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Reproducing kernels in Analysis and beyond – REPKA
Our project consists of several interrelated tasks dealing with topical problems in modern complex analysis, operator theory and their important applications to other fields of mathematics including approximation theory, probability, and control theory. The project is centered around the notion of t
Approximate Bayesian solutions for the interpretation of large datasets and complex models – ABSint
Our central purpose is to rovide a wider and generic array of statistical tools able to handle “big data” without jeopardising either the depth of the statistical analysis or the precision of the statistical predictions derived from such data. The impacts of the project are two-fold: (1) scienti
Enabling Technologies for IoT – ELIOT
ELIOT focuses on the following key objectives to IoT applications: OBJ 1. Energy efficient transceiver design and allocation policies: development of advanced low-energy transmit and receive techniques, including channel estimation for transceivers with coarse quantization (1-3 bits), and to exp
Singular flows: boundary layers, vortex filaments, wave-structure interaction – SingFlows
The project SingFlows aims at a better understanding of three topics in fluid dynamics: i) The description of anisotropic flows, like boundary layers, shallow water or pipe flows. ii) The description of vortex dynamics in slightly viscous fluids. iii) The interaction between water waves and fix
Algorithms with Small Separations acKnowledged: graphs and linear matroids – ASSK
The theme of this project is small separation phenomena on graphs and linear matroids, emphasizing the applications on algorithms design. The concept of separation in theoretical computer science is pervasive, in varying forms depending on the context. It is a fundamental concept that paves the way
Harmonic Analysis for semigroups on commutative and non-commutative Lp spaces – HASCON
please find these on the English website https://lmbp.uca.fr/~kriegler/HASCON/HASCONe.html#x1-40003 We have published a first result on Bochner spaces in Journal d'Anal. Math. The second paper on complementation of radial multipliers has appeared in Archiv der Mathematik. C. Arhancet in collabo
Statistical Modeling and Inference for unsupervised Learning at largE-Scale – SMILES
Large-scale data analysis is an inherently multidisciplinary area and is becoming increasingly important in the today’s society. SMILES is a collaborative fundamental research project that aims at introducing an unsupervised statistical modeling framework and scaled inference algorithms for transfor
Real Analysis and Geometry – RAGE
Heat semigroups on Reimannian manifolds The heat semigroup on differential forms Sobolev algebras The Riesz transform Hardy spaces of differential forms and Riesz transforms The heat kernel on sub-Riemannina geometry Spectral estimates for Schrödinger operators Riesz transforms for Schro¨din
Preprocessing Information for Nontrivial Goals / Advanced Compilation of Knowledge – PING-ACK
The main objective of the PING/ACK project is to contribute to the development of the research field known as knowledge compilation, extending its scope on both the theoretical side to the practical side. In a nutshell, we plan to define new knowledge compilation maps suited to more expressive repre
Computer orbits for Discrete Dynamical Systems – CODYS
We consider two main types of discrete orbits: -finite and periodic orbits (these orbits generally have an arithmetic meaning for the systems we are considering and form a countable set), -orbits for discretizations of dynamical systems (the discretization being generally performed with respect
Variational Methods for Graph Signals – GraVa
Most of the literature neglects, for simplicity, the underlying graph structure, or uses over simplistic linear estimators to overcome these issues. We advocate the use of robust non-linear regularizations to deal with inverse problems or classification tasks on such signals. This stance raises seve
Fibrations and algebraic group actions – FIBALGA
The initial scientific objective of the project is to classify and study the geometry of certain families of algebraic varieties with “many” symmetries by applying Mori theory and other advanced techniques from different fields of algebraic geometry and geometry. complex. More precisely, the three m
Foundations of (Boolean) automata networks – FANs
The FANs project deals with automata networks (ANs). These mathematical objects are widely used in an application framework related to the modeling of biological networks and most of the studies on them are carried out within this framework, so that the field suffers from an imbalance between their
HybrId Self-adPAtive muLtI-agent systems for microgridS – HISPALIS
The aim here is to control electronic converters: DC-DC, DC-AC, AC-DC and AC-AC ensuring stability, robustness and energy efficiency, as well as, the possibility to be physically implemented. To this aim, we consider Hybrid Dynamical System Theory (HDS) theory applied to switched systems. We lead ou
Stein's Method and Analysis – MESA
This project aims at developing new techniques and applications, by leveraging ideas from mathematical analysis (PDE techniques, variational methods, optimal transport, functional analysis). Fields of application we shall explore include statistics, random matrix theory and free probability, stochas
Efficient Techniques and Tools for Verification and Synthesis of Real-Time Systems – TickTac
Formal verification, in particular model checking, consists in proving the correctness of safety critical systems. The correctness of several classes of real-time systems depend not only on whether the system computes the right output, but also on quantitative measures such as execution time, and en
Shape optimization – SHAPO
This project comes within the scope of shape optimization, which can be seen as the study of optimization problems whose unknown is a set, and arise generally from applied fields like physics, biology and engineering. We propose to deal with four main objectives, whose common vision is to reduce
Hybrid And Networked Dynamical sYstems – HANDY
