Analysis and Theory Number

• Harmonic analysis: Representations of Lie groups, harmonic analysis on Lie groups and their homogeneous spaces, spectral theory of invariant differential operators, Dirac operators, Dunkl operators, Jordan algebras. The members of the thematic organize occasional or regular conferences such as SL2R or ART, and participate in various research networks such as the GDR TLAG or the AIM project « Representation Theory and Operator Algebras ».
• Non-commutative geometry: pseudo-differential calculus on groups and foliations; K-theory calculus of algebras associated to groups, dynamical systems or groupoids; gap-labelling for quasicrystals; twisted K-theory and index theorems.
• Geometrical methods for physics: Study of mathematical structures motivated by the geometrical modeling of mechanics or field theory, often in relation with the classical/quantum transition. The topics covered range from Lie groups and algebras (possibly with homotopy) to graded varieties, via (multi-)symplectic and singular foliations, but also infinite dimensional geometry and the analysis underlying it. The members of this theme participate, among others, in networks with mechanics (Granum, inter-disciplinary GDR)

A seminar common to these three themes, sometimes accompanied by working groups, takes place on Thursday afternoons on both sites.

• Number theory: Research in the « number theory » theme is reflected in the following keywords: analytic and probabilistic number theory, additive combinatorics, distribution of prime numbers, distribution of arithmetic functions, Riemann zeta function, Dirichlet L-functions and other generalizations, smooth integers, sums of exponentials, sums of characters, number systems, diophantine approximation, irrationality measures, algorithmic number theory.

The sessions of the Nancy-Metz number theory seminar are held on Thursday afternoons and are sometimes followed by working groups led by PhD students.