Research

The Institute of Mathematics (UR en Mathématiques) is active in the follwoing research areas:

Geometry and the Mathematical Theory of Quantization

• Research Group Norbert Poncin : Homological algebra and algebraic topology, algebraic aspects in geometry, Lie algebraic approaches to (super)space, differential, Poisson and supergeometry, equivariant quantization, sigma models
• Research Group Martin Schlichenmaier : Algebraic geometry, Kähler geometry, quantization, moduli space problems, infinite-dimensional Lie algebras, Conformal Field Theory, mathematical methods in Theoretical Physics
• Research Group Ping Xu: Differential geometry, mathematical physics and applications, in particular symplectic and Poisson geometry, noncommutative geometry, Lie groupoids and Lie algebroids, differentiable Stacks and twisted K-theory

Non commutative Harmonic Analysis and related fields

• Research Group Carine Molitor-Braun : Harmonic analysis on non-commutative locally compact groups, especially solvable Lie groups, representation theory, convolution algebras, differential operators on Lie groups
• Research Group Martin Olbrich : Harmonic analysis on locally symmetric spaces, representations and structure theory on Lie groups and Lie algebras, global analysis, homological algebra, dynamical systems

Probability Theory and its Applications

• Research Group Anton Thalmaier : Stochastic analysis on manifolds, stochastic differential geometry, stochastic Riemannian geometry (also in infinite dimensions), Mathematical Finance
• Research Group Jean-Luc-Marichal : Mathematics of Operations Research and Decision Making: Aggregation function theory, Functional equations, Boolean functions and applications, Combinatorics and logic, System reliability theory
• Research Group Giovanni Peccati

Invited Professor:

• Pierre Schapira : Algebraic analysis and microlocal analysis, Categories and sheaves, D-modules and analytic partial differential equations, Deformation quantization on complex Poisson manifolds, Applications of sheaf theory to symplectic topology.