I am a member of the Galaad group at INRIA Sophia Antipolis.

Sujet de thèse 2016pour candidature à l’école doctorale SFA de l’université de Nice Sophia Antipolis : sujet.

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.

**Upcoming events :**

- 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.
- Conference MEGA 2017 at the University of Nice, June 12-16, 2017.