- With Matthieu Calvez, Morse elements in Garside groups are strongly contracting. Slides of a short talk on this paper and a long version.
- With Matthieu Calvez, Hyperbolic structures for Artin-Tits groups of spherical type, Contemporary Mathematics, 766 (2021), 83-98
- Garside groups and geometry, in memory of Patrick Dehornoy, preprint (2020)
- With Saul Schleimer, Garside theory and subsurfaces: some examples in braid groups , Groups Complexity Cryptology, 11 (2019), no. 2, 61–75.
- With María Cumplido, Volker Gebhardt and Juan Gonzáles-Meneses, On parabolic subgroups of Artin-Tits groups of spherical type, Advances in Mathematics 352, 572-610 (2019).
- With María Cumplido, A positive proportion of elements of mapping class groups is pseudo-Anosov, Bulletin of the London Mathematical Society 50(3), 390-394 (2018)
- With Matthieu Calvez, Acylindrical hyperbolicity and Artin-Tits groups of spherical type, Geometriae Dedicata 191(1) (2017), 199-215.
- With Matthieu Calvez, Curve complexes and Garside groups, Geometriae Dedicata 188(1) (2017), 195-213. Slides of a talk on this paper.
- On the genericity of loxodromic actions. Israel J of Mathematics 220 (2017), 559-582.
- With Sandrine Caruso, On the genericity of pseudo-Anosov braids II: conjugations to rigid braids, J Groups, Geometry, and Dynamics 11(2), 2017, 549-565. Slides of a talk on this paper, and a video of this talk.
- With Matthieu Calvez, A fast solution to the conjugacy problem in the 4 strand braid group, Journal of Group Theory 17 (2014), no.5, 757-780.
- With Tetsuya Ito, Lawrence-Krammer-Bigelow representations and dual Garside length of braids, Geometry and Topology 19 (2015), 1361-1381 Slides of a talk on this paper.
- With Evgeny Fominykh, Upper bounds for the complexity of torus knot complements, Journal of Knot Thy. Ram. 22 (9), 2013.
- With Valery Bardakov and Andrei Vesnin, Dynnikov coordinates on virtual braid groups, Journal of Knot Thy. Ram. 21 (5), 2012
- With Juan Gonzáles-Meneses, Reducible braids and Garside theory, Algebraic & Geometric Topology 11 (2011) 2971-3010
- With Matthieu Calvez, Fast algorithmic Nielsen-Thurston classification of four-strand braids, Journal Knot Thy. Ram. 21 (5). Slides of a talk on this paper.
- With Andrés Navas, Nielsen-Thurston orderings and the space of braid orderings, Bulletin of the London Mathematical Society 43, 5 (2011) 901-911
- How to read the length of a braid from its curve diagram, Groups, Geometry and Dynamics 5 (2011) 673-681. The version of the paper on arXiv contains a correction of a mistake which is unfortunately present in the published version. An erratum has been published again in the journal Groups Geom. Dyn. 7 (2013) 495-496.
- With John Crisp and Eddy Godelle: A linear time solution to the conjugacy problem in right-angled Artin groups and their subgroups, Journal of Topology, 2 (2009), 442 - 460. Slides of a talk on this paper.
- The book Ordering braids by Patrick Dehornoy, with Ivan Dynnikov, Dale Rolfsen, and me, Mathematical Surveys and Monographs of the AMS, Vol 148 (2008). This book replaces and supersedes the book "Why are braids orderable?", which had appeared in the "Panoramas et synthèses" series of the French mathematical society.
- My thèse d'habilitation à diriger des recherches, and the associated talk at my "thesis" defense.
- With Jose Burillo and Sean Cleary: Computational explorations in Thompson's group F. Appeared in the Proceedings of the Geneva and Barcelona 2005 conferences in Geometric Group Theory. (Geometric group theory, 21--35, Trends Math., Birkhäuser, Basel, 2007.)
- With John Crisp: Quasi-isometrically embedded subgroups of braid and diffeomorphism groups. Trans. Amer. Math. Soc. 359 (2007), no. 11, 5485-5503.
- With Patrick Dehornoy: On word reversings in braid groups. Internat. J. Algebra Comput. 16 (2006), no. 5, 941-957.
- With Ivan Dynnikov: On the complexity of braids. J. Eur. Math. Soc. 9 (2007), no. 4, 801-840. Slides of a talk on this paper.
- With Juan Gonzalez-Meneses: On the structure of the centralizer of a braid. Annales de l'ENS 37 (2004), 729-757.
- With John Crisp: Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups, Alg. and Geom. Topology 4 (2004), 439-472.
- An algorithm for the word problem in braid groups (pdf-version). I don't know what to do with this paper: I think it's very exciting, unfortunately it consists mainly of conjectures, and only some very weak theorems, so it's hardly publishable. I'm working on proofs for stronger results (see e.g. the more recent paper with Ivan Dynnikov).
- Diagram groups, braid groups, and orderability, Journal of Knot Theory and its Ramifications, Vol 12 (2003), 321-332. (ps version)
- With Steve Boyer and Dale Rolfsen: Orderable 3-manifold groups, Annales de l'Institut Fourier 55 (2005), 243--288.
- With Estelle Souche: An elementary approach to quasi-isometries of tree x R^n, appeared in the special issue of Geometriae Dedicata on the 2000 Haifa conference on Geometric group theory. In ps or pdf.
- With Dale Rolfsen: Free group automorphisms, invariant orderings and topological applications, Algebraic and Geometric Topology 1 (2001, 311-319.
- With Hamish Short: Orderings of mapping class groups after Thurston, L'enseignement Mathématique 46 (2000), 279-312.
- With Colin Rourke: Order automatic mapping class groups , Pac. J. Math. 194 (2000), 209-227
- Dehornoy's ordering of the braid groups extends the subword-ordering Pac. J. Math. 191, 183-188 (A better proof is in my paper with H.Short.)
- With Roger Fenn, Michael T. Greene, Dale Rolfsen, and Colin Rourke: Ordering the braid groups , Pacific J Math 191 (1999), 41-74
- With Michael T. Greene, A natural framing of knots, Geometry and Topology, Vol 2 (1998), and
- With Michael T. Greene, On compressing disks of torus knots, Quarterly J Math. 52 (2001), 25-32
- With Rosa Antolini: The singular cubical set of a topological space. Appeared in revised form in the Math. Proc. Camb. Phil. Soc. 126 (1999), p 149-154.
- Loop spaces and the compression theorem, Proc. AMS, 128 (2000)
- "Rack spaces and loop spaces", J. Knot Thy. Ram., Vol 8 (1999), p 99-114.