# Jussieu Mathematics Institute - UMR 7586

The JMI is a laboratory for research in mathematics. This term refers to the science of form and number, which leads to a better understanding of concepts and to the reconciliation of seemingly foreign notions and methods which, however, are unified by a single structure. This abstract science also deals with applications. Indeed, mathematics have for centuries constituted the language of physics, and have recently conquered biology and life sciences, followed by economy and finance. Mathematics research as practiced at the JMI is therefore inseparable from the technical progress that transforms our daily life. JMI currently brings together 152 academics from Sorbonne Université and Paris Diderot and 49 CNRS research scientists. This makes it the biggest laboratory on the Chevaleret site, uniting the majority of central Paris mathematics and constituting the heart of the Paris Mathematical Science Foundation (*Fondation Sciences Mathématiques de Paris*). The JMI also brings together over 120 students from all over the world who are studying for their PhD in mathematics.

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##### Research

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.

##### Keywords

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

##### Scientific advances, significant results

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.

##### Graduate Schools

ED 386 – Mathematical Sciences of Central Paris

##### Scientific partnerships

###### 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*)

##### Contact Informations

Director ELIASSON Hakan 01 44 27 43 31 hakane@upmc.fr | Physical address Site Chevaleret 175, rue Chevaleret 75013 Paris Laboratory's mail Website http://www.institut.math.jussieu.fr/ |

Mailing address Case 247 4 place Jussieu 75252 Paris cedex 05 | Communications Contact CABANES Marc 01 44 27 75 68 cabanes@math.jussieu.fr |

Administrative Contact ZADVAT Zoubeir 01 44 27 75 68 zadvat@math.jussieu.fr |

### Also in the section

- Intelligent systems and robotics institute - UMR 7222
- Jean Le Rond d'Alembert Institute - UMR 7190
- Paris Electrical and Electronic Engineering (GeePs) Laboratory - UMR 8507
- Probabilities and random models laboratory - UMR 7599
- Theoretical and applied statistics laboratory - UR1
- Electronics and electromagnetism laboratory - UR2
- Paris 6 computer science laboratory - UMR 7606
- Jacques-Louis Lions Laboratory (LJLL) - UMR 7598
- Science and Technology of Music and Sound - UMR 9912
- Biomedical Imagery Laboratory - UMR S1146/UMR7371
- Medical Computing and Knowledge Engineering Laboratory for e-Health (LIMICS) - UMR S 1142