Denis Poisson Institute (IDP)

The Denis Poisson Institute (IDP) is a Mathematics and Theoretical Physics laboratory located on the campuses of the Universities of Orléans and Tours. It was created when the Denis Poisson Federation, which included the Orléans Mathematics Laboratory (MAPMO) and the Tours Mathematics and Theoretical Physics Laboratory (LMPT), was transformed into a UMR in 2018. It brings together professors and researchers in mathematics and theoretical physics from the Centre - Val de Loire region. The Institute, which is organised into 4 teams, develops high-quality research in mathematics and theoretical physics, both fundamental and applied, paying particular attention to the interfaces with other scientific disciplines and to industrial and societal applications. The presence of mathematicians and theoretical physicists in the same laboratory is an original feature of the national scene.

Research themes:

Theoretical physics:

Research focuses on three areas: gravitation on a classical or quantum scale, classical or quantum field theory (high-temperature superconductivity, gauge theories, protein folding, etc.), integrable systems and complex systems (conformal theories, spin chains, quantum chaos, statistical physics, etc.).

Partial differential equations-Modelling-Simulations:

Research topics cover a broad spectrum, including analysis and numerical analysis of different types of PDEs (conservation laws, elliptic and parabolic PDEs, dispersive equations, Hamilton-Jacobi equations), PDE control and optimal control, modelling and scientific computing, with applications in particular in image processing, life sciences, fluid mechanics, aerospace and road and pedestrian traffic.Analysis and geometry:

Research topics include harmonic analysis, complex analysis, PDE analysis, semi-classical analysis and spectral theory, operator algebras, C*-algebras, non-commutative geometry, dynamical systems, potential theory, Riemannian geometry, analysis on varieties, knot theory.

Statistics, probability, algebra, combinatory and ergodic theory:

The team's research includes non-parametric and functional statistics, with various applications; random walks, random trees, stochastic differential equations and statistical mechanics; representation theory and additive theory; combinatorial number theory, flows on varieties of negative curvature. There are close links between probabilists and algebraists around conditional random walks.