Research interests :
My research interests focus on the geometry of algebraic curves and surfaces and their applications in geometric modeling. In this context, I have strong interests in elimination theory, computer algebra and computational algebraic geometry.
- Elimination theory for systems of polynomial equations: multivariate resultants over blow-up or determinantal varieties, iterated discriminant, multivariate discriminants, closed image of rational maps and equations of their Rees algebras.
- Geometry of curves and surfaces : singularities and pencils of adjoint of rational plane curves, singularities of surfaces, spectrum and total irreducibility of pencils of algebraic plane curves.
- Algebraic methods in Computer Aided Geometric Design: Implicitization and inversion of rational algebraic curves and surfaces (Bézier patches and NURBS) through various matrix-based representations, intersection and self-intersection problems by exploiting and enhancing the link between algebraic and numerical linear algebra technics.
Ongoing research projects :
- ARCADES (2016-2019) : ITN (Innovative Traning Network) funded by the European Community (H2020 program) on the topic « Algebraic Representation in Computer-Aided Design for Complex Shapes ».
- SYRAM (2015-2016) : MathAmSud research program on « SYzygies of RAtional Maps with applications to geometric modeling » composed by research teams from Argentina, Brasil and France.
- GEOLMI (2011-2015) : ANR research projet on « GEOmetry and algebra of Linear Matrix Inequalities with systems control applications ».
Upcoming events :
- SEME at SophiaTech, « Semaine d’Etudes Maths-Entreprise », January 25-29 2016, co-organized with D. Auroux and C. Boulbe.
- Conference in Honor of A. Dickenstein, « Computational Algebra, ALgebraic Geometry and Applications », Buenos Aires, Argentina, August 1-3 2016.
- BIRS-CMO workshop on Computational Algebra and Geometric Modeling in Oaxaca, Mexico, August 7-12, 2016, co-organized with Ron Goldman and Hal Schenck.