Camille Horbez

French version

I am "chargé de recherche" at the CNRS at the Laboratoire de Mathématiques d'Orsay, in the Topology and Dynamics team.
Here you can find a CV.

Contact information

Laboratoire de Mathématiques d'Orsay
Université Paris-Saclay, Batiment 307
F-91405 Orsay Cedex, France
Office: 3R17
Tel: +33 1 69 15 57 99
E-mail: camille.horbez "at" cnrs.fr

ERC Starting Grant project

I am the PI of the ERC StG project "Artin groups, mapping class groups and Out(Fn): from geometry to operator algebras via measure equivalence" (Artin-Out-ME-OA, Grant 101040507).

Research interests

My research domain is geometric group theory, I am particularly interested in the study of the group Out(F_N) of outer automorphisms of a free group through its action on geometric complexes, such as Outer space or some hyperbolic complexes, and their boundaries. In this context, I have been interested in subgroup classification and rigidity questions. I have also been working on random walks on mapping class groups of surfaces, and on Out(F_N). More recently, I have developed interest in measured group theory and its application to operator algebras, in particular through the study of measure equivalence rigidity phenomena for groups that have features of negative curvature.

Seminar

Groups and actions, co-organized with Matthieu Joseph
(This replaces the seminar Groups and operator algebras, that I co-organized with Cyril Houdayer in 2021-2022 and 2022-2023.)

Research work

Preprints

Graph products and measure equivalence: classification, rigidity, and quantitative aspects, with Amandine Escalier, arXiv:2401.04635
Integrable measure equivalence rigidity of right-angled Artin groups via quasi-isometry, with Jingyin Huang, arXiv:2309.12147
Measure equivalence rigidity among the Higman groups, with Jingyin Huang, arXiv:2206.00884
Measure equivalence rigidity of the handlebody groups, with Sebastian Hensel, arXiv:2111.10064
Measure equivalence rigidity of Out(F_N), with Vincent Guirardel, arXiv:2103.03696
Boundary amenability and measure equivalence rigidity among two-dimensional Artin groups of hyperbolic type, with Jingyin Huang, arXiv:2004.09325
The Tits alternative for the automorphism group of a free product, arXiv:1408.0546

Accepted papers

Rigidity of the Torelli subgroup in Out(F_N), with Sebastian Hensel and Richard D. Wade, accepted in Rev. Math. Iberoam., arXiv:1910.10189
On the homology growth and the l²-Betti numbers of Out(Wn), with Damien Gaboriau and Yassine Guerch, accepted in Ann. Inst. Fourier, arXiv:2209.02760

Published papers

Proper proximality in non-positive curvature, with Jingyin Huang and Jean Lécureux, Amer. J. Math. 145(2023)(5), 1327-1364, arXiv version
Orbit equivalence rigidity of irreducible actions of right-angled Artin groups, with Jingyin Huang and Adrian Ioana, Compos. Math. 159(2023)(4), 860-887 arXiv version
Boundary amenability of Out(F_N), with Mladen Bestvina and Vincent Guirardel, Ann. Sci. Ec. Norm. Supér. (4) 55(2022)(5), 1379-1431 arXiv version
Big mapping class groups with hyperbolic actions: classification and applications, with Yulan Qing and Kasra Rafi, J. Inst. Math. Jussieu 21(2022)(6), 2173-2204 [article, arXiv version]
Cocycle superrigidity from higher rank lattices to Out(F_N), with Vincent Guirardel and Jean Lécureux, J. Mod. Dyn. 28(2022), 291-344 [arXiv version]
Measure equivalence classification of transvection-free right-angled Artin groups, with Jingyin Huang, J. Ec. Polytech. Math. 9(2022), 1021-1067 [arXiv version]
Boundaries of relative factor graphs and subgroup classification for automorphisms of free products, with Vincent Guirardel, Geom. Topol. 26(1)(2022), 71-126 [arXiv version]
Acylindrical hyperbolicity of automorphism groups of infinitely-ended groups, with Anthony Genevois, J. Topol. 14(3)(2021), 963-991 [arXiv version]
On the topological dimension of the Gromov boundaries of some hyperbolic Out(F_N)-graphs, with Mladen Bestvina and Richard D. Wade, Pacific J. Math. 308(1)(2020), 1-40 [article, arXiv version]
Commensurations of subgroups of Out(F_N), with Richard D. Wade, Trans. Amer. Math. Soc. 373(4)(2020), 2699-2742 [paper, arXiv version]
A compactification of outer space which is an absolute retract, with Mladen Bestvina, Ann. Inst. Fourier 69(6)(2019), 2395-2437 [paper, arXiv version]
Algebraic laminations for free products and arational trees, with Vincent Guirardel, Alg. Geom. Topol. 19(5)(2019), 2283-2400 [paper, arXiv version]
Spectral theorems for random walks on mapping class groups and Out(F_N), with François Dahmani, Int. Math. Res. Not. 9 (2018), 2693-2744 [article, arXiv version]
Central limit theorems for mapping class groups and Out(F_N), Geom. Topol. 22(1) (2018), 105-156 [paper, arXiv version]
The boundary of the outer space of a free product, Israel J. Math. 221(1) (2017), 179-234 [paper, arXiv version]
The hyperbolicity of the sphere complex via surgery paths, with Arnaud Hilion, J. Reine Angew. Math. 730 (2017), 135-161 [paper, arXiv version]
The horoboundary of outer space, and growth under random automorphisms, Ann. Scient. Ec. Norm. Sup. (4) 49(5) (2016), 1075-1123 [paper, arXiv version]
A short proof of Handel and Mosher's alternative for subgroups of Out(F_N), Groups Geom. Dyn. 10(2) (2016), 709-721 [paper, arXiv version]
Hyperbolic graphs for free products, and the Gromov boundary of the graph of cyclic splittings, J. Topol. 9(2) (2016), 401-450 [paper, arXiv version]
The Poisson boundary of Out(F_N), Duke Math. J. 165(2) (2016), 341-369 [paper, arXiv version]
Spectral rigidity for primitive elements of F_N, J. Group Theory 19(1) (2016), 55-123. [paper, arXiv version]
Automorphisms of graphs of cyclic splittings of F_N, with Richard D. Wade, Geom. Dedic. 178(1) (2015), 171-187. [paper, arXiv version]
Sphere paths in outer space, Alg. Geom. Topol. 12(4) (2012), 2493-2517. [paper, arXiv version]

