Publications

Submitted articles

  1. “Abnormal subanalytic distributions and minimal rank Sard Conjecture”, with Adam Parusinski and Ludovic Rifford, hal-03741318, [matj.DG], 2022.
  2. “On rank Theorems and the Nash points of subanalytic sets”, with Octave Curmi and Guillaume Rond, arxiv:2205.03079, [math.AG], 2022.
    See G. Rond’s talk on the Fields Institute for real geometers here.

Published or accepted articles

  1. “A remark on first integrals of vector fields”, with Martin Klimes, Julio C. Rebelo and Helena Reis, to appear in Publicacions Matemàtiques.
    See arXiv version arXiv:2110.13072, [math.CA], 2021.
  2. “Polar exploration of complex surface germs”, with Lorenzo Fantini, András Némethi and Anne Pichon, to appear in Transactions of the American Mathematical Society.
    See arXiv version arXiv:2103.15444 [math.AG], 2021.
    See our talk at the CIRM here (starts at 1h57:50).
  3. 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, 229pages 395–448 (2022).
    See hal version here.
    See our talks : for algebraic geometers here; for sub-Riemannian geometers here.
  4. On Lipschitz Normally Embedded complex surface germs“, with Lorenzo Fantini and Anne Pichon, Compositio Mathematica, Volume 158, Issue 3, 2022 , pp. 623 – 653.
    See arXiv version 2006.01773 [math.AG], 2020.
    See Lorenzo Fantini’s talk at the CIRM here (starts at 1h02:00).
  5. “Monomialization of a quasianalytic morphism”, with Edward Bierstone, to appear in the Annales scientifiques de l’École normale supérieure.
    See arXiv version 1907.09502 [math.AG], 2019.
    See our talk at the GTM here.
    See our mini-course at the Fields Institute: Video 5 (2h); Video 6 (1h); Video 7 (2h).
  6. 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.
    See arXiv version here.
    See our talk in the Fields Institute here.
  7. Inner Lipschitz geometry of complex surfaces: a valuative approach“, with Lorenzo Fantini and Anne Pichon. Geometry & Topology, 26, (2022) 163–219.
    See arXiv version here.
  8. Sharp Estimates for Blowing Down Functions in a Denjoy-Carleman Class“, with Edward Bierstone and Avner Kiro, IMRN, rnaa367, 2021.
    See arXiv version here.
  9. 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.
  10. Generalized Flow-Box property for singular foliations, with Daniel Panazzolo, RACSAM, 113pages 3949–3965. 2019.
    See arXiv version here.
  11. “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.
    See arXiv version here.
  12. Composite quasianalytic functions, with Edward Bierstone and Michael Chow, Compositio Mathematica, Volume 154, Issue 9 (2018) pp. 1960-1973.
    See arXiv version  here.
  13. The Sard conjecture on Martinet surfaces, with Ludovic Rifford, Duke Mathematical Journal, Volume 167, Number 8 (2018), 1433-1471.
    See arXiv version here.
  14. Local monomialization of a system of first integrals of Darboux type”, Revista Matemática Iberoamericana, Volume 34, Issue 3, (2018), pp. 967–1000.
    See arXiv version here.
  15. “Solutions of quasianalytic equations”, with Iwo Biborski and Edward Bierstone, Selecta Mathematica, Volume 23, Number 4, (2017), 2523-2552 pp.
    See arXiv version here.
  16. 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.
    see arXiv version here.
  17. Local Resolution of Ideals Subordinated to a Foliation, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales – RACSAM, (2016) Volume 110, Issue 2, pp 841–862.
    See arXiv version here.
  18. Global resolution of singularities subordinated to a 1-dimensional foliation, Journal of Algebra, 2016, Volume 447, Pages 397-423.
    See arXiv version here.
  19. Examples of infinitesimal non-trivial accumulation of secants in dimension three, Journal of Dynamical and Control Systems, 2016, Volume 22, no. 1, 45-54.
    See arXiv version here.
  20. Analytic varieties as limit periodic sets, Qualitative Theory of Dynamical Systems, 2012, Volume 11, issue 2, 449-465.
    See arXiv version here.

Proceedings and book chapters

PhD and Master Thesis