• Aeronautics - Aerospace - Defence
  • Complex systems and software engineering
  • Digital
  • Energy, Ecology, Environment
  • Mobility and transport
  • Quality of life - Health - Food

Laboratoire de Mathématiques d'Orsay (LMO)

Research unit


The research themes on which LMO focuses are varied and range from the most fundamental mathematics to the most applied ones. The lab is structured in 5 teams : Harmonic Research, Numerical Analysis and Partial Differential Equations, Arithmetics and Algebric Geometry, Probabilities and Statistics, Topology, and Dynamics and Geometry.
The mathematics studied at LMO allow the lab to cover varied application fields like health, biology, environment, aeronautics, automobile, safety, defense.... LMO also heavily interacts with entities like CEA, INRA, INRIA, INSERM ... As a part of several partnerships with the industry, LMO is a major actor in structuring the interface between mathematiciens and the industry : creation of the GDR CNRS Mathématiques et Entreprises in 2010, launched the concept of Semaine d'Etude Mathématiques et Entreprises, and participation in the AMIES LabEx.


  • Mr Frederic ROUSSET

Innovation themes

Map and access

Département de Mathématiques, Bâtiment 425, Faculté des Sciences d'Orsay Université Paris-Sud
91400 ORSAY

Our research areas


Probability, statistics, machine learning and artificial intelligence
- random graphs and matrices
- Markov process and stochastic flows
- branching and coalescence process
- big deviations and statistical mechanics
- statistical learning: classification, dimensional reduction
- statistical theory of signal and forecast
- concentration and selection of estimators
- non-parametric Bayesian models
- statistical modeling of living things
- applications to real data, data science

Numerical Analysis and Partial Differential Equations
- mathematical physics
- fluid mechanics
- hyperbolic or dispersive nonlinear equations
- crowd movements
- optimal transport
- mathematical modeling
- scientific calculation
- reaction systems
- diffusion

Harmonic analysis
- harmonic analysis applied to PDEs
- geometric theory of measurement
- complex analysis and dynamics in several variables

Arithmetic and algebraic geometry
- algebraic geometry in positive characteristic, l- and p-adic cohomologies, Galois representations, Iwasawa theory, representations of p-adic and adelic groups, automorphic forms, varieties of Shimura and Drinfeld and their applications to functoriality of Langlands, classic complex algebraic geometry
- arithmetic of linear algebraic groups and rationally related varieties
- Analytical Theory of Numbers, Diophantine Geometry and Arakelov, Model Theory

Topology and dynamics
- dynamic systems
- groups: random walks and probabilities, group geometry, operator algebras
- analysis and geometry: conformal field theory, topological invariants and differential operators
- differential geometry: symplectic and contact, Riemannian and pseudo-Riemannian, differential

Applications sectors

  • Aeronautics / Aerospace
  • Textile / clothing industry

Total number of employees

Total number of employees : 309
Number of researchers : 180
Number of doctoral students : 111

Equipment(s) open to collaboration

Academics and industry: Calculation cluster : 160 cores, 1Tb RAM


Our results

Valuation offer

Patent :
- Procédé de mise à jour continu d'un paramètre représentatif d'un grandeur physique dépendant de sa localisation, et dispositif associé (E. Gassiat et T. Dumont).

Software :
- MIXMOD: supervised and unsupervised classification software for qualitative, quantitative and mixed data
- SCOPI: granular flow and crowd behavior
- Clematis: real geometry crowd behavior
- PyLBM: (Python module) numerical simulations via Boltzmann lattice method
- Multiflow: porous media simulation
- software development in partnership with CEA-DAM

Projects examples

Recent ANR projects :
- Arithmetic of Shimura varieties and automorphic forms and applications (ARSHIFO 2010/2014)
- Statistical calibration (2012/2015)
- Non auto-transposed operators, semiclassical analysis of evolution problems (NOSEVOL 2012/2015)
- Impact of Helium-Oxygen inhalation on ventilation, asthma ...(OXHELEASE 2012/2016)
- Geometry and dispersion for non linear waves (GEODISP 2012/2016)
- Intercation systems, optimal transport, applying simulation to economics (ISOTACE 2012/2016)
- On the fringes on harmonic analysis (HAB 2013/2016)
- Frontiers, information, dispersion (BOND 2013/2017)
- Contact spectral invariants (COSPIN 2014/2017)
- Asymptotal analysis of evolution PDE (ANAE 2014/2017)
- Valuation, Combination and Model Theory (ValCoMo 2014/2017)
- Groups, Actions, Metrics, Measures and ergodic theory (GAMME 2014/2019)

Industrial and scientific relations

Scientific collaborations

- France: labs located in Ile de France, in Bordeaux, Lille, Lyon, Nancy, Nantes, Nice,Marseille, Rennes, Toulouse,? Engineering Schools such as Ecole Polytechnique, Telecom ParisTech, CentraleSupelec, l'Ecole Normale Supérieure research organisms such as CNRS, INRIA, INRA (Jouy-en-Josas et Toulouse), INSERM (Bordeaux et Paris), CEA (Bruyères-le-Châtel, Saclay), EDF (Clamart, Chatou), ONERA (Palaiseau)
- International: Germany, UK, Australia, Canada, Chile, Corea, Scotland, Spain, Israel, Italy, Sweden, USAA, Vietnam

Private collaborations

- collaboration with several companies


Establishments of affiliation