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Analytic and algebraic aspects of q-difference equations – Q-DIFF
Whereas the theory of differential equations has known a considerable development during the past centuries, the theories of finite difference or $q$-difference equations have been relatively neglected. Recently, in particular, since $q$-difference equations appears, expected or not, in numerous
DEformable MOdels in Statistics for signal and image analysis. – DEMOS
In many fields of interests including biology, medical imaging or chemistry, observations are coming from n individuals curves or grey-level images. Such observations are typically high-dimensional data, and models involving such data have been recently extensively studied in statistics, and signal/
Mathematical MOdels and NUMerical simulations for the biological deterioration of MONUMENTs and ALGae proliferation. – MONUMENTALG
This project deals with the treatment of two topical issues, namely biodegradation of monuments and toxic algae proliferation within the Mediterranean Sea through mathematical modeling and analysis. Conservation of cultural heritage is a fundamental issue of these last decades. Indeed the degrada
Higher dimensional contact topology – TCGD
Contact topology is a relatively young field of geometry that originated as a subarea of symplectic topology, but has since achieved a prominence of its own. Most efforts in this field in the last 30 years were directed towards understanding 3-dimensional contact manifolds. In contrast, contact geom
Circulations of algebraic and arithmetic practices and knowledge (1870-1945). Sources and exchanges : France, Europe, USA. – CaaFÉ
The investigation of algebra and number theory in the 19th and the 20th centuries raises some important historical issues. Although prominent algebraists and number theorists such as Dickson made extensive references to papers published in France, and despite the roles played by algebra and arithmet
Interface Dynamics in Evolution Equations – IDEE
In some classes of reaction diffusion equations, solutions may develop sharp internal layers, or interfaces, that separate the spatial domain into different phase regions. This happens, in particular, when the reaction term is very large compared with the diffusion term.This project is concerned wit
Classification theories and birational geometry of algebraic varieties and of their linear series. – CLASS
The classification of algebraic varieties has always been one of the main questions of algebraic geometry. The minimal model program (MMP) is one approach to classification initiated at the beginning of the '80s by the joint efforts of Kawamata, Kollár, Mori, Reid, Shokurov and many others. Its ini
Hamiltonian and Dispersive equations : Dynamics – HANDDY
HANDDY project intends to take an active part in the description of a global dynamics for Hamiltonian partial differential equations, by - detecting some fine nonlinear effects in Hamiltonian PDEs, - combining dispersive and Hamiltonian approaches, - studying the impact of geometry on the dyna
Ergodic properties of the geodesic flow on noncompact manifolds with nonpositive curvature – GEODE
The aim of this project is the study of ergodic properties of geodesic flows on noncompact manifolds with nonpositive curvature. This study is growing rapidly these last few years. Our project gathers together young french researchers who are already working on the subject, to create a dynamical and
Arithmetic of varieties in families – ARIVAF
The main topics of the project under submission is how properties of arithmetic nature vary in families of varieties. The notion of family has to be understood either in its geometric classical meaning of a flat morphism of schemes or in its categorical one of algebraic stack. The researchers inv
Asymptotic Methods Applied to Materials science – AMAM
Mathematical models for material instabilities, phase transitions, plasticity, fracture, or micromagnetics are such examples of equations whose analysis is the source of challenging issues for mathematicians. In particular, recent works have been devoted to the justification of effective theories (a
Biological films and Respiratory Dysfunction – BioFiReaDy
The BioFiReaDy project aims at investigating mechanical dysfunction and airway clearance efficiency (or lack thereof) of the respiratory system, by a quantitative analysis of mucus motion. A large part of the project is dedicated to healthy configuration, cystic fibrosis (mucoviscidosis) and epithel
Laminations: spaces of tilings and systems of partial isometries – LAM
The goal of the ANR LAM project is to gather a small team of young researchers which are working on laminations in several geometric contexts, in particular: spaces of tilings and systems of partial isometries (on real trees for instance).