Nicolás MATTE BON

Chargé de recherche CNRS
Institut Camille Jordan (ICJ)
Université Claude Bernard Lyon 1
Equipe Algèbre, Géométrie, Logique (AGL)

E-mail: mxttxbxn(at)math(dot)univ-lyon1(dot)fr (replace x)

About me

My research focuses on various aspects of infinite groups with an emphasis on interactions with dynamics. Here is a short CV:

• Sep 2013-Aug 2016: Ph.D. at ENS Paris and Université Paris Sud-Orsay, under the direction of Anna Erschler.
• Sep 2016 - Aug 2019: Postdoc at ETH Zürich, under the mentorship of Marc Burger
• Sep 2019- Jan 2020: Postdoc at EPF Lausannne, in the chair of Nicolas Monod
• Feb 2020-present: CNRS researcher affiliated to the Institut Camille Jordan , Université Claude Bernard Lyon 1.
  

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• I defended my habilitation (HDR) thesis on 11/01/2024 at Université Claude Bernard Lyon 1. The memoir is available here, and contains a survey of of some of my work in the period 2016-2023.
  (Warning : Chapter 2 became in part obsolete after a major revision of the paper "Locally moving groups.. " with J. Brum, C. Rivas and M. Triestino --in particular it contains older versions of the results there, and it uses the terminology "R-focal action", that we abandoned.)
• I am one of the organisers of the Geometry Seminar at ICJ.
• I am the advisor of Martín Gilabert Vio
  

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  Publications and preprints

  • Subexponential growth and C¹ actions on one-manifolds (with S.-h. Kim, M. de la Salle and M. Triestino)
    Int. Math. Res. Not. IMRN 2025, Issue 13, July 2025, rnaf202. (2024). [arXiv]
  • On the growth of actions of free products (with A. Le Boudec and V. Salo)
    Groups Geom. Dyn. 19 (2025), no. 2, 661–680. [arXiv]
  • A realisation result for moduli spaces of group actions on the line (with J. Brum, C. Rivas and M. Triestino)
    J. Topol. 17 (2024), no. 4, e12357. [arXiv]
  • Liouville property for groups and conformal dimension (with V. Nekrashevych and T. Zheng)
    Invent. Math., published online (2025). [arXiv]
  • Solvable groups and affine actions on the line (with J. Brum, C. Rivas and M. Triestino)
    J. Éc. polytech. Math. 12 (2025), 23–69.
  • Some torsion-free solvable groups with few subquotients (with A. Le Boudec)
    Math. Proc. Cambridge Philos. Soc. 176 (2024), no. 2, 279–286. [arXiv]
  • Growth of actions of solvable groups (with A. Le Boudec)
    Submitted (2022). [arXiv]
  • A quantitative Neumann lemma for finitely generated groups (with E. Gorokhovsky and O. Tamuz)
    Israel J. Math. 262 (2024), no. 1, 487–500. [arXiv]
  • Locally moving groups and laminar actions on the line (with J. Brum, C. Rivas and M. Triestino)
    Astérisque (to appear), 205 pp (v1 2021, final version in 2024 with new title and improved results). [arXiv]
  • Piecewise strongly proximal actions, free boundaries and the Neretin groups (with P.-E. Caprace and A. Le Boudec)
    Bull. Soc. Math. France 150 (2022), no. 4, 773–795. [arXiv]
  • Confined subgroups and high transitivity (with A. Le Boudec)
    Ann. H. Lebesgue 5 (2022), 491–522. [arXiv]
  • A commutator lemma for confined subgroups and applications to groups acting on rooted trees (with A. Le Boudec)
    Trans. Amer. Math. Soc. 376 (2023), no. 10, 7187–7233. [arXiv]
  • Triple transitivity and non-free actions in dimension one (with A. Le Boudec)
    J. Lond. Math. Soc. (2) 105 (2022), no. 2, 884–908. [arXiv]
  • Groups of piecewise linear homeomorphisms of flows (with M. Triestino)
    Compos. Math. 156 (2020), no. 8, 1595–1622. [arXiv]
  • Property FW, differentiable structures, and smoothability of singular actions (with Y. Lodha and M. Triestino)
    J. Topol. 13 (2020), no. 3. [arXiv]
  • Rigidity properties of full groups of pseudogroups over the Cantor set
    (A previous version was entitled: Rigidity of graphs of germs and homomorphisms between full groups)
    Preprint (2018). [arXiv]
  • Locally compact groups whose ergodic or minimal actions are all free (with A. Le Boudec)
    Int. Math. Res. Not. 2020, no. 11, 3318–3340. [arXiv]
  • Realizing uniformly recurrent subgroups (with T. Tsankov)
    Ergodic Theory Dyn. Syst. 40 (2020), no. 2, 478–489. [arXiv]
  • A remark on groups defined by slowly growing trees (appendix to Groups with minimal harmonic functions as small as you like by G. Amir and G. Kozma)
    Groups Geom. Dyn. 18 (2024), no. 1, 1–24.
  • Subgroup dynamics and C^*-simplicity of groups of homeomorphisms (with A. Le Boudec)
    Ann. Sci. Éc. Norm. Supér. 51 (2018), no. 3, 557–602. [arXiv]
  • Full groups of bounded automaton groups
    J. Fractal Geom. 4 (2017), no. 4, 425–458. [arXiv]
  • Extensive amenability and an application to interval exchanges (with K. Juschenko, N. Monod, M. de la Salle)
    Ergodic Theory Dyn. Syst. 38 (2018), no. 1, 195–219. [arXiv] Here is a link to a video.
  • Topological full groups of minimal subshifts with subgroups of intermediate growth
    J. Mod. Dyn. 9 (2015), 67–80. [arXiv]
  • Subshifts with slow complexity and simple groups with the Liouville property
    Geom. Funct. Anal. 24 (2014), no. 5, 1637–1659. [arXiv]
  • The Liouville property for groups acting on rooted trees (with G. Amir, O. Angel, B. Virág)
    Ann. Inst. Henri Poincaré Probab. Statist. 52 (2016), no. 4, 1763–1783. [arXiv]
  
  

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