Welcome to the Bielefeld Representation Theory website!
Representation theory has a long and colourful history, which began with the study of structures like permutation groups and matrix algebras. One of the fundamental objectives in this area is to classify the representations of a given finite dimensional algebra. This particular subject took off in the 1970s, when the language of quivers and methods from homological algebra dramatically changed the way we view representation theoretic problems altogether.
Today, structures like Auslander-Reiten quivers, representation varieties, triangulated categories and Hochschild cohomology comprise only a handful of the various tools one can use to study representations of finite dimensional algebras. There are also beautiful connections to Lie theory, quantum groups, singularity theory and cluster algebras.