Research

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

Algebra and Number Theory

• Research Group Gabor Wiese : Algebraic number theory, arithmetic geometry, computer algebra; in particular: Galois representations, modular forms, modularity questions, inverse Galois problem

Geometry and the Mathematical Theory of Quantization

• Research Group Norbert Poncin : Category theory, algebraic topology, operads, higher algebraic structures; algebraic aspects in geometry; differential geometry 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 (Prof. Ping Xu moved to Penn State University, USA): 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, Mathematical Finance, Decision Theory

• 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: Stochastic analysis on Wiener and other spaces, Random measures, Exchangeability, Limit theorems, Gaussian processes, Bayesian methods, Random matrix theory, Mathematical finance, Mathematical statistics, Combinatorics, Group representations, Harmonic Analysis on Groups & Homogeneous spaces, Survival Analysis

 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.