Categorical tools for low-dimensional field theories

On the basis of a few specific examples, I will indicate how concepts and
tools from category theory can help to solve problems in low-dimensional
quantum field theories. Specifically I will discuss:
1) The classification of rational two-dimensional conformal field theories.
2) The classification of topological defect lines in 2(+1)-dimensional
topological orders.
3) The elimination of the dependece on auxiliary data which arise in a
construction of conformal field theory correlators that is based on
pair-of-pants decompositions of surfaces.
Pertinent concepts from category theory will be explained on the spot;
no prior knowledge of category theory is assumed.


Ingemar Bengtsson and Edwin Langmann

PS: Unusual time because of PhD defence