Search

The goal of this project is to gather mathematicians working on questions related to index theory in noncommutative geometry. Let us mention a few research themes: - index theorem for noncommutative spaces (stratified manifolds, foliations, Lie groupoids...); - study of necessary tools for the

Considerable breakthroughs have occurred recently in representation theory. The general purpose of the project is to study the application of new tools to some classical subjects in this field : the category O of semi-simple complex Lie algebras (and their affine version) and the representations o

The LEDA project (Logistics of Algebraic Differential Equations) focuses on systems described by algebraic differential equations (DAE). The goal consists in carrying out a global logistics for the modeling, the transformation and then the efficient symbolic and/or numeric solving, of systems descri

SHEPI is « un projet suite », after ANR LHMSHE (Limites hydrodynamiques et mécanique statistique hors équilibre ; coordination Thierry BODINEAU ; from 15/11/2007 to 2010). The involved research group has increased from 14 to 22 members. The characterization and theoretical understanding of non-eq

This project is devoted to the development of a new class of mathematical models in biology called hybrid models. They describe the evolution of cell populations (tissue, organ, organism) on the basis of coupled discrete-continuous approaches. Biological cells are considered as individual (discrete)

The aim of the present project is to make significant progress on the following topics: 1. AdS/CFT correspondence 2. Parabolic structures (CR geometry, contact structures, Weyl connections,...) 3. Non-linear analysis (Yamabe problem, positive mass theorem, constraint equations, non-linear probl

Several fundamental questions of Kähler geometry boil down to solving certain complex Monge-Ampère equations. This is for instance the case of the Kähler- Einstein equation solved by Aubin and Yau in the 70's when the curvature is non-positive. The case of positive curvature has motivated ma

The concept of digital expansion is fundamental to various branches of mathematics and computer science. Beside the instances of so-called q-ary numeration systems (binary, hexadecimal etc.), there are plenty of other digital systems which have been studied in recent years. Mention, for instance, di

This project is concerned about the study, from a mathematical perspective, of linear and nonlinear models arising in quantum physics and which serve as tools to describe matter at the microscopic and nanoscopic scales. The project will focus on two main (non-independent) issues: the description o

We propose to develop methods to analyse conjointly phenotypes from behavioural and neuroimaging data, and genetic data (Single Nucleotype Polymorphism) of large dimension. Neuroimaging should act as an intermediate endophenotype and help to understand the link between genetic and phenotypic variabi

This proposal regards the study and the development of a new class of numerical methods to simulate natural or laboratory plasmas and in particular magnetic fusion processes. In this context, we aim in giving a contribution, from the mathematical, physical and algorithmic point of view, to the ITER

This project unifies four teams stemming from research laboratories in mathematics and theoretical physics having high world-wide scientific reputation of experts in the field of the classical and quantum integrable systems. It aims at developping new themes of research in the field of the quantum

The members of this project are mainly united by questions in arithmetic geometry whose solution resides in positivity properties of certain geometric structures. This positivity is most often expressed in analytic conditions (existence of particular metrics on bundles, inequalities of Schwarz l

1. Finishing the classification of class VII surfaces, 2. Proving a new analytic version of the Grothendieck-Riemann-Roch theorem in the non-Kählerian framework. 3. Proving existence, classification and deformation theory results for special metrics on non- Kählerian manifolds 4. Studying existe

Main challenge: improving dynamical cores of the general circulation models (atmosphere and ocean). Main goals: construction of efficient numerical schemes for shallow-water equations on the rotating sphere, including «non-standard« terms. Management of date produced by such models. Inclusion of

The idea of understanding a geometry via the group of transformations preserving it, dating back to Felix Klein and the Erlangen program, has gradually come to be used in the reversed order: to try to understand a group via its actions on some (metric) space with a good structure. Several of the mos

In this project a multi-university team of researchers plans to attack a variety of challenging problems in Diophantine Geometry and Transcendence theory. They can be loosely partitioned into four tasks, Bogomolov-Lehmer problems, Diophantine geometry and transcendence, Zilber-Pink conjecture, Modul

In recent years, p-adic methods (Fontaine Theory, Galois deformations) and geometric methods (deformations of varieties, local methods for Shimura varieties) have been used successfully to solve central problems of modern Number Theory. Let us mention -Serre's modularity conjecture, proven by Kh

The purpose is to obtain several breakthroughs in the analysis of long-run stochastic or differential games, with an emphasis on information issues. These questions are particularly relevant in economic theory. The main idea is to combine techniques coming from continuous time and from discrete tim

Many signal classifiers must be optimized with few training samples, which requires to build structured signal representations. This project first considers unsupervised problems where the representation is constructed without knowing the classification task and any class label. A goal of this rese

The aim of proposed research is to study various models of non-Markovian random walks modeling the dynamical properties of disordered media. Among these models, the focus is on random walks in random environments, random walks on random graphs like percolation clusters or random trees, reinforced

This project comes under fundamental research. It is at the crossing between two federative themes: the modelisation of metamaterials from on one hand, and Transformation Optics on the other hand. Metamaterials are artificial structures made of a set of elementary components (wires, split rings, nan

The mathematical understanding of two-dimensional models from statistical mechanics has undergone a profound paradigm shift with the introduction of the SLE processes by Oded Schramm in 1999. In several cases (such as the loop-erased random walk, the uniform spanning tree, the Gaus

Extreme events are a key manifestation of complex systems, in both the natural and human world. By definition, they are rare and unexpected. Extreme modeling for stationary time series is well-established, and a major effort is now underway to develop models and methods for dealing with more complex

We wish to expand the Stein/Malliavin approach beyond the framework of Gaussian (or Gamma) approximations - as developed in a recent series of papers by Nourdin, Peccati and coauthors. One of our principal aims is to develop a unified approach to central and non-central phenomena appearing in sev

Bayesian non parametric approaches have developped increasingly over the last 10 years, both in theory and applications. Indeed Bayes methods provide a useful paradigm that while retaining a fully model-based probabilistic framework, are flexible and adaptable. This project is concerned with develop

The goal of this project is to study a few questions related to random perturbations of dynamical systems. These problems are at the center of the growing field of statistical properties of dynamical systems with a particular emphasis on the stability of the measures describing them. The big effort

The general framework of this project is the study of dynamical systems and partial differential equations. We are primarily interested in those equations which appear either as infinite dimensional dynamical systems or as geometric structures. Our goal is to study remarkable solutions, invariants