Submitted articles
- “Partial desingularization”, with Edward Bierstone and Ramon Ronzon Lavie, arxiv:2211.15713 [math.AG], 2022.
- “Abnormal subanalytic distributions and minimal rank Sard Conjecture”, with Adam Parusinski and Ludovic Rifford, hal-03741318, [matj.DG], 2022.
See our talk at the Conference “Foliations in Algebraic and Birational geometry” here.
- “On the Nash points of subanalytic sets”, with Octave Curmi and Guillaume Rond, arxiv:2303.07699, [math.AG], 2023.
See G. Rond’s talk on the Fields Institute for real geometers here.
- “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 for real geometers here.
Published or accepted articles
- “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.
- “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).
- “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).
See hal version here.
See our talks : for algebraic geometers here; for sub-Riemannian geometers here.
- “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).
- “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).
- “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.
- “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.
- “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
PhD and Master Thesis
Mini-course
I recently gave a mini-course in the Fields institute about
Resolution of singularities in quasianalytic classes from (see more
here). Below, you can find my lecture notes and videos:
Like this:
Like Loading...