Algebra and geometry of link homology
This is an informal reading course on Khovanov-Rozansky homology and its corresponding algebro-geometric models
including:
-
Hilbert schemes of points on singular curves
-
Compactified Jacobians and affine Springer fibers
-
Braid varieties
-
Sheaves on the Hilbert scheme of points on the plane
following lecture notes
https://arxiv.org/abs/2108.10356 .
The course runs on Mondays 3-4pm in Math 2112.
Program
1/10 (note unusual day!) (Eugene) Overview Notes
1/17 (note unusual day!) (Eugene) Definition of HOMFLY homology [3.1-3.2] Notes
1/23 (Yuze) Hilbert schemes on singular curves [6.1-6.2]
1/30 (Eugene) Two-strand computations Notes
2/6 (Eugene) General properties of HHH Notes
2/13 (Soyeon) Recursions Notes
2/20 No seminar
2/27 (Josh) Affine Springer fibers Notes
3/6 (Josh) Affine Springer fibers continued Notes
3/13 (Eugene) Cell decompositions and recursions Notes
4/3 (Eugene) Braid varieties Notes
4/10 (Eugene) Braid varieties continued Notes
4/17 (James) Weaves and cluster structures on braid varieties Notes
4/24 (Eugene) Homology of braid varieties Notes
5/1 (Eugene) Y-ification: definition Notes
5/1 (Eugene) Y-ification: properties Notes