Miscellaneous

Morphisms from higher rank lattices to Out(F_N), avec Vincent Guirardel, appendix to the article "Hyperbolic rigidity of higher rank lattices" by Thomas Haettel, Ann. Sci. Ec. Norm. Supér. (4) 53(2)(2020), 439-468 [article, arXiv version]

Memoirs

Habilitation: Ergodic geometry at infinity of Out(F_N), measure equivalence, rigidity
PhD thesis: Random walks on Out(F_N) and automorphism groups of free products

Events I organized

Upcoming events

Orbit equivalence, Workshop in Besse, 8-12 July, 2024 (with Matthieu Joseph, François Le Maître et Romain Tessera)
Rigidity in group theory: geometric and ergodic aspects, Conference organized in Orsay, March 19-22, 2024

Past events

Groups Acting on Fractals, Hyperbolicity and Self-similarity, Thematic trimester at the IHP (April-July 2022), organized with François Dahmani, Anna Erschler and Dani Wise. Au sein de ce semestre, j'ai participé à l'organisation des deux conférences suivantes :
- Introductory school at the CIRM (organized with François Dahmani, Tullia Dymarz and Peter Haïssinsky)
- Mapping class groups and Out(Fn) (organized with Hyungryul Baik, Mladen Bestvina, Kasra Rafi and Karen Vogtmann)
Right-angled Artin groups and their automorphisms (workshop organized in Orsay in the framework of the ANR DAGGER, with Rémi Coulon and Arnaud Hilion)

Videos

Cours Peccot

Here are the links to the videos of my `Cours Peccot': I gave four lectures at the Collège de France in January 2018 on "Asymptotic geometry of the outer automorphism group of a free group" (in French).

Leçon du 10/01/2018 (Out(F_N) actions (Outer space, hyperbolic complexes))
Leçon du 17/01/2018 (Classification of subgroups of Out(F_N))
Leçon du 24/01/2018 (Rigidity phenomena in Out(F_N))
Leçon du 31/01/2018 (Amenability at infinity of Out(F_N))

Mini-course ``Measure equivalence, negative curvature, rigidity''

Given in Bangalore in March 2023 : Part 1, Part 2, Part 3, Part 4.

Talks

Measure equivalence rigidity among the Higman groups, talk given at the Fields Institute (Toronto) during the "Workshop on Borel and Measurable Combinatorics in Algebra and Dynamics" (03/21/2023)
Rigidities in measure equivalence, talk given (in French) at the Séminaire virtuel francophone Groupes et Géométrie (09/22/2022)
Right-angled Artin groups, orbit equivalence and von Neumann algebras, talk given during the online conference "von Neumann algebras and geometric group theory" (10/07/2021)
Measure equivalence and right-angled Artin groups, talk given at the CIRM during the conference "Measured and Geometric Group Theory, Rigidity, Operator Algebras" (10/08/2020)
Abstract commensurator of some normal subgroups of Out(F_N), talk given in Warwick during the conference "Graphs, surfaces and cube complexes" (07/12/2018).
Automorphisms of hyperbolic groups and growth, talk given at the CIRM during the conference "Geometry of groups and 3-manifolds: state of the art and perspectives" (20/02/2018).
Growth under automorphisms of hyperbolic groups, talk given at the Isaac Newton Institute (Cambridge) during the conference "Non-positive curvature in action" (01/09/2017).
A multiplicative ergodic theorem for mapping class groups, talk given at the MSRI (Berkeley) during the conference "Geometry of mapping class groups and Out(Fn)" (22/08/2016).
Topological dimension of the boundaries of some hyperbolic Out(F_N)-graphs, talk given at the MSRI (Berkeley) during the conference "Introductory workshop: Geometric group theory" (22/08/2016).
Growth under random products of automorphisms of a free group, talk given at the CIRM during the conference "Impact of geometric group theory" (07/14/2015).
Horoboundary of outer space and growth under random automorphisms, talk given at the University of Notre-Dame during the conference "Boundaries and Ergodic Geometry" (06/01/2015).
The Tits alternative for the automorphism group of a free product, talk given at the University of Illinois at Urbana-Champaign (02/19/2015).