Networked dynamical systems are ubiquitous in current and emerging technologies. From energy grids, fleets of connected autonomous vehicles to online social networks, the same scenario arises in each case: dynamical units interact locally to achieve a global behavior. When considering a networked sy
Dimers: from combinatorics to quantum mechanics – DIMERS
The dimer model has been introduced in statistical mechanics to describe the adsorption of molecules on the surface of the crystal in chemistry. Mathematically, it is defined as a probability measure on perfect matchings of a graph, also called dimer configurations. The dimer model on a planar
Graph Reconfiguration – GrR
Local search heuristics have long been known to be extremely efficient in practice. Recently, major breakthroughs have shown that good theoretical guarantees can also sometimes be obtained. Such algorithms are usually very easy to implement, once a meaningful way to locally perturb a solution has be
Efficient querying of incomplete and inconsistent data – QUID
Data management systems nowadays need to cope with large data sets, often integrated from many heterogeneous sources, containing redundant, inconsistent and incomplete data. Moreover, data is often not available in its whole, due to prohibitively large data volumes or access restrictions. In this sc
Galois representations, automorphic forms and their L-functions – GALF
The GALF project represents an inter-European and transatlantic fundamental research project with the broad objective to study several of the most relevant problems in current Number Theory using p-adic methods. The team consists of internationally renowned and leading experts from Paris, Lille and
Study of special solutions to dispersive equations – ESSED
This project is about nonlinear dispersive partial differential equations (PDEs) coming from physics, more specifically quantum mechanics, statistical physics, quantum field theory, or wave turbulence. The idea behind the whole project is that there exist special solutions to some PDEs around which
Expansions, dyanmical Systems and Tilings – EST
In everyday life we need to represent numbers. Besides the omnipresent decimal expansion, we not only use binary, octal and hexadecimal representations but also signed binary or Zeckendorf expansion and continued fractions. An understanding of uniqueness, how to perform mathematical operations a
Periods in Arithmetic and Motivic Geometry – PERGAMO
Periods are a class of complex numbers obtained by integrating algebraic differential forms over algebraically defined domains which only involve rational coefficients. Examples include logarithms of integers, multiple zeta values and certain amplitudes in string and quantum field theory. From the m
Free boundary and PDE analysis – BLADE-JC
Seemingly distant problems in Geometric Analysis – ranging e.g. from harmonic maps theory and its generalizations to prescribed curvature problems – share strong, common features: conformal invariance properties, existence of conservation laws, min-max phenomena are some examples of them. The syst
Random and deterministic waves – ODA
In the last 30 years there has been a considerable progress on the theoretical understanding of non linear wave phenomena both in the deterministic and the random settings. The goal of this project is to fit in this line of research aiming to make new significant advances. We will focus on the macro
Matching Architectures that Connect heterogeneous users and healthcare Efficient Systems – MATCHES
In the current boom of numerical economy and on-line services, billion dollar firms promote applications that offer their users an interface to interact and collaborate. In many cases, we can think of the users as members gathered in classes, using the application as an interface to find a match amo
CATEGORIFICATIONS IN TOPOLOGY AND REPRESENTATION THEORY – CATORE
Recently, new methods have appeared in representation theory and quantum topology, based on the notion of categorical representations of Kac-Moody algebras. They have already had remarkable applications. In representation theory, categorifications give a proof of important particular cases of Broué’
The p-adic Langlands correspondence: a constructive and algorithmic approach – CLap-CLap
The p-adic Langlands correspondence has become nowadays one of the deepest and the most stimulating research programs in number theory. It was initiated in France in the early 2000's by Breuil and aims at understanding the relationships between the p-adic representations of p-adic absolute Galois g
PAC-Bayesian Agnostic Learning – BEAGLE
BEAGLE roots in statistical learning theory (see the monographs Vapnik, 2000, and Shalev-Shwartz and Ben-David, 2014), which can be viewed as the theoretical foundations of machine learning. Statistics and its subfield statistical learning are now core parts of numerous research domains, especially
Symplectic, real, and tropical aspects of enumerative geometry – ENUMGEOM
Classical enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions, for instance the number of curves in a variety that intersect given subvarieties in a prescribed manner. This field was revolutionized through ideas of theoretical
Digital set-valued and homogeneous sliding mode control and differentiators: the implicit approach – DIGITSLID
Sliding mode control is a well-known and widely used nonlinear feedback control technique. It owes its success to its robustness with respect to large classes of disturbances, finite-time stability of the closed-loop, and the ease of tuning. Such controllers are in essence set-valued, and they yiel
Foundations of Clustering Algorithms – FOCAL
Partitioning a dataset in such a way that data elements in the same part share common features is a fundamental problem that arises in a broad range of applications. This is key in various areas: in machine learning or data analysis for example, this is used to preprocess and analyze a dataset. I
Applications of Hecke Algebras: Representations, Knots and Physics – AHA
Hecke algebras originally appeared in the theory of modular forms in the 30's. Since then the name "Hecke algebras" has been progressively used to refer to a wide variety of objects, appearing and extensively studied in several areas of mathematics. Classes of examples of Hecke algebras of special i