IMPA Meeting: Quantum Groups and 3-Manifold Invariants

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source: Winston Cheong    2015年8月8日
From http://video.impa.br/index.php?page=quantum-groups-and-3-...
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.

Christopher Douglas - Topological field theory in dimensions 1 and 2 59:14
Christopher Douglas - Extended field theories in dimension 3, tensor categories, and Hopf algebras 1:00:11
André Henriques - Lie algebras and their representations 1:00:30
André Henriques - Deformation of the universal enveloping algebra of a Lie algebra 1:03:49
Christopher Douglas - Braided tensor categories and braided Hopf algebras 59:59
André Henriques - The quantum group and its modules 1:01:25
André Henriques - The braided structure on the quantum group 1:07:47
Christopher Douglas - The ribbon structure on the fusion category 1:08:39
André Henriques - Ribbon Hopf algebras and ribbon categories 1:06:36
André Henriques - Quantum dimension and the fusion category of a quantum group 1:02:57
Christopher Douglas - 3-manifold invariants from the fusion category 1:07:01
Christopher Douglas - Modularity of the fusion category 1:05:54