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Title:
Knot Homologies from Instanton Counting With Ramification
Speaker:
Abstract:
I will explain a connection between (equivariant) cohomology of vortex moduli spaces and homological invariants of knots. This connection comes from a physical interpretation of Khovanov-Rozansky homology (as well as its colored variants) that was proposed almost 10 years ago. As it often happens in physics, the same system can be looked at from a number of different angles, which give rise to relations or dualities between seemingly different mathematical objects. A famous example of exactly this sort of relation is the relation between Donaldson and Seiberg-Witten invariants of 4-manifolds. Similarly, the physical framework for knot homologies admits a number of equivalent descriptions which were actively explored in recent years, including a relation to enumerative invariants of Hilbert schemes and vortex moduli spaces. This talk is based on a series of papers with T.Dimofte, L.Hollands, A.Schwarz, M.Stosic, J.Walcher, C.Vafa, and others.
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