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Towards a categorification of WRT invariant of 3-manifolds

Pavel Putrov
Institute for Advanced Study
Luigi Stasi Seminar Room, ICTP
Wednesday, December 6, 2017 - 14:00

In my talk I will conjecture existence of certain new homological invariants of closed 3-manifolds.

The invariants provide a categorification of the analytically continued Witten-Reshetikhin-Turaev (WRT) invariant, have some similarities with Heegaard/monopole Floer homology and generalize Khovanov homology of knots to compact 3-manifolds. Physically such invariants can be defined as Hilbert spaces of M-theory in certain backgrounds.

I will describe mathematical properties of such invariants, and how to calculate them for some specific types of 3-manifolds.

The talk is mainly based on a joint work with S. Gukov, D. Pei and C. Vafa. 

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