Publications

Preprints

1. 2025
   Dense and comeager conjugacy classes in zero-dimensional dynamics, with M. Doucha and T. Tsankov, preprint. [PDF] [arXiv]

To appear

1. 2026
   Some aspects of topological dynamics of Polish groups (with an introduction to descriptive set theory), to appear in Cours Spécialisés de la SMF. [PDF] [arXiv]
2. 2025
   A dynamical proof of Matui's absorption theorem, to appear in Annales Henri Lebesgue. [PDF] [arXiv]

Published papers

1. 2025
   Clopen type semigroups of actions on 0-dimensional compact spaces, Groups, Geometry and Dynamics 19 (2025), 957–987. [PDF] [arXiv] [DOI]

   This document corrects a few inaccuracies; in particular, Question 6.3 as stated in the text is easy to answer.

2. 2025
   A topometric Effros theorem, with I. Ben Yaacov, Journal of Symbolic Logic 90 (2025), no. 1, 310–320. [PDF] [arXiv] [DOI]
3. 2023
   From invariant measures to orbit equivalence, via locally finite groups, with S. Robert, Annales Henri Lebesgue 6 (2023), 259–295. [PDF] [arXiv] [DOI]

   One of the main arguments of this paper contains a mistake. Please see the corrigendum.

4. 2023
   Generic properties of homeomorphisms preserving a given dynamical simplex, Ergodic Theory and Dynamical Systems 43 (2023), no. 2, 646–662. [PDF] [arXiv] [DOI]
5. 2022
   Homogeneous actions on Urysohn spaces, with P. Fima, F. Le Maître and S. Moon, Colloquium Mathematicum 167 (2022), no. 1, 21–61. [PDF] [arXiv] [DOI]
6. 2021
   Dense locally finite subgroups of automorphism groups of ultraextensive spaces, with M. Etedadialiabadi, S. Gao and F. Le Maître, Advances in Mathematics 391 (2021), no. 107966. [PDF] [arXiv] [DOI]
7. 2020
   Dynamical simplices and Borel complexity of orbit equivalence, Israel Journal of Mathematics 236 (2020), no. 1, 317–344. [PDF] [arXiv] [DOI]
8. 2019
   Dynamical simplices and Fraïssé theory, Ergodic Theory and Dynamical Systems 39 (2019), no. 11, 3111–3126. [PDF] [arXiv] [DOI]
9. 2017
   Metrizable universal minimal flows of Polish groups have a comeagre orbit, with I. Ben Yaacov and T. Tsankov, Geometric and Functional Analysis 27 (2017), no. 1, 67–77. [PDF] [arXiv] [DOI]
10. 2017
    A Polish metric space whose group of isometries induces a universal relation for Polish group actions, Fundamenta Mathematicae 239 (2017), no. 1, 43–49. [PDF] [DOI]
11. 2017
    Dynamical simplices and minimal homeomorphisms, with T. Ibarlucía, Proceedings of the AMS 145 (2017), no. 11, 4981–4994. [PDF] [arXiv] [DOI]
12. 2016
    From isolated subgroups to generic permutation representations, with Y. Glasner and D. Kitroser, Journal of the LMS (2) 94 (2016), no. 3, 688–708. [PDF] [arXiv] [DOI]
13. 2016
    Polish groups and Baire category methods, Confluentes Mathematici 8 (2016), no. 1, 89–164. [PDF] [DOI]

    Contains almost all of the text of my habilitation thesis.

14. 2016
    Isometrisable group actions, with I. Ben Yaacov, Proceedings of the AMS 144 (2016), no. 9, 4081–4088. [PDF] [arXiv]
15. 2016
    Polish groups with metrizable universal minimal flows, with L. Nguyen Van Thé and T. Tsankov, International Mathematics Research Notices (2016), no. 5, 1285–1307. [PDF] [arXiv] [DOI]
16. 2016
    Full groups of minimal homeomorphisms and Baire category methods, with T. Ibarlucía, Ergodic Theory and Dynamical Systems 36 (2016), no. 2, 550–573. [PDF] [arXiv] [DOI]
17. 2015
    Grey subsets of Polish spaces, with I. Ben Yaacov, Journal of Symbolic Logic 80 (2015), no. 4, 1379–1397. [PDF] [arXiv] [DOI]
18. 2014
    Extensions of generic measure-preserving actions, Annales de l'Institut Fourier 64 (2014), no. 2, 607–623. [PDF] [arXiv] [DOI]
19. 2013
    Elements of finite order in automorphism groups of homogeneous structures, with D. Bilge, Contributions to Discrete Mathematics 8 (2013), no. 2, 88–119. [PDF]
20. 2013
    Generic representations of abelian groups and extreme amenability, with T. Tsankov, Israel Journal of Mathematics 198 (2013), no. 1, 129–167. [PDF] [arXiv] [DOI]
21. 2013
    Polish topometric groups, with I. Ben Yaacov and A. Berenstein, Transactions of the AMS 365 (2013), no. 7, 3877–3897. [PDF] [arXiv] [DOI]
22. 2010
    A note on Hjorth's oscillation theorem, Journal of Symbolic Logic 75 (2010), no. 4, 1359–1365. [PDF]
23. 2010
    Topology of the isometry group of the Urysohn space, Fundamenta Mathematicae 207 (2010), no. 3, 273–287. [PDF] [DOI]
24. 2008
    Linearly rigid metric spaces, with F. Petrov and A. M. Vershik, Fundamenta Mathematicae 199 (2008), no. 2, 177–194. [PDF] [arXiv] [DOI]

    A short announcement appeared as Espaces métriques linéairement rigides (with F. Petrov and A. M. Vershik), Comptes Rendus de l'Académie des Sciences de Paris 344 (2007), 235–240.

25. 2008
    Some geometric and dynamical properties of the Urysohn space, Topology and its Applications 155 (2008), no. 14, 1531–1560. [PDF] [DOI]
26. 2008
    Compact metrizable groups are isometry groups of compact metric spaces, Proceedings of the AMS 136 (2008), no. 4, 1451–1455. [PDF] [arXiv] [DOI]
27. 2007
    Computing the complexity of the relation of isometry between separable Banach spaces, Mathematical Logic Quarterly 53 (2007), no. 2, 128–131. [PDF]
28. 2007
    On the geometry of Urysohn's universal metric space, Topology and its Applications 154 (2007), no. 2, 384–403. [PDF] [arXiv]
29. 2006
    Stabilizers of closed sets in the Urysohn space, Fundamenta Mathematicae 189 (2006), no. 1, 53–60. [PDF] [DOI]