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Reasoning And Programming with Infinite Data Objects – RAPIDO
Rapido aims at gathering young researchers to investigate the applicability of proof-theoretical methods to reason and program on infinite data objects. The goal of the project is to develop logical systems capturing infinite proofs (proof systems with least and greatest fixed points as well as
Games and graphs – GAG
Two-player games certainly belong to the most complex problems in the field of combinatorics. One can indeed figure out this complexity when trying to answer the following question: whatever the strategy of my opponent is, does there exist a move that would lead me to victory? This hardness as well
Expanding Logical Ideas for Complexity Analysis – ELICA
Static complexity analysis aims at providing methods for determining how many computational resources (time units, memory cells) will be required by a program for its execution. Although this task subsumes, in general, a well known undecidable problem, it is possible to devise sound methods covering
Groups, Actions, Metrics, Measures and Ergodic theory – GAMME
These subjects have witnessed major progress in the last fifteen years, thanks to an increasing convergence between them. Our goal is to internationally disseminate the knowledge on these thematics, through postdoctoral positions, conferences and advanced courses. We also wish to stimulate young mat
Stochastic Methods in Quantum Mechanics – StoQ
Quantum mechanics is deterministic and probabilistic by nature, but until recently tools from stochastic processes are surprisingly underused in quantum mechanics. The situation has however rapidly changed in recent years. Experimental progresses in realizing stable and controllable quantum systems
PERfectoids, Completed cohomology, LAnglands correspondence and TORsion in the cohomology – PerCoLaTor
Recent work of Scholze on perfectoids, infinte level Shimura varieties and finiteness of de Rham cohomology on adic spaces, have generated a lot of new approachs ont the Langlands program. Thanks to works of Berger, Breuil, Colmez , Emerton, Kisin and Paskunas, the theory of p-adic representatio
Asymptotic Capturing for HYperbolic conservation Laws with LargE Source terms – ACHYLLES
The ACHYLLES project focuses on Long-Time Asymptotic-Preserving (LTAP) numerical schemes for hyperbolic systems of conservation laws supplemented by potentially stiff source terms. It ambitions to perform a breakthrough in the understanding and efficiency of LTAP schemes by: 1. analyzing the be
Analysis on singular and non-compact spaces: a C*-algebra approach – SINGSTAR
Many problems in Mathematical Physics, Number Theory, Geometry, Partial Differential Equations and other areas of science lead to advanced questions in Functional Analysis. An example of such a question is to understand analysis on non-compact and singular spaces. Classical analysis on euclidean spa
Energy Diffusion in Noisy Hamiltonian Systems – EDNHS
For these noisy Hamiltonian systems the challenging problems (and the tasks of the present project) are: 1. To derive Euler equations (hyperbolic system of conservation laws) beyond the shocks; 2. To derive the heat equation in the diffusive case; 3. To understand the nature of the anomalous di
Extremal metrics and relative K-stability – EMARKS
Kähler geometry is at the intersection of various fields of research in pure mathematics and is a very active world for the last 40 years. Without being exhaustive, it is intrinsically related to symplectic geometry, complex analysis, algebraic geometry, Riemannian geometry, PDE analysis, deformatio
Mathematical Analysis of Topological Singularities in some physical problems – MAToS
The central theme of this project lies in the area of nonlinear analysis (nonlinear partial differential equations and calculus of variations). Our main focus will be on the structure and dynamics of topological singularities arising in some variational physical models driven by the Landau-Lifshitz
Higher structures in Algebra and Topology – SAT
The theory of categories has proven to be a valuable algebraic tool to state and to organize the results in many areas in mathematics. In the same way, the notion of an operad, which emerged from the study of iterated loop spaces in the early 1970's, now plays a structural role by organizing the ma
Time and Events in Computer Science, Control Theory, Signal Processing, Computer Music, and Computational Neurosciences and Biology – Chronos
The Chronos interdisciplinary network aims at placing in close contact and cooperation researchers of a variety of scientific fields: computer science, control theory, signal processing, computer music, neurosciences, and computational biology. The scientific object of study will be the understandin
Fast Reliable Approximation – Fast Relax
Numerical computation is performed more and more efficiently, thanks to the progress of high performance computing and better and better numerical libraries. However, in most cases, the validity or quality of the approximations that are returned is difficult if not impossible to assess. Yet, in crit
Aggregation Queries – Aggreg
The main goal of the Aggreg project is to develop efficient algorithms for answering aggregate queries for databases and data streams of various kinds. Aggregate queries are central for computing statistics on various data collections such as Rdf stores, NoSQL databases, streams of data trees in Jso
Structural geometric approximation for algorithms – SAGA
Combinatorial optimization arises naturally in a variety of resource management problems in public transportation companies, industrial manufacturing, financial and health-care institutions. Standing out are two categories of optimization problems, packing and covering, with applications in material
Arakelov geometry and Diophantine geometry – Gardio
Since the end of the 19th century, the analogy between number fields and function fields has played a crucial role in arithmetic geometry. The interpretation of this analogy in the geometric framework has led to the definition of arithmetic varieties over the ring of integers of a number field.
Random Graphs and Trees – GRAAL
The past ten years have witnessed an intense research activity on the scaling limits of random graphs and random maps. These probabilistic questions are motivated by physics models, and the results that have been obtained often rely on sophisticated combinatorial constructions. Two of the main tools
Propagation phenomena and nonlocal equations – NONLOCAL
Our goal in the NONLOCAL project is to accomplish a leap forward of the knowledge on propagation phenomena in nonlocal reaction-diffusion equations with long-range interactions, the typical example being when the diffusion is modeled by an integral operator, such as the fractional Laplacian. We want
a network for Slow-fast Dynamics applied to the Biosciences – SloFaDyBio
Theoretical research in slow-fast dynamics (also known as singular perturbation theory) advances rapidly and is increasingly making a significant impact in various research areas, in particular in the life sciences (neuroscience, epidemiology, ecology, etc.). For example, the “slow-fast dissection”