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Symbolic Methods for Biological Networks – SYMBIONT
SYMBIONT is an interdisciplinary project ranging from mathematics via computer science to systems biology and systems medicine. The project has a clear focus on fundamental research on mathematical methods, and prototypes in software, which is in turn benchmarked against models from computational bi
Mathematical Investigation of Neuroscience Dynamics for Meditative Model Identification, Control, Estimation And Observation – MindMadeClear
The general goal of this project is threefold. Firstly elaborate simple yet representative dynamical quantitative models for contemplative neuroscience. The latter aims at discovering the short and mid term effects as well as the underlying mechanisms of spirit training (the classical definition for
New points of view in rational dynamics in several variables – Fatou
FATOU is a project in pure mathematics, in the field of dynamical systems. Its purpose is the study of phase space and parameter spaces of holomorphic dynamical systems in several complex variables. Recent developpements in the field suggest that those dynamical systems can have fundamentally differ
BAyeSian nonparametrics, uncertainty quantifICation and random Structures – BASICS
In the contemporary society, statisticians receive on a daily basis data and questions from diverse fields such as genomics, ecology, social sciences and astrophysics. This data is often heterogeneous and of large dimension. In this context, mathematical statistics has an important role to play. Pro
Analytical, Numerical and Integrable systems approaches for nonlinear dispersive partial differential equations – ANuI
Dispersive partial differential equations (PDEs) have important applications such as hydrodynamics, nonlinear optics, plasma physics and Bose-Einstein condensates. In this project these PDEs, mainly in higher dimensions, will be studied with a unique innovative combination of analytic and numerical
Curvature constraints and space of metrics – CCEM
A fundamental problem in Riemannian geometry is to understand `spaces of metrics’ defined by putting constraints on certain geometric quantities, in particular various notions of curvature. One studies either a set of Riemannian metrics on a fixed manifold, or a class of Riemannian manifolds. Those
Structures on Surfaces – SoS
The central theme of this project is the study of geometric and combinatorial structures related to surfaces and their moduli. Even though they work on common themes, there is a real gap between communities working in geometric topology and computational geometry and SoS aims to create a long lastin
IDEAL-BASED ALGORITHMS FOR VASSES AND WELL-STRUCTURED SYSTEMS – BRAVAS
Vector additions systems, aka VASSes, have been investigated intensely since the 1960s, often under the form of Petri nets. Their reachability problems have been shown decidable in the early 1980s, opening the way to decide many problems. However, the decidability proof and the associated KLM
Multiscale models and hybrid numerical methods for semiconductors – MoHyCon
There exists a hierarchy of semiconductors models, which corresponds to different scales of observation: microscopic, mesoscopic and macroscopic. At the microscopic scale, the particles are described one by one, leading to a huge system almost impossible to study, both theoretically and numerically.
Group Actions and Model Theory – AGRUME
The past few years have seen increasingly close connections between Model Theory, Dynamics (topological, measurable) and Combinatorics (Ramsey Theory), all revolving around dynamical systems of various kinds. By this we refer to several striking results proved in one of these domains using techniqu
Numerical boundaries and coupling – Nabuco
This project deals with the interplay between boundary conditions and transport or dispersive phenomena. It is motivated by the modeling of physical processes in which wave propagation is mainly governed by dispersion, be it encoded either in the underlying governing equations or in the chosen numer
Optimal control of microbial cells by natural and synthetic strategies – Maximic
The growth of microorganisms is fundamentally an optimization problem which consists in dynamically allocating resources to cellular functions so as to maximize growth rate or another fitness criterion. Simple ordinary differential equation models, called self-replicators, have been used to formulat
Lipschitz geometry of singularities – LISA
This project focuses on the very active field of Lipschitz geometry of singularities. Its essence is the following natural problem. It has been known since the work of Whitney that a real or complex algebraic variety is topologically locally conical. On the other hand it is in general not metrically
HOmomorphisms of SIgned GRAphs – HOSIGRA
The project is to develop the theory of homomorphisms of signed graphs whose study has begun in 2010 as a postdoc project of Reza Naserasr under the supervision of Éric Sopena. The theory is motivated by several extensions of the 4-Color Theorem: the Hadwiger conjecture, further extension of it (kno
Frontiers of operator theory – FRONT2017
Over the past decade, the interplay between operator theory (a classical subject of functional analysis) and other fields of pure and applied mathematics has substantially increased. This interplay is interesting in both directions (from operator theory to other fields, and conversely). Let us give
Dynamics of relativistic quantum systems – DYRAQ
The aim of this project is the study of relativistic quantum systems in interaction within the framework of time-dependent partial differential equations (PDEs). We will derive and analyze effective equations in various asymptotic regimes, obtaining a simpler description of complex physical phenomen
Metric graph theory – DISTANCIA
This proposal is concerned with theoretical foundations and applications of the metric graph theory that studies the structure and algorithmics of graph classes whose metric satisfies the main properties of classical metric geometries. Such applications can be found in many different areas. The h
Categorification in algebraic geometry – CatAG
Derived algebraic geometry goes back to intersection theory and particularly to the famous Serre's intersection formula introduced in the 50'. This formula express an intersection number as an alternating sum of dimensions of the higher Tor's of the structure sheaves of two algebraic sub-varieties.
