International Research Projects
IRPs are 5-year collaborative research projects between researchers from one or more CNRS laboratories and researchers from laboratories in one or more foreign countries. They are designed to consolidate existing collaborations through short or medium-term scientific exchanges. Their purpose is to organise working meetings or seminars, develop joint research activities and supervise students. The French and foreign teams must have already demonstrated their ability to work together (for example through joint publications or by having worked together within another scheme, such as the IEA or another).
The Insmi supports the following IRPs:
IRP AMMaC (2026–2028): The project ‘Applied Mathematics and Mathematical Biology in Cuba’ centres on several research themes, primarily focusing on the modelling of biological problems using PDEs, ODEs and probability theory: mathematical modelling of cancer; mosquito population control; the Krein-Rutman theorem for parabolic equations in a general framework; reliability and ageing of stochastic systems; and sampling of data from phylodynamic models.
Countries: France and Cuba
IRP ANIS (2026–2028): The project ‘Anisotropic Dirichlet-to-Neumann Maps: Heat Kernels and Spectral Theory’ seeks to move beyond assumptions of regularity on a domain in order to study the Dirichlet-Neumann operator and obtain accurate estimates in the case of Lipschitz regularity. It draws on elliptic problems and spectral theory to understand and solve key problems in the Dirichlet-Neumann (DtN) map.
Countries: France, Portugal and New Zealand
IRP BaDSing (2026–2028): The project ‘From Low Dimensions to Singularities: Modern and Classical Tools’ focuses on low-dimensional topology and singularity theory and is developed along two main lines: the topology of singular curves in the complex projective plane and the topology of Milnor fibres of non-isolated singularities of complex hypersurfaces in 3-dimensional complex space.
Countries: France, Hungary and Poland.
IRP BPSVAR (2026–2028): The project ‘BPS Sheaves for commuting varieties and Langlands duality’ focuses on several important applications in representation theory of the explicit computation of the BPS sheaf. It stems from the fundamental result on BPS cohomological integrality and its link to Donaldson–Thomas cohomology theory obtained in 2024.
Countries: France, Japan
IRP CHaNCoDi (2026–2027): The project ‘Conservation Laws and Hamilton–Jacobi Equations: Nonlocal Effects, Control and Discontinuities’ focuses on scalar conservation laws and Hamilton–Jacobi equations, combining several contemporary research areas represented by the French and Norwegian teams. It addresses in particular the appropriate notions of weak solutions, namely entropic or kinetic solutions for conservation laws, and viscosity solutions for Hamilton–Jacobi equations, as well as non-local equations, control theory, discontinuous flows and numerical methods.
Countries: France, Norway
IRP DERIENG (2026–2028): The ‘Derived Enumerative Geometry’ project focuses on the field of algebraic geometry, and more specifically on Gromov–Witten theory and derived algebraic geometry.
Countries: France, United Kingdom
IRP ECDS (2026–2028):
The ‘Efficient Control of Distributed Systems: Bridging Robustness, Time-Sparsity and PDEs’ project concerns the control and stabilisation of partial differential equations and aims to solve specific problems (desensitisation control, constrained stabilisation, time-sparse control).
Countries: France, Chile
IRP FRALEA (2026–2028): The project ‘Fractality, Multifractality and Randomness’ focuses on the multifractal analysis of functions, which has developed within both theoretical and numerical frameworks with applications in fields such as turbulence modelling, medical image processing, and art history. The aim of the project is to study the properties of changes in the regularity of stochastic processes.
Countries: France, Belgium
IRP GEOSUBMAN (2026–2030): The project ‘Geometric Analysis on sub-Riemannian Manifolds’ focuses on sub-Riemannian geometry, a branch of mathematics linked to harmonic and complex analysis, sub-elliptic PDEs, geometric measure theory, optimal transport, the calculus of variations and potential analysis. Furthermore, it features in several practical applications, notably image reconstruction, the neurobiology of vision, robotics, magnetic resonance, the description of quantum particles in magnetic fields, and the movement of self-propelled microorganisms.
Countries: France, Italy
IRP GLIOMATH (2026–2027): The project ‘Understanding the impact of glioma on the glymphatic system using mathematical models’ aims to contribute to the search for new therapeutic and imaging strategies for gliomas, using mathematical modelling and integrating patient data. The objective is to achieve a biologically accurate model of the glymphatic system and its alterations caused by gliomas, tailored to each individual patient.
Countries: France, Norway
IRP HYPERGEO (2026–2028): The project ‘Geometry of curves on Riemannian and hyperbolic manifolds’ is structured around two strands: one on min-max inequalities in Riemannian geometry and the other on the systolic geometry of hyperbolic manifolds.
