Quantum Invariants in Low-Dim Topology

Trinity Term 2011. Class TR11-12:30 in SGSR1; office hours R14-15 in SGS7.

Course description

The course will cover a proper subset of the following topics: classical perspectives on 2-dimensional and 3-dimensional topological quantum field theory; modular tensor categories, Hopf algebras, quantum groups, and their associated 3-manifold and link invariants; local field theory and the cobordism hypothesis; classification of local field theories in dimensions 2 and 3; categorified quantum groups and homological link invariants; the Jones polynomial of links and the Khovanov homology of links and 4-manifolds.

No prerequisites will be assumed, beyond a working knowledge of classical category theory, and references will be provided to help students fill in any needed background material. Needless to say, students and others in geometry, representation theory, algebra, and other disciplines, are all welcome.


The syllabus contains a page of references and resources.

Contact information

Christopher Douglas
Office: SGS7
Email: cdouglas at maths