OURAGAN focus on the transfer of computational algebraic methods to some related fields (computational geometry, topology, number theory, etc.) and some carefully chosen application domains (robotics, control theory, evaluation of the security of cryptographic systems, etc.).
We are working equally on the use (modeling, know – how) and on the development of new algorithms.
An original aspect of the OURAGAN is to blend into an environment of fundamental mathematics, at the Institut de Mathématiques de Jussieu — Paris Rive Gauche (IMJ-PRG CNRS 7586), and to be cross-functional to several teams (Algebraic Analysis, Complex Analysis and Geometry, Number Theory, Algebraic Topology and Geometry to name only the main ones).
OURAGAN works on four general directions with five particular targets:
- Algebraic analysis of functional systems
- Number theory
- Algorithmic number theory
- Rigorous numerical computations
- Topology in small dimension
- Character varieties
- Knot theory
- Computational geometry
- Algebraic topology
These actions come, of course, in addition to the study and development of a common set of core elements of
- Basic theory and algorithms in algebra and geometry
The tools and objects developed for research on algorithmic number theory as well as on topology in small dimension apply quite directly on some selected connected challenging subjects:
- Security of cryptographic systems
- Control theory
- Signal processing