Search

The digitalization of our societies comes with increasing risks in security and privacy. Formal methods based on logic initially developed for verification of critical software have been progressively applied to cryptography and privacy. In particular some domain-specific proof-assistant tools like

The language Esterel has proven successful for real-time, safety-critical applications, and is used in many industrial systems including Airbus and Dassault Aviation airplanes. This success of Esterel in domains requiring strong safety guarantees is attributable to its synchronous reactive programm

Storing a graph in a computer (von Newmann architecture) implicitly defines an ordering of its vertices. We observe that graph algorithms may benefit from a clever use of such an ordering. One can think of the strongly connected component algorithm (Kosaraju-Sahrir, 1981) for which linear time can

Mixed Integer Linear Programming (MILP) is an important computational problem and is often solved on large scale inputs across academia and industry. Sophisticated software packages exist for this purpose, and the algorithmic paradigm used by these packages is well-documented. These algorithms, w

This project proposes a new methodology able to tame discontinuities for the control of a class of nonsmooth partial differential equations (PDEs), namely transport equations subject to dynamic controllers. Indeed, such systems model many applications such as the drilling system or the earthquake ph

In recent years, the scientific field of distributed computing has been subject to a revolutionary discovery that goes against the conventional wisdom that saving energy means slowing down calculations: it is actually possible to design algorithms that are both time and energy efficient. In a nutshe

Automata networks are general models of interacting entities, exhibiting "complex" collective behaviors. Relating the local rules followed by the entities, the architecture of interactions, and the global dynamics, motivates the community. ALARICE aims at understanding these relations through the fo

Post-quantum cryptography aims to design the cryptographic primitives that can be executed by classical computers, but resist to attacks by quantum computers. Lattice-based cryptography, standardized by the American National Institute of Standards and Technology, will be deployed in our daily life i

Bilinear inverse problems (BIPs) are ubiquitous in engineering and applied sciences as they are naturally fit to model unknown linear systems. Nonetheless, BIPs come with many statistical and algorithmic challenges. They demand stringent structural assumptions on each variable for identifiability, s

The objectives of this project are focused on the analysis and experimental validation of multivalued control laws and observers/differentiators based on the theory of sliding mode, in discrete time, mainly using implicit and semi-implicit Euler algorithms. Indeed, it has been recognized for some ye

Optimizing maps is a persistent challenge in computational mathematics, serving as a crucial component for generating high-quality quadrangular and hexahedral meshes essential for simulating highly anisotropic physical phenomena. Additionally, the significance of these maps has resurfaced in the rea

Ordinal Time Computation (OTC) is a new frontier of the research in theoretical computer science which aims to go beyond the limits of current computation paradigms by relaxing (in a controlled way) the constraints of finite time and finite space. The project aims at studying promising computat

The robust optimization framework allows addressing uncertainty in optimization problems through bounded uncertainty sets, thus avoiding the need of the precise knowledge of probability distributions. Recently, there has been considerable methodological advances in this field under the assumption th

Hypergraph dualization appears in disguise in countless areas of computer science ranging from logic to database theory. Over the years, it has undoubtedly become one of the most important open problems in algorithmic enumeration. The generation version of the problem, Trans-Enum, takes as input a h

Real and complex algebraic curves play a crucial role in many applications of mathematics, physics and engineering, like automatic geometric theorem proving, computer-aided geometric design, motion planning in robotics or nonlinear wave equations. Their algorithmic treatment is at the core of comput

The theoretical study of programming languages is rooted in discrete structures. However, the computation and approximation of continuous objects are two of the main applications of computer science. The DiPLo project aims to bring programming theory closer to applied mathematics. It will rely on ne

In the field of computational geometry, we are addressing the complex task of efficiently computing provably-correct triangulations of manifold with singularities, that can be seen as stratifolds. These structures are prevalent in various domains including robotics, control theory and learning from

PH-DIPSY is a fundamental research project that focuses on the development of novel control and estimation strategies for complex physical systems modeled by Distributed Parameter Systems (DPS) subject to hybrid phenomena (such as switching dynamics). The project's ultimate goal is to achieve guaran

The recent development of new radio telescopes such as LOFAR or SKA, consisting of several thousands of elementary antennas, leads to consider new design approaches, especially regarding their antenna configuration. These new instruments will make it possible to achieve unprecedented imaging accurac

In 2020, the principal investigator of this project introduced a proof technique with applications in many areas related to combinatorics. This proof technique relies on a counting argument and belongs to a family of techniques such as the Lovasz Local Lemma and entropy compression. These techniques

This project is in the field of the theory of regular languages of words and trees. Its objective is to understand classes of such languages. The standard way of "understanding" a class of regular languages is the "membership problem", which consists in designing an algorithm to decide whether an