Thursday and Friday 14:00 - 16:00, ESI lecture hall
on April 30; Mai 6, 7, 13, 14, 27, and 28; June 3, 4, 11, 17, and 18;

 
Two-dimensional conformal field theory (CFT) has numerous applications in statistical mechanics, condensed matter physics and string theory. While the historical development of CFT was strongly tied to such applications in physics and thereby often involved heuristic concepts from these areas, many aspects of CFT can actually be analyzed rigorously.

The course gives an introduction to the mathematical structures that are needed in such a rigorous description. This includes in particular: the geometry of surfaces, including the mapping class group and moduli spaces and the concept of a complex cover; vertex algebras and their representation theory; conformal blocks and the Verlinde conjecture; modular tensor categories; three-dimensional topological field theory; and non-commutative algebra in tensor categories. Finally it is explained how these ingredients can be combined so as to allow for the construction of arbitrary correlations functions, including also e.g. effects of boundary conditions and defect lines.

Recommended literature.