite this video Sabok, Marcin (16/09/2021). Perfect matchings in hyperfinite graphings. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19809703
URL https://dx.doi.org/10.24350/CIRM.V.19809703

Domain(s)

Bibliography

Bowen, Matthew, Gabor Kun, and Marcin Sabok. "Perfect matchings in hyperfinite graphings." arXiv preprint arXiv:2106.01988 (2021). - https://arxiv.org/abs/2106.01988

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