Publications

Preprints and Submitted articles

  1. Logarithmic resolution of singularities in characteristic 0 using weighted blow-ups,
    with Dan Abramovich, Ming Hao Quek, Michael Temkin and Jarosław Włodarczyk
    arXiv:2503.13341, [math.AG], 2025.
  2. Principalization on logarithmically foliated orbifolds,
    with Dan Abramovich, Michael Temkin and Jarosław Włodarczyk
    arXiv:2503.00926, [math.AG], 2025.
  3. The analytic minimal rank Sard Conjecture,
    with Adam Parusinski and Ludovic Rifford,
    hal-03741318, [math.DG], 2022.
    See our talk at the Conference “Foliations in Algebraic and Birational geometry” here.
  4. Abnormal subanalytic distributions in sub-Riemannian geometry,
    with Adam Parusinski and Ludovic Rifford,
    hal-04881557, [math.DG], 2025.
  5. On rank Theorems for morphisms of local rings,
    with Octave Curmi and Guillaume Rond,
    arxiv:2205.03079, [math.AG], 2022.
    See G. Rond’s talk on the Fields Institute here.

Published or accepted articles

  1. Abnormal Singular Foliations and the Sard Conjecture for generic co-rank one distributions,
    with Adam Parusinski and Ludovic Rifford,
    To apper in Revista Matemática Iberoamericana.
    ArXiv version here.
  2. Partial desingularization,
    with Edward Bierstone and Ramon Ronzon Lavie,
    Transactions of the American Mathematical Society, 378, No. 4, 2829-2879 (2025).
    ArXiv version here.
  3. On the Nash points of subanalytic sets,
    with Octave Curmi and Guillaume Rond,
    Journal of Singularities, volume 27 (2024), 68-88.
    See G. Rond’s talk on the Fields Institute here.
    ArXiv version here.
  4. A remark on first integrals of vector fields,
    with Martin Klimes, Julio C. Rebelo and Helena Reis,
    Publicacions Matemàtiques, 68(1): 103-109 (2024).
    ArXiv version here.
  5. Monomialization of a quasianalytic morphism,
    with Edward Bierstone,
    Annales scientifiques de l’École normale supérieure, 56, tome 5, 1583-1651, (2023).
    ArXiv version here.
    See our talk at the GTM here and our mini-course at the Fields Institute: Lectures 5; 6; and 7.
  6. Strong Sard Conjecture and regularity of singular minimizing geodesics for analytic sub-Riemannian structures in dimension 3,
    with Alessio Figalli, Adam Parusinski and Ludovic Rifford,
    Inventiones Mathematicae, 229, pages 395–448 (2022).
    Hal version here.
    See our talks : for algebraic geometers here; for sub-Riemannian geometers here.
  7. Polar exploration of complex surface germs,
    with Lorenzo Fantini, András Némethi and Anne Pichon,
    Transactions of the American Mathematical Society, 375 (2022), 6747-6767.
    ArXiv version here.
    See our talk at the CIRM here (starts at 1h57:50).
  8. On Lipschitz Normally Embedded complex surface germs,
    with Lorenzo Fantini and Anne Pichon,
    Compositio Mathematica, Volume 158, Issue 3, pp. 623 – 653, (2022).
    ArXiv version here.
    See L. Fantini’s talk at the CIRM here (starts at 1h02:00).
  9. Inner Lipschitz geometry of complex surfaces: a valuative approach,
    with Lorenzo Fantini and Anne Pichon.
    Geometry & Topology, 26, (2022) 163–219.
    ArXiv version here.
  10. A proof of A. Gabrielov’s rank Theorem,
    with Octave Curmi and Guillaume Rond,
    Journal de l’École polytechnique, Mathématiques, Tome 8 (2021), pp. 1329-1396.
    ArXiv version here.
    See our talk in the Fields Institute here.
  11. Sharp Estimates for Blowing Down Functions in a Denjoy-Carleman Class,
    with Edward Bierstone and Avner Kiro,
    IMRN, rnaa367, 2021.
    ArXiv version here.
  12. A general system of differential equations to model first order adaptive algorithms,
    with Maxime Gazeau,
    Journal of Machine Learning Research, 21(129):1−42, 2020.
    ArXiv version here.
  13. Generalized Flow-Box property for singular foliations,
    with Daniel Panazzolo,
    RACSAM, 113, pages 3949–3965. 2019.
    ArXiv version here.
  14. Topological classification of limit periodic sets of polynomial planar vector fields,
    with José Ginés Espín Buendía,
    Publicacions Matemàtiques, Volume 63, Number 1 (2019), 105-123pp.
    ArXiv version here.
  15. Composite quasianalytic functions,
    with Edward Bierstone and Michael Chow,
    Compositio Mathematica, Volume 154, Issue 9 (2018) pp. 1960-1973.
    ArXiv version here.
  16. The Sard conjecture on Martinet surfaces,
    with Ludovic Rifford,
    Duke Mathematical Journal, Volume 167, Number 8 (2018), 1433-1471.
    ArXiv version here.
  17. Local monomialization of a system of first integrals of Darboux type,
    Revista Matemática Iberoamericana, Volume 34, Issue 3, (2018), pp. 967–1000.
    ArXiv version here.
  18. Solutions of quasianalytic equations,
    with Iwo Biborski and Edward Bierstone,
    Selecta Mathematica, Volume 23, Number 4, (2017), 2523-2552 pp.
    ArXiv version here.
  19. Resolution of singularities of the cotangent sheaf of a singular variety,
    with Edward Bierstone, Vincent Granjean and Pierre Milman,
    Advances in Mathematics, Volume 307, (2017), 780-832 pp.
    ArXiv version here.
  20. Local Resolution of Ideals Subordinated to a Foliation,
    RACSAM, (2016) Volume 110, Issue 2, pp 841–862.
    ArXiv version here.
  21. Global resolution of singularities subordinated to a 1-dimensional foliation,
    Journal of Algebra, 2016, Volume 447, Pages 397-423.
    ArXiv version here.
  22. Examples of infinitesimal non-trivial accumulation of secants in dimension three,
    Journal of Dynamical and Control Systems, 2016, Volume 22, no. 1, 45-54.
    ArXiv version here.
  23. Analytic varieties as limit periodic sets,
    Qualitative Theory of Dynamical Systems, 2012, Volume 11, issue 2, 449-465.
    ArXiv version here.

Proceedings and book chapters

PhD and Master Thesis

Mini-course

Resolution of singularities in quasianalytic classes: