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.

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

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).

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

- 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

- 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

- 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]

- 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]

- 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

- 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

- 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)

- 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))

- 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).