The Mathematics Institute of Jussieu–Paris Rive Gauche (, , IMJ-PRG) is a French research institute in fundamental mathematics. It is a "mixed research unit", with three parent organizations: the

Centre national de la recherche scientifique The French National Centre for Scientific Research (, , CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 eng ...

Sorbonne University Sorbonne University () is a public research university located in Paris, France. The institution's legacy reaches back to the Middle Ages in 1257 when Sorbonne College was established by Robert de Sorbon as a constituent college of the Unive ...

, and the

University of Paris The University of Paris (), known Metonymy, metonymically as the Sorbonne (), was the leading university in Paris, France, from 1150 to 1970, except for 1793–1806 during the French Revolution. Emerging around 1150 as a corporation associated wit ...

. It is located in

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...

, split between two campuses: Jussieu and Paris Rive Gauche. It is the largest research center for fundamental mathematics in

France France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan ...

. More than 200 permanent researchers work at the institute, around 100 PhD students, as well as emeritus professors, postdocs, invited researchers, and ATERs, and support staff. The IMJ-PRG is the largest research unit linked to the

doctoral school In France, a doctoral school () is an educational structure similar in focus to a graduate school but restricted to PhD level. The concept was created in 2000. Doctoral schools have the responsibility of providing students with structured doctoral ...

of mathematical sciences of Paris center (''École doctorale de sciences mathématiques de Paris-Centre''). It has its own

journal A journal, from the Old French ''journal'' (meaning "daily"), may refer to: *Bullet journal, a method of personal organization *Diary, a record of personal secretive thoughts and as open book to personal therapy or used to feel connected to onesel ...

, the ''Journal de l'institut de mathématiques de Jussieu'', published by

Cambridge University Press Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessme ...

and covering all areas of fundamental mathematics. Each year since 2001, the institute organizes an international

summer school Summer school (or summer university) is a school, or a program generally sponsored by a school or a school district, or provided by a private company, that provides lessons and activities during the summer vacation. Participation in summer school ...

dedicated to a hot topic in current mathematical research.

History

The institute was created on January 1, 1994, under the name ''Institut de mathématiques de Jussieu''. It moved in 1999 to the Chevaleret location in Paris. In 2010, half of the institute moved back to Jussieu; in 2013, the other half moved to Paris Rive Gauche and the institute changed its name to the current one. The institute is one of the founding members of the Research Federation in Mathematics of Paris Center (''Fédération de recherche en mathématiques de Paris centre''). Since 2007, it has been affiliated with the Mathematical Sciences Foundation of Paris (''Fondation sciences mathématiques de Paris'').

Distinctions

Several members of the IMJ-PRG received national and international awards for their research. Most prominently,

Artur Avila Artur Avila Cordeiro de Melo (; born 29 June 1979) is a Brazilian mathematician working primarily in the fields of dynamical systems and spectral theory. He is one of the winners of the 2014 Fields Medal, being the first Latin American and lusop ...

received the

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place e ...

in 2014, and

Claire Voisin Claire Voisin (born 4 March 1962) is a French mathematician known for her work in algebraic geometry. She is a member of the French Academy of Sciences and held the chair of algebraic geometry at the Collège de France from 2015 to 2020. Work Sh ...

received the CNRS Gold medal in 2016.

Themes

The research at the IMJ-PRG covers most of fundamental mathematics. It is subdivided in twelve team-projects: algebraic analysis;

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

and

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

;

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, Inner product space#Definition, inner product, Norm (mathematics ...

;

operator algebra In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication given by the composition of mappings. The results obtained in the study o ...

;

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

and

optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfiel ...

;

automorphic form In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group ''G'' to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G o ...

s; history of mathematical sciences; geometry and dynamics; groups,

representations ''Representations'' is an interdisciplinary journal in the humanities published quarterly by the University of California Press. The journal was established in 1983 and is the founding publication of the New Historicism movement of the 1980s. It ...

, and

;

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

;

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

; and

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

and (algebraic) geometry.

References

{{DEFAULTSORT:Institut de mathematiques de Jussieu - Paris Rive Gauche Research institutes in France Mathematical institutes French National Centre for Scientific Research Paris Diderot University Paris-Sorbonne University French UMR