### 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 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

- “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

- 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

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:

- 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).