The goal of this study group is to understand Webster knot homology theories from three perspectives: diagrammatic, algebraic geometry, symplectic geometry. We will start with the diagrammatic perspective, reviewing the construction of Khovanov homology, discussing Webster's discovery that it can be recovered from bimodules over KLRW algebras, and the following generalization to all Dynkin types. We will continue with the algebraic geometry perspective, seeing how KLRW algebras have Morita-equivalent models as coordinate rings of additive Coulomb branches X, with bimodules realized by correspondences between such branches. In the final symplectic geometry perspective, we will discuss Aganagic-Gaiotto-Witten's proposed LG model (Y,W) for X, where Y is the multiplicative partner of X, and review the evidence that homological mirror symmetry DCoh(X)=DFuk(Y,W) holds.
Time: Fridays 10:30-12:00
Location: Columbia University, Mathematics Hall, Room 407
| Date | Speaker | Title | Reference |
|---|---|---|---|
| Feb 13 | Ross Akhmechet | Khovanov homology and Bar-Natan refinement | [8,3] |
| Feb 20 | Fan Zhou | Webster homology | [10] |
| Feb 27 | Felix Roz | Khovanov homology is a particular Webster homology | [9] |
| Mar 06 | Tommaso Botta | Additive/multiplicative Coulomb branches X/Y | [4] |
| Mar 13 | Tianqing Zhu | Coulomb branches of quiver type | [5] |
| Mar 27 | Ivan Danilenko | How to recover Webster homology from DCoh(X) | [11] |
| Apr 03 | Elise LePage | Aganagic-Gaiotto-Witten LG potential W:Y->C | [1, 6] |
| Apr 10 | Johan Asplund | Fukaya category Fuk(Y,W) | [7] |
| Apr 17 | Filip Zivanovic | DCoh(X) embeds into DFuk(Y,W) | [2] |