Algebra and geometry of link homology

This is an informal reading course on Khovanov-Rozansky homology and its corresponding algebro-geometric models including:

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