Many problems in scientific computation and in applications such as CAGD, robotics, computer vision, molecular biology, signal processing... involves algebra and geometry. The objective of the project is to develop algorithmic methods for effective and reliable resolution of these geometric and algebraic problems.
Our research in effective algebraic geometry includes methods to solve polynomial equations, to compute resultants, to factorise polynomials, to detect and analyse singularities of algebraic varieties, to describe the topology of semialgebraic sets. We are specially interested in problems on semialgebraic curves and surfaces, such as intersection, singularity, topology, arrangement computations. These geometric investigations lead to algebraic questions, and particularly to the resolution of polynomial equations. We work on the design and analysis of new methods based for instance on normal form computation, resultants or subdivision techniques.

