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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.

IMPA - Instituto de Matemática Pura e Aplicada ©
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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 represe...
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