Representation Theory & Categorification

In modern representation theory we often study the category of modules over an algebra, in particular its intrinsic and combinatorial structures. Vice versa one can ask the question: which categories have a given combinatorics? This is the basic insight into the concept of categorification. Categorification is a recent development which often provides finer invariants and is used in different areas of mathematics (such as knot theory). We will explain a crucial ingredient in categorification: diagrammatics of tensor categories. We will focus on a few examples that arise in current research, such as Deligne categories. This course provides a categorical framework for the structures studied in the elementary course.