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Quantum gl(1|1) and tangle Floer homology

Algebra & Discrete Mathematics

Speaker: Alexander Palen Ellis, U Oregon
Location: 1147 MSB
Start time: Mon, Feb 8 2016, 1:10PM

The Reshetikhin-Turaev construction associates a polynomial link invariant to a quantum Kac-Moody algebra and a choice of representation. The work of Khovanov, Lauda, Rouquier, and Webster on the 2-representation theory of these algebras has given us link homology theories for all these Kac-Moody types. By contrast, the knot Floer homology of Ozsváth-Szabó, which categorifies the Alexander polynomial, arises from pseudoholomorphic curve counting. We start to bridge the gap between Lie-theoretic and Floer-theorietic link homology theories by showing that the recent combinatorial tangle Floer homology of Petkova-Vértesi categorifies the construction of the Alexander polynomial as the Reshetikhin-Turaev construction for quantum gl(1|1)'s vector representation. This is joint work with Ina Petkova and Vera Vértesi.

Alex arrives Sunday, so if you'd like to meet with him, let him or Monica know