The Ouragan team has a transverse activity, working on effective computations of algebraic objects of all kinds. We are especially concerned by efficient algorithms that compute with these objects and wish to promote their use in various fields.
One important focus is the study of algebraic varieties and semi-algebraic sets, the ultimate goal being to propose efficient solutions for providing pertinent geometric information (such as solutions of algebraic or semi-algebraic systems) from various algebraic computations (Ideals, Resultants, etc.).
To keep our research effort focused, our strategy consists in selecting a few research or application targets for which the exact computation of some algebraic objects represents a clear and identifiable added value. These topics are selected to permit longstanding developments and studies, and the corresponding research is performed in collaboration with specialists. Our seminal transfer activities are :
- Topology in low dimension : collaboration with the teams Analyse Algébrique and Analyse Complexe et Géométrie from IMJ-PRG (Institut de mathématiques de Jussieu – Paris Rive Gauche)
- Computational Geometry : collaboration with the VEGAS Project team – INRIA Nancy Grand Est
- Robotics (Kinematics) : collaboration with the Robotics team from IRRcYN – CNRS Nantes
As our core developments can naturally apply to many other fields, we also constantly prospect for new subjects that could drive our core research. We currently start new projects on :
- Cryptology : collaboration with the chair of cryptology from the University Pierre and Marie Curie.
- Control theory : collaboration driven by Alban Quadrat from the NON-A Project team – INRIA Lille Nord Europe.