Countries: France, Canada
IRP KINEQ (2026–2028): The project ‘Kinetic equations: coupling and asymptotic regimes’ aims to study the mathematical analysis and modelling of particle systems using kinetic theory. The equations considered are fundamental in physics (plasma dynamics, gas flows), but also appear in biology and social systems. The project aims to understand how complex macroscopic behaviour arises from microscopic interactions between particles. It focuses on the study of asymptotic regimes derived from simplified macroscopic models and on the analysis of stability and the formation of singularities.
It focuses on theoretical understanding and computational methods in kinetic theory and, more generally, on certain areas of applied mathematics.
Countries: France, United States
IRP LANGSPEC (2026–2028): The project ‘Locally presentable categories for programming language specification’ aims to establish a rigorous mathematical foundation for skeletal semantics, a programming ecosystem designed to automatically generate programming languages and prototype tools from simple specifications. This ecosystem has been used to describe the semantics of fragments of JavaScript and Python.
Countries: France, Sweden
IRP MASC (2026–2028): The project ‘Mathematics for the Atomic Scale’ focuses on mathematical modelling, applied analysis and numerical computation of phenomena at the atomic scale to advance the mathematical foundations of modelling and simulation in theoretical chemistry, physics, materials science and computational biology.
Countries: Germany, Switzerland, Italy
IRP METAPLEC (2026–2027): The project is entitled ‘Metaplectic geometric Langlands program: local and global’. The classical Langlands correspondence is a collection of results and conjectures linking number theory and representation theory. Establishing the Langlands correspondence in the arithmetic framework has proved extremely difficult. This is why a number of mathematicians have proposed a geometric version of the correspondence. The proof of the geometric correspondence was announced in 2024. The aim of the proposed research is to construct a new orbital method within the geometric Langlands programme.
Countries: France, United States, Greece
IRP MOCETIBI (2022–2026): The ‘Modelling Cell and Tissue Biomechanics’ project focuses on the modelling of cellular and tissue biomechanics. It addresses the problem of mathematically understanding the cellular processes underlying the growth and deformation of living tissues. It combines the expertise of four teams of mathematicians and mechanical engineers in France and Italy.
Countries: France, Italy
IRP MPHC (2026–2030): The project ‘Mathematics, HPC and Neural Networks: New Perspectives for Molecular Simulation’ is jointly led by members from CNRS Mathematics and CNRS Chemistry and involves colleagues based at US institutions. This project is part of an ambitious and resolutely innovative research area: the development of artificial intelligence methods for the high-performance simulation of rare events in biological systems. At the interface of applied mathematics, theoretical chemistry and biophysics, this research theme opens up scientific avenues that break with traditional approaches. It brings together complementary, world-class expertise to address fundamental challenges in the modelling of complex systems.
Countries: France, United States
IRP PICASSO (2025–2029): The project entitled ‘Hyperbolic models, numerical analysis and scientific computation’ aims to advance key themes in mathematical modelling, numerical analysis and scientific computation, primarily related to environmental applications. It focuses on the development and mathematical analysis of models, numerical methods and simulation codes dedicated to solving fluid flow problems arising from real-world geophysical and environmental applications.
Countries: France, Spain, Portugal
IRP QUIPROQUA (2026–2027): The ‘Quasi Probabilities for Quantum Information’ project focuses on quantum systems to deepen our understanding of the boundary between the quantum and the classical and to achieve ‘quantum advantages’. The team proposing the project has chosen to concentrate its efforts on problems that are clearly motivated by fundamental physics and/or the development of quantum technologies, and in which the role of mathematics (functional and harmonic analysis, group theory, probability theory) is paramount.
Countries: France, United Kingdom
IRP SPEC (2026–2027): The project ‘Spectrum of critical exponents for hyperbolic groups’ focuses on group actions on metric spaces, in particular the study of the growth spectrum of a group acting on a space with negative curvature.
Countries: France, Italy
IRP SPEDO (2026–2030): This project, renewed in 2026, is entitled ‘Spectral Analysis of Dirac Operators’ and brings together specialists to analyse the spectral properties of Dirac operators. The questions addressed are motivated by the study of quantum confinement and the electrical properties of two-dimensional materials (graphene) subjected to magnetic constraints. The IRP enables the formation of an international community to address the technical challenges posed by the mathematical study of these physical phenomena.
Countries: France, Denmark, Chile
IRP STATVAL (2026–2028): The project ‘Statistical analysis of extreme values in complex data structures’ focuses on mathematics for finance in particular. The work falls within the field of extreme value theory (EVT), an important area in finance and insurance.
The aim for mathematicians is to propose estimators for extreme risk measures that take censored data into account.
Countries: France, Denmark
Contact: insmi.international@cnrs.fr