Quantum Groups and 3-Manifold Invariants

The aim of this meeting is to introduce the theory of quantum groups and their representations, and to investigate associated 3-dimensional topological quantum field theories (TQFTs). We will investigate the braided tensor structure of the representation category of a quantum group and the modularity property of the semisimple quotient, when the quantum parameter q is a root of unity. We will then discuss the Reshetikhin-Turaev construction of a 3-dimensional TQFT from a modular category. Finally, we will describe the modern, higher-categorical perspective on TQFTs that includes not only invariants of 2- and 3-manifolds but also algebraic data associated to manifolds of every codimension.

 

Videos

 

Wednesday 05-09-2012

Christopher Douglas (Oxford) - Topological field theory in dimensions 1 and 2 | download

Christopher Douglas (Oxford) - Extended field theories in dimension 3, tensor categories, and Hopf algebras | download

André Henriques (Utrecht) - Lie algebras and their representations | download

André Henriques (Utrecht) - Deformation of the universal enveloping algebra of a Lie algebra | download

 

Thursday 06-09-2012

Christopher Douglas (Oxford) - Braided tensor categories and braided Hopf algebras | download

André Henriques (Utrecht) - The quantum group and its modules | download

André Henriques (Utrecht) - The braided structure on the quantum group | download

Christopher Douglas (Oxford) - The ribbon structure on the fusion category | download

Thursday 07-09-2012

André Henriques (Utrecht) - Ribbon Hopf algebras and ribbon categories | download

André Henriques (Utrecht) - Quantum dimension and the fusion category of a quantum group | download

Christopher Douglas (Oxford) - 3-manifold invariants from the fusion category | download

Christopher Douglas (Oxford) - Modularity of the fusion category | download

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