Jussieu Mathematics Institute - UMR 7586

The study and development of mathematical structures, be they geometrical, algebraic or arithmetical in nature. The knowledge and intuition of mathematicians guide them towards fundamental, and therefore versatile, concepts. However, it is essential to understand that this work is by no means driven purely by curiosity, nor is it undertaken in isolation. The astonishing applicability of mathematics to structure and understand the world around us is the most significant factor driving its development. It is of course difficult to explain to the lay reader the scope of any recent results, but fortunately history provides good examples of the analog power of mathematical abstraction. For instance, polynomial algebra showed that many geometric problems fall within the same equation. Then, the analysis of polynomial factorization led Galois to subordinate the study of algebraic equations and of finite groups. Then, the classification of these groups was addressed and completed in the late 20th century. This made it possible to perceive the full scope of the universal concept of symmetry, from mineralogy to arithmetic via coding and the modeling of elementary particles.

functional analysis, real and complex analysis, algebra, geometry, group theory, number theory, topology, partial differential equations, history of science, mathematical physics.

Since the 18th century, astronomers and mathematicians have been interested in the stability of the solar system in its mathematical version as presented by Newton. Despite great efforts, it was not until 1960 that the Russian mathematician VI Arnold was able to give evidence of stability where the masses of all the planets are sufficiently small. It became apparent, however, that Arnold had overlooked a critical point and that the demonstration was not complete. It was not until 2004 that Sorbonne Université lecturer Jacques Fejoz was able to complete this demonstration, rendering it entirely rigorous. In this work, he was greatly inspired by the work of M. Herman.

The mechanics of Newton are best formulated within a geometric structure now called a symplectic manifold. The Kohler manifolds are a particularly important class of symplectic manifold, particularly in relation to the general theory of relativity. In 1960, in his work to try to understand the structure of Kohler manifolds, the Japanese mathematician K. Kodaira formulated a conjecture. This conjecture is true for surfaces, but recently CNRS research director Claire Voisin was able to construct a counter example for Kodaira’s conjecture, which earned her a CNRS silver medal in 2006 and the Clay Research Award in 2008.

ED 386 – Mathematical Sciences of Central Paris

Local

FR 2830 – Mathematics of Central Paris Research Federation (Fédération de Recherche en Mathématiques de Paris Centre)

National

Paris Mathematical Science Foundation (Fondation Sciences Mathématiques de Paris)