Uniqueness and branching of knot homologies More Info
Paul Wedrich (Imperial College London)
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When 
Apr 15, 2016 from 01:00 pm to 02:00 pm 
Where  Bonn, Raum 1.008, MathematikZentrum, Endenicher Allee 60 
Contact Name  sachinidis 
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Knot homology theories are categorified versions of classical (and quantum) knot polynomials that are (conjecturally/almost) functorial under knot cobordisms. The goal of this talk is to present two examples of the role of higher representation theory in the study of categorifications of the ReshetikhinTuraev invariants of knots colored with 𝔰𝔩(N) representations. As a first example, I will explain how categorical versions of skew Howe duality have been used to prove that several, superficially very different constructions of 𝔰𝔩(N) knot homologies (via matrix factorizations, category , coherent sheaves...) produce isomorphic invariants. The second example concerns categorified branching rules, which provide relationships between these knot homologies in the form of spectral sequences, which are also interesting from a topological perspective. If time permits, I will talk about some open problems related to colored HOMFLYPT homologies, whose underlying higher representation theory is less well understood.