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OURAGAN Research team

OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs

Team presentation

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.).

Our team is located at the Institut de Mathématiques de Jussieu - University Pierre and Marie Curie Paris-VI

Research themes

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, 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 a new project on :

  • Cryptology : collaboration with the team Théorie des nombres from l'IMJ-PRG and the chair of cryptology from the University Pierre et Marie Curie.
  • Control theory : collaboration driven by Alban Quadrat from the NON-A Project team – INRIA Lille Nord Europe.

International and industrial relations

  • Waterloo Maple Inc
  • CURVE project

Keywords: Polynomial System Solving Topology Computational Geometry Software Robotics.