• Digital World and Robotics

The Paul Painlevé Laboratory (LPP)

Research unit - UMR 8524


Our research covers virtually the entire spectrum of fundamental and applied mathematics. Our main topics include geometric analysis, functional analysis, numerical analysis, theory of partial differential equations, geometry, topology, arithmetic, mathematical physics, random matrix theory, probability and statistics in the broad sense, and statistical learning. Our laboratory is structured in five teams: Analysis (Ana), Numerical Analysis and Partial Differential Equations (AN-EDP), Arithmetic and Algebraic Geometry (AGA), Geometry and Topology (GT) and Probability and Statistics (PS). We also have three joint project teams with Inria, Modal, Paradyse and Rapsodi.


  • Benoît Fresse
  • Nicolas Wicker


Bâtiment M2, Avenue Carl Gauss
Campus Cité scientifique


The Paul Painlevé Laboratory


Effectif total : 223

Personnel de recherche : 165

Personnel d'appui à la recherche : 13



• Algebraic geometry
• Topology
• Singular complex spaces in geometry
• Statistics
• Functional analysis
• Numerical analysis
• Complex analysis
• Random matrices in probability
• Dynamical systems
• Representation theory
• Nonlinear dynamics
• Quantum chaos
• Nonlinear optics
• Probabilistic modeling
• Statistical modeling

Example(s) of projects

• Numerical Simulation of Corrosion 🡭
• Functional Data Classification, application to dysfunction detection 🡭

Example(s) of publications

• Exposant de Lyapunov sur les feuilletages génériques de CP2 (Nguyen Viêt Anh, Invent. Math. 212, 2018).
• Estimées de Sogge de la croissance des fonctions propres du laplacien (G. Rivière et H. Hezari, Adv. Math. 290, 2016).
• Construction de l’intégrale motivique en caractéristique mixte (R. Cluckers et F. Loeser, J. Reine Angew. Math. 701, 2015).
• Déformations par bandelettes de surfaces hyperboliques (F. Guéritaud, F. Kassel et G. Danciger, Invent. Math. 204).
• Inégalités de transport entropie en probabilités libres (M. Maïda et E. Maurel-Segala, Probab. Theory and Related Fields 159, 2014).

Discover the full list of publications here.

Collaborations/Partners/Scientific clients

Fields Institute (Canada), University of Bristol (UK), University of Aberdeen (UK), University of Leuven (Belgium), University of Louvain-la-Neuve (Belgium), Max-Planck Institute (Germany), SISSA (Italy)

Services offers

Applications sectors

  • Biotechnology
  • Energy
  • Health / wellness
  • Automotive industry
  • Transportation / Logistics
  • Electronic / photonics
  • Agriculture
  • Education / Training
  • Trade / Retail
  • Science / Research
  • Bank / Insurance / Finance

Services provided

• Development of statistical models for data analysis and prediction
• Predictive models for large and biased data.
• Supervised and unsupervised classification in the presence of time-varying descriptors
• Treatment of missing data
• Spatial statistics
• Artificial intelligence for video games
• Optimization
• PDE analysis, application to fluid mechanics, inverse problems
• Numerical analysis
• Numerical methods and scientific computing

Consulting services

We provide consulting services related to all our areas of expertise.


We have a research library in mathematics (B2RM) and computer equipment (calculation, networks, data, virtualization).


Affiliated institutions / organisations

Partner institution(s)



Doctoral schools

Regional strategic areas of activity

  • Digital World and Robotics