Research

Submitted articles

  1. “A proof of A. Gabrielov’s rank Theorem” (with Octave Curmi and Guillaume Rond),  arXiv:2008.13130 [math.CV], 2020.
  2. “Sharp Estimates for Blowing Down Functions in a Denjoy-Carleman Class” (with Edward Bierstone and Avner Kiro), 2006.10580 [math.CV], 2020.
  3. “Lipschitz normal embeddings and polar exploration of complex surface germs” (with Lorenzo Fantini and Anne Pichon) 2006.01773 [math.AG], 2020.
  4. “Monomialization of a quasianalytic morphism” (with  Edward Bierstone), arXiv  1907.09502 [math.AG], 2019.
  5. “Inner Lipschitz geometry of complex surfaces: a valuative approach” (with Lorenzo Fantini and Anne Pichon) 1905.01677 [math.AG], 2019.
  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, hal-01889705, 2018.

Published or accepted articles

  1. 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.
  2. “Generalized Flow-Box property for singular foliations”, with Daniel Panazzolo, to appear in RACSAM, special edition in honour of Felipe Cano (see arXiv version here)
  3. “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).
  4. Composite quasianalytic functions, with Edward Bierstone and Michael Chow, Compositio Mathematica, Volume 154, Issue 9 (2018) pp. 1960-1973. (see arXiv version  here).
  5. The Sard conjecture on Martinet surfaces, with Ludovic Rifford, Duke Mathematical Journal, Volume 167, Number 8 (2018), 1433-1471. (see arXiv version here).
  6. 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).
  7. “Solutions of quasianalytic equations”, with Iwo Biborski and Edward Bierstone, Selecta Mathematica, Volume 23, Number 4, (2017), 2523-2552 pp. (see arXiv version here).
  8. 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)
  9. 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)
  10. Global resolution of singularities subordinated to a 1-dimensional foliation, Journal of Algebra, 2016, Volume 447, Pages 397-423. (see arXiv version here).
  11. 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)
  12. 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