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Groups, Actions and von Neumann algebras

Total Cost €


EC-Contrib. €






Project "GAN" data sheet

The following table provides information about the project.


There are not information about this coordinator. Please contact Fabio for more information, thanks.

 Coordinator Country France [FR]
 Project website
 Total cost 876˙750 €
 EC max contribution 876˙750 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-STG
 Funding Scheme ERC-STG
 Starting year 2015
 Duration (year-month-day) from 2015-04-01   to  2020-03-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITE PARIS-SACLAY FR (SAINT AUBIN) coordinator 844˙473.00


 Project objective

This research project focuses on the structure, classification and rigidity of three closely related objects: group actions on measure spaces, orbit equivalence relations and von Neumann algebras. Over the last 15 years, the study of interactions between these three topics has led to a process of mutual enrichment, providing both striking theorems and outstanding conjectures.

Some fundamental questions such as Connes' rigidity conjecture, the structure of von Neumann algebras associated with higher rank lattices, or the fine classification of factors of type III still remain untouched. The general aim of the project is to tackle these problems and other related questions by developing a further analysis and understanding of the interplay between von Neumann algebra theory on the one hand, as well as ergodic and group theory on the other hand. To do so, I will use and combine several tools and develop new ones arising from Popa's Deformation/Rigidity theory, Lie group theory (lattices, boundaries), topological and geometric group theory and representation group theory (amenability, property (T)). More specifically, the main directions of my research project are:

1) The structure of the von Neumann algebras arising from Voiculescu's Free Probability theory: Shlyakhtenko's free Araki-Woods factors, amalgamated free product von Neumann algebras and the free group factors.

2) The structure and the classification of the von Neumann algebras and the measured equivalence relations arising from lattices in higher rank semisimple connected Lie groups.

3) The measure equivalence rigidity of the Baumslag-Solitar groups and several other classes of discrete groups acting on trees.


year authors and title journal last update
List of publications.
2020 Cyril Houdayer, Yusuke Isono
Factoriality, Connes\' type III invariants and fullness of amalgamated free product von Neumann algebras
published pages: 1-38, ISSN: 0308-2105, DOI: 10.1017/prm.2018.152
Proceedings of the Royal Society of Edinburgh: Section A Mathematics 2020-03-11
2019 Cyril Houdayer, Amine Marrakchi, Peter Verraedt
Fullness and Connes\' Ï„ invariant of type III tensor product factors
published pages: 113-134, ISSN: 0021-7824, DOI: 10.1016/j.matpur.2018.06.018
Journal de Mathématiques Pures et Appliquées 121 2020-03-11
2018 Amine Marrakchi
Strongly ergodic actions have local spectral gap
published pages: 3887-3893, ISSN: 0002-9939, DOI: 10.1090/proc/14034
Proceedings of the American Mathematical Society 146/9 2020-03-11
2019 Cyril Houdayer, Sven Raum
Locally compact groups acting on trees, the type I conjecture and non-amenable von Neumann algebras
published pages: 185-219, ISSN: 0010-2571, DOI: 10.4171/cmh/458
Commentarii Mathematici Helvetici 94/1 2020-03-11
2018 Rémi Boutonnet, Cyril Houdayer
Amenable absorption in amalgamated free product von Neumann algebras
published pages: 583-593, ISSN: 2156-2261, DOI: 10.1215/21562261-2017-0030
Kyoto Journal of Mathematics 58/3 2020-03-11
Asymptotic structure of free product von Neumann algebras
published pages: 489-516, ISSN: 0305-0041, DOI: 10.1017/S0305004116000396
Mathematical Proceedings of the Cambridge Philosophical Society 161/03 2020-03-11
2017 Rémi Boutonnet, Cyril Houdayer
Amenable absorption in amalgamated free product von Neumann algebras
published pages: , ISSN: 2154-3321, DOI:
Kyoto Journal of Mathematics 2020-03-11
2017 Cyril Houdayer, Amine Marrakchi, Peter Verraedt
Strongly ergodic equivalence relations: spectral gap and type III invariants
published pages: , ISSN: 0143-3857, DOI:
Ergodic Theory and Dynamical Systems 2020-03-11
2017 Cyril Houdayer, Yusuke Isono
Unique prime factorization and bicentralizer problem for a class of type III factors
published pages: 402-455, ISSN: 0001-8708, DOI: 10.1016/j.aim.2016.09.030
Advances in Mathematics 305 2020-03-11
2017 Cyril Houdayer, Dimitri Shlyakhtenko, Stefaan Vaes
Classification of a family of non almost periodic free Araki-Woods factors
published pages: , ISSN: 1435-9855, DOI:
Journal of the European Mathematical Society 2020-03-11
2017 Cyril Houdayer, Sorin Popa
Singular MASAs in type III factors and Connes\' Bicentralizer Property
published pages: , ISSN: , DOI:
Advanced Studies in Pure Mathematics 2020-03-11
2016 Cyril Houdayer, Yoshimichi Ueda
Rigidity of free product von Neumann algebras
published pages: 2461-2492, ISSN: 0010-437X, DOI: 10.1112/S0010437X16007673
Compositio Mathematica 152/12 2020-03-11
2016 Rémi Boutonnet, Cyril Houdayer
Structure of modular invariant subalgebras infree Araki–Woods factors
published pages: 1989-1998, ISSN: 2157-5045, DOI: 10.2140/apde.2016.9.1989
Analysis & PDE 9/8 2020-03-11
2017 Amine Marrakchi
Spectral gap characterization of full type III factors
published pages: , ISSN: 0075-4102, DOI: 10.1515/crelle-2016-0071
Journal für die reine und angewandte Mathematik (Crelles Journal) 0/0 2020-03-11
2017 Rémi Boutonnet, Cyril Houdayer, Stefaan Vaes
Strong solidity of free Araki-Woods factors
published pages: , ISSN: 0002-9327, DOI:
American Journal of Mathematics 2020-03-11

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