Dominik Francoeur

About me

Since December 2024, I am a researcher at the Universidad Autónoma de Madrid (Spain), financed by a César Nombela grant from the Community of Madrid. Before joining the UAM, I was a postdoc at Newcastle University (UK), the Instituto de Ciencias Matemáticas (ICMAT) in Madrid (Spain) and at the ENS de Lyon (France). I completed my PhD at the University of Geneva (Switzerland), under the direction of Tatiana Nagnibeda.

I work mainly in geometric group theory. I am very interested in growth in finitely generated groups, and particularly in groups of intermediate growth. I am also very interested in self-similar groups, groups generated by automata, branch groups and other groups with interesting actions on topological spaces. Particularly, I strive to establish connections between algebraic or geometric properties of these groups and properties of their actions.

Contact Information

Publications

Pre-prints

• On closure operations in the space of subgroups and applications (arXiv)
  (with A. Le Boudec)
• On quasi-2-transitive actions of branch groups (arXiv)

Published and accepted papers

• On the structure of finitely generated subgroups of branch groups (arXiv)
  (with R. Grigorchuk, P.-H. Leemann and T. Nagnibeda) To appear in the Journal of Combinatorial Algebra.
• Intersection-saturated groups without free subgroups (arXiv)
  To appear in Groups, Geometry, Dynamics.
• Subgroup induction property for branch groups (arXiv)
  (with P.-H. Leemann) To appear in the Journal of Fractal Geometry.
• Bireversible automata generating lamplighter groups (journal) (arXiv)
  Bulletin of the London Mathematical Society, 2023, vol. 55, no. 2, pp. 990-997.
• Maximal subgroups of non-torsion Grigorchuk-Gupta-Sidki groups (journal) (arXiv)
  (with A. Thillaisundaram) Canadian Mathematical Bulletin, 2022, vol. 65, no. 4, pp. 825-844.
• Normal subgroups of finitely generated branch groups are finitely generated (journal) (arXiv)
  Appendix to CAPRACE, Pierre-Emmanuel et LE BOUDEC, Adrien. Commensurated subgroups and micro-supported actions.
  Journal of the European Mathematical Society, 2022.
• On the Orbits of Automaton Semigroups and Groups (journal) (arXiv)
  (with D. D'Angeli, E. Rodaro and J.P. Wächter) Algebra and Discrete Mathematics, 2022, vol. 33, no. 1, pp. 1-29.
• On the stabilisers of points in groups with micro-supported actions (journal) (arXiv)
  Journal of Group Theory, 2021, vol. 24, no. 3, pp. 533-547.
• On the existence of free subsemigroups in reversible automata semigroups (journal) (arXiv)
  (with I. Mitrofanov) Groups, Geometry, Dynamics, 2021, vol. 15, no. 3, pp. 1103-1132.
• Einstein tori and crooked surfaces (journal) (arXiv)
  (with J.-P. Burelle, V. Charette and W. Goldman) Advances in Geometry, 2021, vol. 21, no. 2, pp. 237-250.
• On maximal subgroups of infinite index in branch and weakly branch groups (journal) (arXiv)
  Journal of Algebra, 2020, vol. 560, p. 818-851.
• Infinite automaton semigroups and groups have infinite orbits (journal) (arXiv)
  (with D. D'Angeli, E. Rodaro and J.P. Wächter) Journal of Algebra, 2020, vol. 553, pp. 119-137.
• On the subexponential growth of groups acting on rooted trees (journal) (arXiv)
  Groups, Geometry and Dynamics, 2020, vol. 14, pp. 1-24.
• Foliations between crooked planes in Minkowski 3-space (journal) (arXiv)
  (with J.-P. Burelle) Internat. J. Math., 2019, vol. 30, no. 1.
• Maximal subgroups of groups of intermediate growth (journal) (arXiv)
  (with A. Garrido) Advances in Mathematics, 2018, vol. 340, pp. 1067-1107.
• Fundamental domains in the Einstein Universe (journal) (arXiv)
  (with V. Charette and R. Lareau-Dussault) Topology and its Applications, 2014, vol. 174, pp. 62-80.