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.
Laboratoire de Mathématiques d'Orsay
Université Paris Sud, Batiment 307
F-91405 Orsay Cedex, France
Tel: +33 1 69 15 57 76
E-mail: camille.horbez "at" math.u-psud.fr
Groups Acting on Fractals, Hyperbolicity and Self-similarity, Thematic trimester at IHP (April-July 2022)
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.
- Measure equivalence classification of transvection-free right-angled Artin groups, with Jingyin Huang, arXiv:2010.03613
- Proper proximality in non-positive curvature, with Jingyin Huang and Jean Lécureux, arXiv:2005.08756
- Cocycle superrigidity from higher rank lattices to Out(F_N), with Vincent Guirardel and Jean Lécureux, arXiv:2005.07477
- Big mapping class groups with hyperbolic actions: classification and applications, with Yulan Qing and Kasra Rafi, arXiv:2005.00428
- Boundary amenability and measure equivalence rigidity among two-dimensional Artin groups of hyperbolic type, with Jingyin Huang, arXiv:2004.09325
- Acylindrical hyperbolicity of automorphism groups of infinitely-ended groups, with Anthony Genevois, arXiv:2002.01388
- Rigidity of the Torelli subgroup in Out(F_N), with Sebastian Hensel and Richard D. Wade, arXiv:1910.10189
- The Tits alternative for the automorphism group of a free product, arXiv:1408.0546
- 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, accepted in Ann. Scient. Ec. Norm. Sup. [arXiv version]
- My thesis: Random walks on Out(F_N) and automorphism groups of free products
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).
- 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).