The Laboratory of Mathematics of Lens (LML) is the UR 2462 research unit of the University of Artois. It is part of the Fédération de Recherche Mathématique FR 2703 of the CNRS, and brings together thirty professors-researchers and researchers working on the themes of algebra, functional analysis, algebraic geometry, algebraic topology, didactics and the history of mathematics as well as deep learning (a branch of research in full spin). The members of the LML, through their research, maintain fruitful collaborations with other mathematics laboratories at the regional, national and international levels. These collaborations extend to the private sector where LML members collaborate with companies in the Hauts-de-France region.
• Witt groups of schemes, K-theory, algebraic cobordism, homotopical theory.
• Algebraic structures and invariant research (quadratic forms, central single algebras, algebraic groups).
• Theory of codes.
• Hopf ring extensions and algebras.
• Study of composition operators on certain analytical function spaces.
• Linear operator dynamics (hypercyclicality, chaos, frequent hypercyclicity, ergodicity).
• Harmonic Analysis.
• Generative problems (GANs).
• Time series (LSTM, RNN).
• Medical applications (remote photoplethysmography, help with hydrocephalus diagnosis, tumor detection).
• Transfer learning, semi-supervised learning, 3D face modeling, 3D morphable models.
• Highoutput screening (semiconductors).
• Message passage algorithms.
• Wasserstein geometry.
Didactics-History of Mathematics
• Math learning in primary and secondary school.
• Analysis of primary school teaching practices.
• Didactic analysis of the use of the history of mathematics as a teaching medium.
• History of mathematics teaching in the modern era (professional mathematics and elementary mathematics).
• Mathematical physics: Quantification by deformation.
• Intersection cohomology, Poincaré duality and Riemannian leaflets.
• Differential invariants.
• Scalar elliptical solitons and KdV equations.
Example(s) of projects
• Linear dynamical systems on Hilbert spaces : typical properties and explicit examples.🡭
• Intersection Cohomology. Simplicial Blow-up and Rational Homotopy 🡭
Example(s) of publications
• De Re Geometrica: Writing, Drawing and Preaching Mathematics in Early Modern Mines. Isis, A Journal of the History of Science Society. 🡭
• Hyperelliptic d-Tangential Covers and d× d-Matrix KdV Elliptic Solitons. International Mathematics Research Notices. 🡭
• Potentiel d'un travail sur les exemples en formation professionnelle d'enseignants. Petit x. 🡭
• Relative Equivariant Motives and Modules. Canadian Journal of Mathematics. 🡭
• The descent of biquaternion algebras in characteristic two. Israel Journal of Mathematics. 🡭
You can find all our publications here.
• Prague Academy of Sciences (Czech Republic)
• Arturo Prat University (Chile)
• University of Algiers (Algeria)
• University of Bielefeld (Germany)
• University of Cambridge, England
• University of Cologne (Germany)
• University of Leuwen (Belgium)
• University of Ohio (USA)
• University of Mons (Belgium)
• University of Montevideo (Uruguay)
• University of Padua (Italy)
• University of Nevada, Reno, USA
• University of Scranton (USA)
• University of Seville (Spain)
• Shahrood University of Technology (Iran)
• University of Talca (Chile)
• University of Tehran (Iran)
• Tianjin University, China
• University of the Basque Country (Spain)
• Uniwersytet Jagielloński (Poland)
• Lebanese University (Lebanon)
• Technical University of Gebze (Turkey)
Several French universities including: ULCO, UPJV, Université de Lille, Université de Lorraine, Université de Marseille, Université Paris 11, Université Paris 13, Université de Paris - INSPE HDF.
• Fipsico (laboratoire commun Emile).
• Unchartech (Peps AMIES).
- Science / Research
Affiliated institutions / organisations
Regional strategic areas of activity
- Digital World and Robotics
- Societal and economic transition & Risk management
- Societal issues, employment, inclusion, social innovation