GALAAD Research team
Geometry, algebra, algorithms
- Leader : Bernard Mourrain
- Research center(s) : CRI Sophia Antipolis - Méditerranée
- Field : Algorithmics, Programming, Software and Architecture
- Theme : Algorithmics, Computer Algebra and Cryptology
- Partner(s) : Université Nice - Sophia Antipolis,CNRS
- Collaborator(s) : U. NICE SOPHIA ANTIPOLIS (UNS), CNRS
Our research focuses on effective algebraic geometry and its applications. Our objective is to develop algorithmic methods allowing us to solve efficiently and in a certified manner the geometric and algebraic problems arising in such domains as CAD, robotics, computer vision, computational biology, ...We are interested in analyzing such methods, in terms of complexity as well as in studying their quality in the context of the interaction between symbolic and numeric computation.
The main directions are geometry, solving algebraic systems, and the links between symbolic and numeric computation; these are further divided as follows:
- Geometry of algebraic varieties, discrete geometry, geometric algorithms for curves and surfaces, invariants, singularity and topology,
- Algebraic methods and quotient structure, duality, residue, interpolation, structured linear algebra and multivariate polynomials, decomposition and factorization, deformation and homotopy,
- Certification, approximation, degeneracy and arithmetic.