The IMSI, present on all continents
The institute currently manages some twenty international structures: International Research Laboratories (IRL, formerly UMI) and International Research Networks (IRN, formerly GDRI). The Insmi also finances shorter international research projects, the International Research Projects (IRP), and, following calls for tender, International Emerging Actions (IEA).
To structure its international activities, the Insmi relies on the CNRS cooperation tools. Each year, researchers and teacher-researchers from CNRS laboratories are temporarily assigned abroad and participate in conferences or research programmes developed in these international structures. At the same time, researchers from all over the world are invited to France.
The IRL (previously UMI)
International Research Laboratories are mixed units whose legal framework is the same as that of mixed research units (UMR) in France. They are managed under the joint supervision of the CNRS and one or more foreign organisations in the country where they are located. It is within the framework of these IRLs that the Insmi maintains links with the major international mathematical schools.
Researchers and teacher-researchers can be assigned to these units for a period of six to twelve months or more. The objective of these units is threefold: to promote the activity of the site, to strengthen the links of cooperation between countries and to contribute to the transfer of knowledge.
These structures are created for a period of five years and are renewable.
IRN (ex-GDRI) and LIA: a long tradition of collaboration
The Insmi supports the international collaborations of the members of its laboratories by inserting them in thematic or geographical networks, the IRNs, International Research Networks, and the LIAs, Associated International Laboratories.
The IRNs are organised around a theme. They encourage the organisation of workshops, seminars and thematic schools by French and foreign partners in order to structure a community. They are for a renewable period of five years.
The notion of LIA is destined to disappear, and these laboratories, when they are renewed, will become either IRLs (International Research Laboratories) with the same framework as the former UMIs, or IRPs (International Research Projects) when their scope or location does not justify the creation of a unit.
Today, these networks are present on all five continents.
The International Research Projects (IRP)
IRPs, or international research projects, are five-year programmes designed to make new international collaborative projects possible or to consolidate research collaborations already established, for example in the framework of an IEA. The purpose of these programmes is to organise working meetings or seminars and to supervise students. The French and foreign teams must have already demonstrated their ability to collaborate together (publications).
IRPs are created at the request of researchers and teacher-researchers to the Insmi and its partners. They receive funding from the Insmi and the partners.
Four IRPs have been launched in 2021 at the IMF
The AAPT project (Algebraic Approach to Theoretical Physics), at the interface between mathematics and theoretical physics, is a joint project between the CNRS Institutes of Mathematics (INSMI) and Physics (INP). It aims to facilitate exchanges between different researchers whose common interest is abstract algebraic studies leading to advances in theoretical physics. More precisely, the links between the theory of algebraic representations, the study of orthogonal polynomials, the exact calculation of quantities relevant to certain models of theoretical physics and the study of integrable systems are at the centre of this project.
The partners are, in France, the Denis-Poisson Institute of the University of Tours, the Annecy-Le-Vieux Laboratory of Theoretical Physics, and the Laboratory of Mathematics of the University of Reims, and, abroad, the Mathematical Research Centre of the University of Montreal (Canada) and the "Clifford Research Group" of the University of Ghent (Belgium).
Hosted by the TU/e Eindhoven, EURANDOM is a centre for colloquia, doctoral and post-doctoral studies hosted by the Stochastics Section of the Department of Mathematics and Informatics (Faculteit Wiskunde en Informatica) of the TU/e in Eindhoven (The Netherlands). The name EURANDOM is an acronym for "European Research Institute for Statistic, Probability, Stochastic Operations Research and their Applications".
Founded in 1997 by the NWO (Nederlandse Organisatie voor Wetenschappelijk) and the TU/e, with the support of the Dutch government and Philips (a multinational company founded in 1891 in Eindhoven), EURANDOM was initially mainly a postdoctoral centre financed by the NWO, before becoming a centre for colloquiums and accommodation of scientific visitors. Among other things, it organises the YEP (Young European Probabilists, since 2004), YEQT (Young European Queueing Theory, since 2007) and YES (Young European Statisticians, since 2007) series of conferences for young scientists.
EURANDOM became an International Mixed Unit (UMI) of the CNRS in 2008, and has always cultivated strong links with the French probabilistic community, by participating in the postdoctoral training of numerous PhD graduates from CNRS units, by hosting numerous conferences organised by mathematicians from CNRS units, or by hosting researchers or lecturers on CNRS delegation. Following the CNRS's phasing out of the UMIs in 2020, EURANDOM becomes an IRP by joining the Labex Bézout within the International Research Project "Random Graph, Mathematical Statistical Mechanics and Random Graphs", led by the LAMA laboratory (UMR 8050 CNRS, UPEC & UGE), which is always able to welcome CNRS researchers on delegation, for scientific visits or to organise specific conferences.
The PIICQ project (Probabilités Intégrables, Intégrabilité Classique et Quantique) aims to facilitate collaboration between several researchers working on integrability in the broad sense: quantum integrability, integrable differential equations and integrable probabilities. The applications of these topics are mainly to determinantal point processes, random growth models in one spatial dimension (Kardar-Parisi-Zhang equation, ASEP-type models) and quantum integrable models. By combining concepts from random matrix theory, asymptotic analysis of differential equations and statistical physics, we propose to develop a systematic and unitary approach for the study of these models.
In France, the project partners are Aix-Marseille University, ENS Lyon, Université d'Angers and Université Claude Bernard - Lyon 1, and abroad, Bristol University (UK), SISSA (Italy), UCLouvain (Belgium) and University of Michigan (US).
The IRP "Spectral Analysis of Dirac Operators" (SPEDO) brings together mathematicians from Denmark, Spain, Chile and France to analyse the spectral properties of Dirac operators. The questions addressed are motivated by the study of quantum confinement and electrical properties of two-dimensional materials (graphene) subjected to magnetic constraints. In recent years, a lot of very promising work has emerged. The IRP allows us to structure an international community to meet the technical challenges posed by the mathematical study of these physical phenomena.
International Emerging Actions (IEA)
International Emerging Actions are developed on topics raised by the community. They are carrier-to-carrier projects. Their aim is to explore new fields of research and new international partnerships through short-term missions, the organisation of working meetings and the initiation of initial joint research work around a shared scientific project. These actions have a duration of 2 years. Exploratory actions from carrier to carrier, they can eventually lead to an IRP or IRN.
The generic calls for projects can be consulted on the Derci website.
IEAs reflect the diversity of mathematics
The topics of study of the IEAs are varied and cover the whole spectrum of mathematics. Some have been devoted to issues close to applications such as statistical and numerical modelling of air quality with Moroccan mathematicians or the study of coastal oceanography (Lebanon), as well as to internal mathematical problems such as low-dimensional geometry and topology (Finland).