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Solving NP-hard problems is still a challenge at the theoretical or practical level. This project aims at solving decision, optimization and counting (discrete integration) problems defined as "graphical models" (constraint or cost function networks, bayesian networks, propositional logic and Markov

This grant proposal is motivated by two things. Firstly, many physical or biological models are multiscale and heterogeneous. Phenomena with multiple scales are found everywhere from the physics of superconductivity, material science or biology to geophysics. A common feature of these systems is tha

Phase-field methods have become a major tool to study a variety of interfacial phenomena, such as equilibrium shapes of vesicle membranes, blends of polymeric liquids, multiphase flows including drop deformation in another fluid and liquid films, dendritic growth in solidification, microstructure ev

The rôle of infinite discrete subgroups of Lie groups originated in Fuchsian equations and in crystallographic groups, and gradually grew as its arithmetical, ergodical, dynamical, and geometrical aspects developed along the years. The objective of the 4 years project "Dynamics and geometric

The theory of random graphs is a field in evolution. Since its beginning at the end of the fifties until the present day, these random discrete structures have been increasingly used in mathematics and, at a larger scale, in computer science, in physics, biology or human sciences. They are commonly

Despite the practical interests of reusable frameworks for implementing specific distributed services, many of these frameworks still lack solid theoretical bases, and only provide partial solutions for a narrow range of services. We argue that this is mainly due to the lack of a generic framework t

We strongly believe that understanding the dynamics of complex systems and how to optimally act in them can have a big positive impact on aspects of human societies that require a careful management of natural, energetic, human and computational resources. We seek an automatic way that can learn to

The ABIM project aims at understanding and quantifying two major features in the modeling of biological systems: the behavior (in short and long time) of stochastic individual-based models and their links with macroscopic models. Deriving macroscopic approximations from individual-based models is th

Scheduling is a very wide topic in combinatorial optimization with applications ranging from production and manufacturing systems to transportation and logistics systems. Stated generally, the objective of scheduling is to allocate optimally scarce resources to activities over time. More specificall

Modern invariants of low-dimensional manifolds and knots come from frictions between symplectic geometry, mathematical physics, geometric topology and dynamical systems. When representing particles in String theory, a lot of algebraic structures emerge from knot invariants, such as Topological Quan

We plan to study the mathematical aspects of percolation and first-passage percolation. We do not plan to focus on the critical two-dimensional percolation, which involves specific tools, such as the SLE process introduced by Schramm in 1999, and was for example the topic of ANR MAC2 (ANR-10-BLAN-01

Mean Field Games (MFG) is new and challenging mathematical topic which models the dynamics of a large number of interacting agents. It has many applications: economics, finance, social sciences, engineering,.. MFG are at the intersection of mean field theory, optimal control and stochastic analysis,

Evolution equations, or more generally dynamical systems, form one of the predominant classes of models in the sciences, ranging from physics and biology to social sciences. The study of their qualitative behaviour for short or large times has always been one of the main purposes in mathematics and

The main topic of this project is the application of techniques of asymptotic and global analysis to Quantum Field Theory on curved spacetimes and General Relativity, with the goal of studying quantum phenomena near and beyond spacetime horizons. In the last two decades, the implementation of met

Hodgefun is a collaborative research project in pure Mathematics around the topology of complex algebraic varieties. It lies at the crossroads of Topology and Algebraic Geometry and aims at studying the relationship between the topology of a complex algebraic variety and its algebraic structur

This project aims at studying the modular representation theory of finite reductive groups (in non-defining characteristic) using the geometric methods that have proven very successful in the ordinary setting (in characteristic zero). Geometric representation theory is a very active area of research

The concept of graph is ubiquitous in modern science: it is a basic notion in combinatorics and algorithmics and it is used as a tool for abstraction in an ever increasing variety of contexts, from social networks to biological process modelling. While the theory of graphs is rich and interesting in

Software systems are ubiquitous, and more and more complex. The automated analysis of computer-generated data and the reliability analysis of complex programs become therefore crucial, and challenging due to the increasing size and intricacy of the objects that software systems have to face. Model-c

Given one or more geometric shapes (tiles), it seems natural to wonder whether they can tile the plane or not - with no overlap or gap. More precisely and in ascending order of complexity, we may wonder if the set of tiles can tile the whole plane; if it can do so in a periodic way; and how many dif

The COCA HOLA project aims at developping complexity analyses of higher-order computations, i.e. that approach to computation where the inputs and outputs of a program are not simply numbers, strings, or compound datatypes but programs themselves. The focus is not on algorithms, i.e. fixed programs,

The project builds upon the new foundations of algebraic topology, with the view to fundamental applications notably in algebraic K-theory and in chromatic homotopy theory. These new foundations have enormous potential throughout mathematics, using higher structures and functorial methods. They ha

The project gathers seven young mathematicians (chargés de recherches and maîtres de conférences for at most 5 years) disseminated in different math departments in France. The common point between them is the interplay between group theory and spaces of non- positive curvature, probability measures

In recent years data-aware systems have been proposed as a comprehensive framework to model complex business workflows by considering data and processes as equally relevant tenets of the system description [19, 28]. This setting is particularly suited to model auctions and auction-based mechanisms i

This project is set in the blooming field of singular stochastic partial differential equations (singular SPDEs) that has undergone a revolution two-three years ago, with the joint introduction by Hairer and Gubinelli-Imkeller-Perkowski of entirely new methods. These works have opened a whole field

The number and size of available data sets of different types has increased dramatically over the past twenty years. This "data deluge" has been accompanied by a shift from hypothesis-driven research to data-driven research in many scientific fields including astronomy, biology, genetics, or medicin

The (real) Monge-Ampère equation is a fully nonlinear elliptic equation with a strong geometric nature. It can indeed be used, following Minkowski, to recover a convex hypersurface from the knowledge of its Gaussian curvature. This equation also plays a central role in the theory of optimal transpor

The members of this project are mainly united by the use of the theory of holomorphic foliations applied to several questions of algebraic geometry. Three directions can be seen to structure our project: 1) Hyperbolicity 2) Analytic and birational geometry 3) Arithmetic geometry. 1) We will study ho

Given a finitely generated group G we want to investigate its outer automorphism group Out(G). This natural object was the source of an intense work when G is one of the following examples: a free abelian group, a surface group or a free group. For these groups one observes a strong growth dichotomy