Search

The Calabi problem seeks to describe compact complex manifolds admitting a Kähler-Einstein metric. While the answer has long been understood in the case of negative or zero curvature, the case of positive curvature (Fano manifolds) turned out to considerably more complicated. It gave rise to the Yau

This project is at the crossroads of algebraic geometry and number theory. It aims at investigating a series of problems arising as consequences or particular cases of `conjectures horizon' (such as the standard conjectures, the Hodge and the Tate conjectures, various conjectures on algebraic cycle

The projet de recherche collaboratif ``Beyond KAM theory'' is a project in Mathematics. Its goal is the study of dynamical systems both in finite and infinite dimensions in view of applications to partial differential equations and spectral theory. More specifically, we will be interested in syste

Statistical mechanics provides the framework for relating macroscopic phenomena, both equilibrium ones like boiling and freezing, and nonequilibrium ones like heat conduction, diffusion, etc., to their origins in the dynamics of atoms and molecules. These fundamental issues, in particular in non-equ

cf pdf cf pdf cf pdf cf pdf Sub-Riemannian manifolds provide an important mathematical model for many problems involving some nonholonomic constraints. Since several years, there has been an impressive revival of interest in sub-Riemannian geometry (in short, SR geometry), together with many emergin

The SATAS project is an ambitious project, which aims to advance the state of the art in massively parallel SAT solving with a particular eye to the applications driving progress in the field. The final goal of the project is to be able to provide a “pay as you go” interface to SAT solving services

The traditional design and analysis of algorithms assumes that complete knowledge of the entire input is available to an algorithm. However, in many cases the input is revealed online over time, and the algorithm needs to make its current decision without knowledge of the future. For example, schedu

The main guidelines of this project can be summarized by the systematization of the methods to solve the following general problems: • how to model the structures of combinatorial constructions and generating series in many applications (concurrent systems, logical expressions, physical models, net

This research project is organized along two seemingly unrelated directions: 2d quantum gravity and 3d turbulence. (1) Mathematical Liouville gravity deals with the geometry of large random planar maps. Historically, conformal invariance was a key ingredient in the construction of Liouville gra

This project is relevant to Lie theory, a well-established domain involving algebra, analysis and geometry. The objectives specifically deal with the interplay between the algebraic and geometric aspects of the theory. The geometric methods pop up with a rich variety: complex algebraic geometry,

Our project aims at a better mathematical understanding of several models for the evolution of inhomogeneous flows. Through three main lines of research (see below), we will pursue a twofold final objective. First, we want to develop the current theory of regular solutions for several equations for

The aim of this project is to analyze systems composed by structures immersed in a fluid. Studies of such systems can be motivated by many applications (motion of the blood in veins, fish locomotion, design of submarines, etc.) but also by the corresponding challenging mathematical problems. Among t

Study of principal algorithmic approaches to establish enumeration algorithms: classical output-sensitive approach and recently proposed input-sensitive approach and parameterized enumeration Algorithms and computer programs to solve fundamental enumeration problems, new algorithmique techniques.Org

The use of model theoretic tools in non-archimedean geometry with applications to number theory can be traced back to the work of Ax-Kochen-Ersov on the Artin conjecture in the sixties. Another spectacular application was provided by Denef in the eighties, with his proof of rationality of the Poinca

The main objective of the Microlocal project is to develop a top level research on the following subjects: - rigidity phenomena in symplectic geometry, especially those which persist when passing to the limit in C° topology; - the relationships between the microlocal theory of sheaves and the

Discrete exterior calculus has emerged in the last decade as a powerful framework for solving discrete variational problems in image and geometry processing. It simplifies both the formulation of variational problems and their numerical resolution, and is able to extract global optima in many cases.

The goal of the HHOMM project is to help the HHO technology ripen and promote its use in engineering applications. The results of this project have been published in top-ranking journals in Numerical Analysis and Scientific Computing. They have also been disseminated through invited presentations i

Fomin and Zelevinsky invented cluster algebras in early 2000 in order to find a combinatorial approach to the study of Luzstig and Kashiwara's canonical bases in quantum groups, and to total positivity in semisimple groups. The formalism they developped found many applications beyond the scope of th

The aerodynamics of insect flight currently receives considerable attention. The fundamentals of insect flight were first explored assuming that insects move in quiescent air. However, natural environment is usually turbulent, but we know very little on how insects manage to fly on windy days. For m

Random sequences are essential for modern computer science. They are used for security and cryptography purposes and are at the heart of randomized algorithms. In practice, pseudo-random sequences are used. The impact of their inherent regularities can be problematic depending on the context. To bet