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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 |
Description
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