FoRmal mEthods for the Design of Distributed Algorithms – FREDDA
Distributed algorithms are nowadays omnipresent in most systems and applications. It is of utmost importance to develop algorithmic solutions that are both robust and flexible, to be used in large scale applications. In the last decades, researchers from the distributed computing community have dev
L functions in families: analysis, interactions, effectiveness – FLAIR
L-functions are ubiquitous objects in Number Theory and Arithmetic Geometry. They are analytic, algebraic, or combinatorial in nature. Recently attempts have been made to formalize the notion of ``good'' family of L-functions. Such families naturally appear in a broad variety of active research fiel
Spectral geometry of intermediate quantum systems – SpInQS
The key objective of this research proposal is to develop and apply methods from number theory to study the geometry of eigenfunctions and the spectral properties of quantum sys- tems in a state of transition. The project will be of a duration of 4 years and consists of two main tasks: to prove delo
Foundations of Stack-Based Automata – LIFOUNDATIONS
Stack-based automata provide a mathematical framework for modeling the sequential behavior of computer programs. They are essentially finite state automata that have access to an infinite memory that can be manipulated in a first-in/last-out fashion. Pushdown automata are probably the most promine
Energy-first Design of LDPC Codes and Decoders – EF-FECtive
EF-FECtive (Energy-First Forward Error-Correction) aims to advance the state-of-the-art in the energy efficiency of LDPC decoders through fundamental contributions to code design methods and VLSI decoder design, and by establishing a close interaction between coding theory and implementation constra
Control of Constrained Interconnected Systems using Variational Analysis – ConVan
Many physical and engineering systems are modeled mathematically by the dynamic equations, and the static relations describing constraints on evolution of trajectories. Interconnections of such constrained dynamical systems are observed in many practical applications and control of such systems is,
Combinatorial Analysis of Polytopes and Polyhedral Subdivisions – CAPPS
This project studies combinatorial problems on (possibly high dimensional) convex polytopes and polyhedral subdivisions. These arise naturally in several research areas in mathematics and computer science, both theoretical and applied. Although many of these problems are strongly related, they are t
Probabilistic Analysis and Simulation of Geometric Algorithms – ASPAG
The analysis and processing of geometric data has become routine in a variety of human activities ranging from computer-aided design in manufacturing to the tracking of animal trajectories in ecology or geographic information systems in GPS navigation devices. Geometric algorithms and probabilistic
Games through the lens of ALgebra and geometry of OPtimization – GALOP
Shapley introduced stochastic games in 1953 and since then they are a subject of intensive study. They model dynamic interactions in an environment that changes in response to the behavior of the players. Their applications include industrial organization, resource economics, market games, communica
Universality for random nodal domains – UNIRANDOM
Nodal sets, i.e. vanishing loci of functions, are central objects in mathematics. Understanding the main features of a purely deterministic nodal set is generally out of reach, as illustrated by several celebrated open problems, such as Hilbert’s sixteenth problem or Yau’s conjecture. In order to ca
QUAntum COntrol: PDE systems and MRI applications – QUACO
The goal of quantum control is to design efficient population transfers between quantum states. This task is crucial in atomic and molecular physics, with applications ranging from photochemistry to quantum information, and has attracted increasing attention among quantum physicists, chemists, compu
NONequilibrium STochastic and OPen Systems – NONSTOPS
From the very beginning of its development statistical mechanics, as a mathematical approach to the generic behavior of complex systems, has been one of the most fruitful cross-fertilization areas between physics and mathematics. Nowadays its use has pervaded a large spectrum of scientific activitie
High-Dimensional Time Series Analysis – HIDITSA
Due to the spectacular development of data acquisition devices and sensor networks, it becomes very common to be faced with high-dimensional time series in various fields such as digital communications, environmental sensing, electroencephalography, analysis of financial datas, industrial monitorin
The Swiss Cheese and the Wiener Sausage – SWiWS
This project considers as its main object paths made by a discrete random walk, or its continuous counterpart, a Wiener Sausage. These are celebrated models of Probability Theory, and bench test models for applications in Biology, Chemistry, or Physics. We consider models of interacting random paths
Adaptive importance sampling methods for Bayesian inference in complex systems – PISCES
Many problems in different scientific domains can be described through statistical models that relate observed data to a set of hidden parameters of interest. This kind of statistical models can be found in a broad range of applications such as biology, medicine, econometrics, computer science, arti
Entropy, flows, inequalities – EFI
This proposal lies at the interface between partial differential equations and probability theory. It aims at developping entropy methods and associated notions and techniques, and at applying them to various models in connection with several fields, such as physics (plasmas, Schrödinger, etc) and m
Multiwave Inverse Problems – MultiOnde
Inverse problems have been a very active field of mathematical and numerical research over the last decades, driven by many applications of important economic and societal impact. Im- proving medical imaging techniques or oil prospection methods, designing sensors at the molecular scale, predicting
Majorization-Minimization algorithms for Image Computing – MajIC
Recent developments in image processing brings the need for solving optimization problems with increasingly large sizes, pushing traditional techniques to their limits. New optimization algorithms need to be designed, paying attention to computational complexity, scalability, and robustness issues.