# ALAN: Algebra & Analysis

Welcome at the Research Group ALAN (ALgebra & ANalysis) of the Department of Mathematics and Data Science of the Vrije Universiteit Brussel, Belgium.

ALAN investigates, by algebraic and anaytic means, mathematical theories and mathematical structures that are important in several basic areas of mathematics, such as

- approximation theory, functional analysis and topology,
- category theory,
- discrete geometry, algebraic geometry and differential geometry,
- number theory,
- probability theory and Lévy processes,
- symmetry, as incorporated by groups, quantum groups and their associated rings, algebras and representation theory.

These investigations are motivated by open classical problems as well as by the advent of exciting new areas of mathematics. Motivation also comes from outside mathematics, such as from computer science or physics, where mathematical structures that are studied are called upon as models.

The scope of the research has many connections with different central topics in mathematics and beyond. We list the main areas in which actively ongoing research is being done, together with the members presently involved.

- S. Caenepeel: Hopf algebras and quantum groups
- Ph. Cara: Incidence Geometry; Permutation Groups
- E. Colebunders/M. Sioen: Theory of approach spaces; Categorical topology
- K. De Commer: Abstract tensor categories; Quantum groups; Operator algebras
- U. Einmahl: General limit theorems of probability; Empirical Processes and their applications; Strong approximations and invariance principles, Lévy processes
- E. Jespers: Group Rings and Unit groups of orders; Ring Theory; Group and Semigroup Theory
- M. Sioen: Pointfree topology
- M. Van den Bergh: Non-Commutative Geometry