The recent discovery of a chain of rotating galaxies within a cosmic filament highlights the crucial importance of large-scale structures in the evolution of the Universe. These filaments, true intergalactic networks composed of galaxies and dark matter, reveal complex formation mechanisms that challenge traditional models. The study published in the Monthly Notices of the Royal … Read more
formation, large structures, organization, skills development, vocational training
Analysis of the Navier–Stokes equations: existence and regularity
Marion Lefevre
The Navier–Stokes equations, at the heart of fluid mechanics, represent a fundamental challenge in contemporary mathematical analysis. Modeling the motion of incompressible fluids, these partial differential equations form the theoretical basis of fluid dynamics. Their richness and complexity lie in particular in the study of the existence and regularity of their solutions. Despite having been … Read more
analyse mathématique, existence of solutions, fluid mechanics, Navier–Stokes equations, regularity of solutions
Optimization on manifolds: applied Riemannian geometry
Marion Lefevre
Riemannian geometry, a pioneering branch of differential geometry, provides a powerful framework for extending classical optimization methods beyond Euclidean spaces. At a time when big data is becoming increasingly complex, modeling on nonlinear structures such as manifolds offers mathematical tools suited to capturing this inherent complexity. Optimization on manifolds has thus emerged as a field … Read more
applied mathematics, optimization, optimization algorithms, Riemannian geometry, varieties
Functional Data Analysis: Statistics on Curves
In the field of statistics, functional data analysis is revolutionizing the way information measured over time or across a continuum is processed. Unlike traditional approaches centered on point data or vectors, this discipline studies data in the form of complete curves, thereby modeling dynamic and complex phenomena. Data visualization, combined with nonparametric methods and curve-smoothing … Read more
The geometry of quotient spaces: group actions
The geometry of quotient spaces imposes itself as a major discipline at the intersection of algebra, topology, and differential geometry. At the heart of this theory, group actions allow us to explore the structure of underlying sets through their symmetry, revealing the mechanisms by which complex spaces simplify into quotient spaces. This dynamic, often illustrated … Read more
Combinatorial optimization: exact algorithms and heuristics
In an increasingly connected world that demands high computing performance, combinatorial optimization emerges as a key discipline for solving complex problems where choices are numerous but limited to discrete sets. Whether it’s effectively planning routes, allocating resources, or optimizing industrial processes, this branch of applied mathematics relies on powerful techniques that combine algorithmic rigor and … Read more