Nicolás Matte Bon — Researcher

My research focuses on various aspects of infinite groups with an emphasis on interactions with dynamics. Since February 2020, I am a CNRS researcher at Institut Camille Jordan, Université Claude Bernard Lyon 1. Before that, I have been a postdoc at ETH Zürich (2016-2019) and, for one semester, at EPFL in Lausanne (Sep 2019- Jan 2020). I did my Ph.D. at ENS Paris and Université Paris Sud–Orsay (2013-2016). My advisor was Anna Erschler.

My habilitation (HDR) memoir, defended on 11 Jan 2024 at Université Claude Bernard Lyon 1, 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.)

I coorganise the Geometry Seminar at ICJ with Klaus Niederkrüger and Rémi Reboulet.

I am the advisor of Martín Gilabert Vio.

Publications and Preprints

Subexponential growth and C¹ actions on one-manifolds (with S.-h. Kim, M. de la Salle & M. Triestino)
Int. Math. Res. Not. IMRN 2025, Issue 13, July 2025, rnaf202. (2024). [journal | arXiv]
On the growth of actions of free products (with A. Le Boudec & V. Salo)
Groups Geom. Dyn. 19 (2025), no. 2, 661–680. [journal | arXiv]
A realisation result for moduli spaces of group actions on the line (with J. Brum, C. Rivas & M. Triestino)
J. Topol. 17 (2024), no. 4, e12357. [journal | arXiv]
Liouville property for groups and conformal dimension (with V. Nekrashevych & T. Zheng)
Invent. Math., published online (2025). [journal | arXiv]
Solvable groups and affine actions on the line (with J. Brum, C. Rivas & M. Triestino)
J. Éc. polytech. Math. 12 (2025), 23–69. [journal]
Some torsion-free solvable groups with few subquotients (with A. Le Boudec)
Math. Proc. Cambridge Philos. Soc. 176 (2024), no. 2, 279–286. [journal | 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 & O. Tamuz)
Israel J. Math. 262 (2024), no. 1, 487–500. [journal | arXiv]
Locally moving groups and laminar actions on the line (with J. Brum, C. Rivas & M. Triestino)
Astérisque (accepted in 2024), 205 pp. [arXiv]
Piecewise strongly proximal actions, free boundaries and the Neretin groups (with P.-E. Caprace & A. Le Boudec)
Bull. Soc. Math. France 150 (2022), no. 4, 773–795. [journal | arXiv]
Confined subgroups and high transitivity (with A. Le Boudec)
Ann. H. Lebesgue 5 (2022), 491–522. [journal | 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. [journal | 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. [journal | arXiv]
Groups of piecewise linear homeomorphisms of flows (with M. Triestino)
Compos. Math. 156 (2020), no. 8, 1595–1622. [journal | arXiv]
Property FW, differentiable structures, & smoothability of singular actions (with Y. Lodha & M. Triestino)
J. Topol. 13 (2020), no. 3. [journal | arXiv]
Rigidity properties of full groups of pseudogroups over the Cantor set
(A previous version was entitled: Rigidity of graphs of germs & 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. [journal | arXiv]
Realizing uniformly recurrent subgroups (with T. Tsankov)
Ergodic Theory Dyn. Syst. 40 (2020), no. 2, 478–489. [journal | 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 & G. Kozma)
Groups Geom. Dyn. 18 (2024), no. 1, 1–24. [arXiv]
Subgroup dynamics & C^*-simplicity of groups of homeomorphisms (with A. Le Boudec)
Ann. Sci. Éc. Norm. Supér. 51 (2018), no. 3, 557–602. [journal | arXiv]
Full groups of bounded automaton groups
J. Fractal Geom. 4 (2017), no. 4, 425–458. [journal | arXiv]
Extensive amenability & an application to interval exchanges (with K. Juschenko, N. Monod & M. de la Salle)
Ergodic Theory Dyn. Syst. 38 (2018), no. 1, 195–219. [journal | 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. [journal | arXiv]
Subshifts with slow complexity & simple groups with the Liouville property
Geom. Funct. Anal. 24 (2014), no. 5, 1637–1659. [journal | 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. [journal | arXiv]