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Heating, Reflectometry ans Waves for Magnetic Plasma – CHROME
The CHROME project seeks to develop advanced mathematical and numerical tools for the simulation of electromagnetic waves in magnetized plasmas in the context of reflectometry and heating. A first result is a new scheme for the coupling of Maxwell equation with a linear current. We now turn to the
Algebraic groups and homology theories – GATHO
Rational points and 0-cycles of degree 1, rational points in A^1-homotopy. Birational motives, Noether's problem and commutativity of G(k)/R-equivalence. Motivic categories, Chow-Witt groups, approximation of homotopy theory of schèmes. Cohomological operations, Chow motivic décompositions. Isot
Geometry and Topology of open manifolds – GTO
The topology of open manifolds is much richer than that of compact manifolds. For instance, in each dimension n, there is (up to homeomorphism) only one manifold homotopically equivalent to the n-sphere: the n-sphere itself. By contrast, there are for every n> 2 uncountably many Whitehead manifolds,
Geometry of Subgroups – GDSous/GSG
This project concerns basic research in fundamental mathematics, more specifically it combines geometry in a broad sense, low dimensional topology, group theory, dynamical systems, and geometric analysis. In recent years, the proof of Thurston's geometrization conjecture has considerably sharpene
Regulators and explicit formulae – REGULATEURS
The aim of the project is to build new bridges between the many mathematical areas represented by its members, with the hope that this will lead to a deeper understanding of regulators. This seems justified by the fact that the members of the project are all scientifically concerned with regulators,
Variational Analysis for photoacoustic, thermoacoustic and ultrasonic tomographies – AVENTURES
The detection of cancer, and in particular of breast cancer, is a major public health issue. This project is about an alternative to conventional imaging techniques for early cancer detection. Thermoacoustic tomography (TAT) is a non invasive imaging technique based on ultrasound waves. Even th
Analysis of Robust Asymptotic Methods In numerical Simulation in mechanics – ARAMIS
Numerical simulation of multiscale phenomena is an important challenge in industry. Performing such a simulation at a low computational cost, typically on a laptop and without spending too much time on mesh generation, is therefore a challenge for scientists. Our group aims at developing methods and
Weak KAM beyond Hamilton-Jacobi – WKBHJ
This project is a continuation of the previous project ANR KAMFAIBLE. Even if, in this project, there is some overlap with members of the previous project, there is an important renewal: of the 34 members of this project, only 11 were in the original previous project, and 10 among the new members a
Stability for the asymptotic behavior of PDEs, stochastic processes and their discretizations. – STAB
Most physical, biological and economic phenomena can be described by evolution equations. Such equations can be linear or more often non-linear, reversible or non-reversible, deterministic or stochastic. It is interesting to know certain qualitative properties of their solutions, in particular their
Dynamic Reconstruction of Region Of Interest Tomography. Theory and Experiments. Reconstruction Dynamique de Région d'Intérêt en Tomographie. Théorie et Expérimentations. – DROITE
In interventional radiographic imaging, the problem of reconstructing patient information from truncated projections of moving organs often arises. This situation is due to the digital radiography detector usually being too small; is because of the need to reduce patient dose; and is because interve
Algebraic Combinatorics, Resurgence, Moulds and Applications – CARMA
Algebraic Combinatorics is traditionally connected with other parts of Mathematics, mainly with representation theory. For example, the combinatorics of symmetric functions may describe the characters of spherical functions of classical groups. It appeared recently that certain algebraic structur
Geometry and dispersion for nonlinear waves – GEODISP
We aim at a better understanding of dispersive properties of wave like equations in inhomogeneous models, including (with emphase on) boundaries. Such situations appear more complicated than just the variable coefficient metrics which have been developped in relation with quasilinear equations. Roug
Geometric measure theory and applications – GEOMETRYA
We shall address several problems within the framework of geometric measure theory, from both theoretical and numerical viewpoints. Our project is divided into 5 topics : 1) Geometric measure theory in singular metric spaces 2) Plateau problems 3) Around the Mumford-Shah functional 4) Irrigatio
Harmonic Analysis at its Boundaries – HAB
The title is a word play on the way modern harmonic analysis can be understood. It is of course a classical attitude in harmonic analysis to define boundaries and to find representation from the boundary. Thus we intend to develop the field of harmonic analysis. Second, harmonic analysis nourishes a
Asymptotic Analysis in General Relativity – AARG
The purpose of this project is to push forward the development of asymptotic analysis in General Relativity in 4 essential directions. 1. Scattering on non stationary backgrounds; conformal scattering. Scattering theory is a precise tool of analysis of the asymptotic behaviour of fields, giving suc
Additive Combinatorics: Sets, Finite Sequences and Remarkable Applications – CAESAR
The field of additive combinatorics is motivated by questions concerning additive structure in sets of integers, and more recently in subsets of more general groups. It is characterized by the wide range of mathematical tools that are employed to solve these problems, ranging from the algebraic thro
Parameter spaces for Efficient Arithmetic and Curve security Evaluation – PEACE
On the one side it involves a better understanding, from an effective point of view, of moduli space of curves, of abelian varieties, the maps that link these spaces and the objects they classify. On the other side, new and efficient algorithms to compute the discrete logarithm problem may have
Shape Optimization – OPTIFORM
This project is devoted to theoretical and numerical analysis of modern shape optimization problems. It gathers leading experts located in the Universities of Nancy, Rennes, Grenoble and Paris-Dauphine. For the theoretical point of view, the main scientific challenge is the qualitative study of opti
Design of Well Being Monitoring Systems – Do Well B.
The aim of « Design of Well Being Monitoring Systems (Do Well B.)» is the building of a Personal Healtth Systems (PHS) for early detection of challenging behaviour (as temper tantrum or self-injury) of people from the ASD (Autism Spectrum Disorder), outside hospital. This building will use and impro
Finsler Geometry and applications – Finsler
The project concerns Finsler manifolds that are not Riemannian. Some new questions on this subject arose recently and, and they are being considered by several researchers in France. The aim of this project is to put together the techniques and the efforts that are made separately by these research
Hamilton-Jacobi equations on heterogeneous structures and networks – HJnet
We propose to launch a research project on Hamilton-Jacobi (HJ) equations on networks, and more generally on heterogeneous structures. This theoretical problem has several potential applications, in particular to traffic flow theory, which is much studied from the point of view of conservation law