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Colored sl(N) homology and SU(N) representations
Algebraic Geometry| Speaker: | Joshua Wang, Harvard University |
| Related Webpage: | https://people.math.harvard.edu/~jxwang/ |
| Location: | 2112 MSB |
| Start time: | Wed, Mar 1 2023, 4:10PM |
The Khovanov homology of a rational knot or link happens to coincide with the cohomology of its space of SU(2) representations that send meridians to traceless matrices. This coincidence is closely related to the spectral sequence from Khovanov homology to an SU(2) instanton homology defined by Kronheimer and Mrowka. Motivated by a conjectural spectral sequence from colored sl(N) homology to a hypothetical colored SU(N) instanton homology, I'll explain how the colored sl(N) homology of the trefoil agrees with the cohomology of its space of SU(N) representations that send meridians to a conjugacy class associated to the color. This gives the first computation of colored sl(N) homology of a nontrivial knot. I'll also discuss work in progress with Michael Willis on the colored sl(N) homology of (2,m) torus knots and links.