Introduction to topological quantum field theory, invariants of 3-manifolds, quantum moduli spaces, and conformal field theory.
This course lasts one year. The course consists of three parts.
First part concerns the geometry of the moduli space of flat G-bundles over surfaces (also known as representation varieties of the fundamental group of a surface). There are several approaches to this subject. Fock and Reshetikhin will explain the algebraic approach, Andersen will explain how geometric quantization works in this context.
In the second part, some known constructions of invariants of 3-manifolds will be explained. The functorial arrangement of these invariants is known as a topological quantum field theory (TQFT). It can be regarded as a functor from the category of cobordisms to the category of vector spaces (linear systems).
The third part will start with the review of Segal's axioms of conformal field theory, and then some of the constructions used in the TQFT part will be extended to corresponding conformal field theories.
Topology
3-4 hours of lectures per week.
Jørgen Ellegaard Andersen, Vladimir Fock and Nicolai Reshetikhin
There is a vast literature on TQFT and conformal field theories. There is also a substantial amount of literature on the quantization of moduli spaces. As lectures will progress, the relevant references will be given.
Some references for preliminary reading can be found at Andersen's web-site.
Revised 19.12.2006
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