Structure of the colored HOMFLY knot homology

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• Marko Stosic, Lisbon
• Wednesday 01 May 2013, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

In this talk I’ll present the conjectures that predict a very rigid structure on colored HOMFLY homology (that categorifies colored HOMFLY knot polynomial). The main ingredients are the “colored” differentials that relate homological invariants of knots colored by different representations. Surprisingly, we found new symmetries that cannot be seen on the polynomial level. The conjectures are motivated by the physics/geometry insights that include BPS states counting and Landau-Ginzburg theories. This very large structure on colored HOMFLY homology theories also enables computation of homologies for various knots, and relates them to the super-A-polynomial that categorifies the A-polynomial of a knot. This talk is based on joint work with Sergei Gukov and Eugene Gorsky.

This talk is part of the Differential Geometry and Topology Seminar series.

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