Algebra and Analysis
The ALAN research group (ALgebra and ANalysis) specializes in the two core domains ALGEBRA and ANALYSIS within mathematics. These domains have a rich history, and cover a broader spectrum in modern mathematics than is traditionally thought of. ALGEBRA studies discrete structures such as groups (study of symmetries) and categories (study of relationships). ANALYSIS studies continuous structures, and develops theories in which approaches to exact solutions play an important role. Important applications can be found in geometry and probability theory / stochastics.
approximation theory, topology, theoretical stochastics and random matrices. The expertise of the research group makes specific use of techniques from category theory, non-commutative algebra, abstract harmonic analysis, operator algebras and theoretical probability theory.
Motivation of the research also comes from outside mathematics, from computer sciences or physics, where some mathematical structures being investigated are invoked as models. The research group also foresees close collaboration with the DIMA (DIgital MAthematics) research group, through the application of harmonic analysis within signal processing, the finite geometry and algebra within coding theory and cryptography, and the category theory within the study of networks and complex systems.