Research area :
- Resolution of singularities;
- Local uniformization of quasi-excellent schemes;
- Valuations theory;
- Key polynomials and generalized Puiseux expansions;
- Algebraic closure of complete local regular rings;
- Valuative tree, tree of sphere and Berkovich space in holomorphic dynamics.
I'm also a member
of
GDR
singularités et applications and of
SMF.
Publications -
Preprints :
- A simplified proof that Abhyankar valuations admit local uniformization, with Josnei Novacoski, 2016, in preparation.
- Equivalence between Puiseux expansions and key polynomials, 2016, in preparation.
- Ramification theory and key polynomials, arXiv:1602.08284, 2016, submitted.
- Uniformisation locale des schémas quasi-excellents de caractéristique nulle, arXiv:1311.3525, 2013, submitted.
- Defect of an extension, key polynomials and local uniformization, Journal of Algebra, Vol. 481, 2017, p. 91-119.
- Théorème de
Kaplansky effectif pour des valuations de rang 1 centrées sur des
anneaux locaux réguliers et complets, Ann. Inst. Fourier, Vol. 64 (3), 2014, p. 1177-1202.
Talks :
Séminaire
de géométrie de Bordeaux, February 17, 2017 : Polynômes-clés, séries de Puiseux et résolution des singularités.
"Young researchers in singularities", CIRM of Marseille, February
9-13, 2015 : Local uniformization of
quasi-excellent schemes in zero or positive characteristic.
Séminaire singularités, Marseille, March
13, 2014 : Uniformisation locale des schémas quasi-excellents de
caractéristique nulle.
Séminaire sur les singularités de Jussieu, Paris, February 10, 2014 : Polynômes-clés et uniformisation locale.
Séminaire
étudiant, February 8, 2012 : Extensions de corps valués.
Séminaire
de géométrie de Bordeaux, December 2, 2011 : Un théorème de
Kaplansky
constructif pour des anneaux locaux réguliers complets
munis d'une valuation de rang 1.
Séminaire
étudiant, January 20, 2010 : Introduction
au langage des catégories.
Séminaire
étudiant, November 18, 2009 : Caractérisation des surfaces compactes
de premier nombre de Betti pair.
Séminaire
étudiant, October 21, 2009 : Théorie de Hodge.
Events :
"Two approaches towards local uniformization and resolution of singularities in characteristic p > 0" may 23-27, 2016, Mittag-Leffler Institute, Stockholm (Sweden).
"Young researchers in singularities" February 9-13, 2015, CIRM, Marseille (France).
Workshop on singularities in geometry, topology, foliations and dynamics, a celebration of the 60th birthday of Pepe Seade, december 8-19, 2014, Merida (Mexico).
"Resolution of threefolds in positive characteristic" October 1-11, 2013, Regensburg
(Germany).
80th birthday of
Heisuke Hironaka: "Resolution of Singularities
and Related Topics" September 18-23, 2011, Tordesillas
(Valladolid, Spain).
"Second
International Conference and Workshop on Valuation Theory" July
18-29, 2011, Segovia and El Escorial (Spain).
60th
birthday of Vincent Cossart: "Resolution of
Singularities Problems" March 15-19, 2010, Tordesillas
(Valladolid, Spain).