Descartes' rule for multivariate polynomials

Descartes' rule is one of the first main result of algebraic geometry. Formulated in 1637 in the appendix entitled "La Géométrie" of the famous "Discours de la Méthode" [S], this rule gives an upper bound of the number of positive roots of a polynomial of one real-valued variable. The formulation of a similar rule for multi-variate polynomials has gone through new developements with the works of Frédéric Bihan and his collaborators who propose in [BD] a new upper bound for the number of roots with positive coordinates.

The second Call for Porposals of the Interreg Sudoe Programme is open

The Interreg Sudoe Programme supports regional development in Southwest Europe financing transnational projects through the European Regional Development Fund (ERDF).

The Programme promotes transnational cooperation to solve common problems in Southwest Europe, such as low investment in research and development, weak competitiveness of the small and medium-sized enterprises and exposure to climate change and environmental risks.

Thomas Jefferson Fund: Addressing 21st-Century Challenges through Transatlantic Research

The French Embassy and the FACE Foundation are launching the Thomas Jefferson Fund to support new, innovative collaborations between promising young researchers in France and the United States in the fields of Science, Technology, Engineering and Mathematics (STEM), Humanities and Social Sciences (SSH) and Sciences for Society (interdisciplinary STEM-SSH projects). The Thomas Jefferson Fund will fund up to nine original, two-year collaborative projects, addressing the most pressing global challenges.

A step in the diretion of a general description of derived self-intersections

In algebraic geometry, intersection theory aims at describing how algebraic manifolds intersect one another in an ambient space. Recent progress about self-intersections have been made by studying how an algebric manifold intersects its infenitesimal perturbations. These results open the way to a better  understanding of derivate self-intersections. 

For a more complete description of this result (in french), click here.

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