- “A remark on first integrals of vector fields” (with Martin Klimes, Julio C. Rebelo and Helena Reis), arXiv:2110.13072, [math.CA], 2021.
- “Polar exploration of complex surface germs” (with Lorenzo Fantini, András Némethi and Anne Pichon), arXiv:2103.15444 [math.AG], 2021.
See our talk in CIRM here (starts at 1h57:50).
- “On Lipschitz Normally Embedded complex surface germs” (with Lorenzo Fantini and Anne Pichon) 2006.01773 [math.AG], 2020.
See Lorenzo Fantini’s talk in CIRM here (starts at 1h02:00).
- “Monomialization of a quasianalytic morphism” (with Edward Bierstone), arXiv 1907.09502 [math.AG], 2019.
See our talk at the GTM here (for a general public of geometers and model theorists).
- “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.
See our talks :
for general algebraic geometers specialists here;
for sub-Riemannian geometers specialists here.
Published or accepted articles
- “A proof of A. Gabrielov’s rank Theorem” (with Octave Curmi and Guillaume Rond), arXiv:2008.13130 [math.CV], 2020, to appear in Journal de l’École polytechnique.
See our talk in the Fields Institute here.
- “Inner Lipschitz geometry of complex surfaces: a valuative approach” (with Lorenzo Fantini and Anne Pichon) to appear in Geometry & Topology, 2021 (see arXiv version here).
- “Sharp Estimates for Blowing Down Functions in a Denjoy-Carleman Class” (with Edward Bierstone and Avner Kiro), IMRN, rnaa367, 2021, (see arXiv version here).
- “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.
- “Generalized Flow-Box property for singular foliations“, with Daniel Panazzolo, RACSAM, 113, pages 3949–3965. 2019. (see arXiv version here).
- “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).
- “Composite quasianalytic functions“, with Edward Bierstone and Michael Chow, Compositio Mathematica, Volume 154, Issue 9 (2018) pp. 1960-1973. (see arXiv version here).
- “The Sard conjecture on Martinet surfaces“, with Ludovic Rifford, Duke Mathematical Journal, Volume 167, Number 8 (2018), 1433-1471. (see arXiv version here).
- “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).
- “Solutions of quasianalytic equations”, with Iwo Biborski and Edward Bierstone, Selecta Mathematica, Volume 23, Number 4, (2017), 2523-2552 pp. (see arXiv version here).
- “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)
- 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)
- Global resolution of singularities subordinated to a 1-dimensional foliation, Journal of Algebra, 2016, Volume 447, Pages 397-423. (see arXiv version here).
- 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)
- 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
- Resolution of singularities of differential forms and Hsiang-Pati coordinates, with Edward Bierstone, Advanced Lectures in Mathematics, Volume 39: Hodge theory and L2 analysis, edited by Lizhen Ji, International Press, (2017), 127-150 pp.
PhD and Master Thesis
- Resolution of singularities in foliated spaces, PhD thesis, Université de Haute-Alsace, France (2013). Adviser: Daniel Panazzolo.
- Bifurcation analysis of a system of population dynamics, Master Thesis, Universidade de São Paulo, Brazil, (2010). Adviser: Jorge Manuel Sotomayor Tello.