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

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 ».  

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