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Hidden Algebraic Structure in Topology

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Sergei Gukov
Wed, 2019-09-18 11:30 - 12:20
MPIM Lecture Hall

Which 4d TQFTs and  4-manifold invariants detect the Gluck twist? Guided by questions like this, we will look for new invariants of smooth 4-manifolds and knotted surfaces in 4-manifolds. Traditionally, a construction of most such invariants and TQFTs involves a choice of certain algebraic structure, so that one can talk about "invariants for $SU(2)$" or a "TQFT defined by a Frobenius algebra." Surprisingly, recent developments lead to an opposite phenomenon, where algebraic structures are labeled by 3-manifolds and 4-manifolds, so that one can speak of VOA-valued invariants of 4-manifolds or MTC-valued invariants of 3-manifolds. Explaining these intriguing connections between topology and algebra will be the main goal of this talk.

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