Preprints and Submitted articles
- 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. - Principalization on logarithmically foliated orbifolds,
with Dan Abramovich, Michael Temkin and Jarosław Włodarczyk
arXiv:2503.00926, [math.AG], 2025. - 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. - Abnormal subanalytic distributions in sub-Riemannian geometry,
with Adam Parusinski and Ludovic Rifford,
hal-04881557, [math.DG], 2025. - 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
- 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. - Partial desingularization,
with Edward Bierstone and Ramon Ronzon Lavie,
Transactions of the American Mathematical Society, 378, No. 4, 2829-2879 (2025).
ArXiv version here. - 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. - 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. - 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. - 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. - 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). - 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). - Inner Lipschitz geometry of complex surfaces: a valuative approach,
with Lorenzo Fantini and Anne Pichon.
Geometry & Topology, 26, (2022) 163–219.
ArXiv version here. - 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. - Sharp Estimates for Blowing Down Functions in a Denjoy-Carleman Class,
with Edward Bierstone and Avner Kiro,
IMRN, rnaa367, 2021.
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.
ArXiv version here. - Generalized Flow-Box property for singular foliations,
with Daniel Panazzolo,
RACSAM, 113, pages 3949–3965. 2019.
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.
ArXiv version here. - Composite quasianalytic functions,
with Edward Bierstone and Michael Chow,
Compositio Mathematica, Volume 154, Issue 9 (2018) pp. 1960-1973.
ArXiv version here. - The Sard conjecture on Martinet surfaces,
with Ludovic Rifford,
Duke Mathematical Journal, Volume 167, Number 8 (2018), 1433-1471.
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.
ArXiv version here. - Solutions of quasianalytic equations,
with Iwo Biborski and Edward Bierstone,
Selecta Mathematica, Volume 23, Number 4, (2017), 2523-2552 pp.
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.
ArXiv version here. - Local Resolution of Ideals Subordinated to a Foliation,
RACSAM, (2016) Volume 110, Issue 2, pp 841–862.
ArXiv version here. - Global resolution of singularities subordinated to a 1-dimensional foliation,
Journal of Algebra, 2016, Volume 447, Pages 397-423.
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.
ArXiv version here. - 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
- 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.
Mini-course
Resolution of singularities in quasianalytic classes:
- Lecture 1 : Introduction to resolution of singularities in quasianalytic classes, Video 1 (1h);
- Lecture 2 : Statement of Resolution of singularities, Video 2 (2h);
- Lecture 3 : The Uniformization Theorem, Video 3 (1h);
- Lecture 4 : Local Resolution of singularities, Video 4.1 (2h) and Video 4.2 (1h);
- Lecture 5 : Monomialization of morphisms : Statement, and modifying the Target, Video 5 (2h);
- Lecture 6 : Monomialization of morphisms : Applications, Video 6 (1h);
- Lecture 7 : Monomialization of morphisms : modifying the Source, Video 7 (2h).