With José Simental Rodriguez, we are organizing a seminar studying recent calculations of link invariants "from the A side" via affine Springer theory and "from the B side" via Hilbert schemes at UNAM (Universidad Nacional Autónoma de México).
Thanks to Omar Antolín for sharing his notes of the seminar !
Please feel free to write to either of us for more information if you are interested in participating !
Schedule : Starting from August 5th 2024, Mondays and Fridays 12-2pm.
(Eric) Main theorems of [OR] and physical motivation from [OR1].
(José) Introduction to the conjecture of [ORS].
(Eric) Computations of the unknot, the Hopf link, and the trefoil [ORS].
(José) Hilbert schemes as Springer fibers [GK].
(Eric) Introduction to matrix factorization I : Koszul complexes and Knörrer periodicity [OR].
(Eric) Introduction to matrix factorization II : equivariance, convolution, and key application of OR [OR].
(José) Soergel bimodules and Rouquier complexes.
(José) Khovanov--Rozansky homology.
References (not in any particular order)
The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link by A. Oblomkov, J. Rasmussen, V. Shende. [ORS]
3D TQFT and HOMFLYPT homology by A. Oblomkov, L. Rozanksy. [OR1]
Generalized Springer Theory and Hilbert Schemes on Planar Curves by N. Garner, O. Kivinen. [GK]
Knot homology and sheaves on the Hilbert scheme of points on the plane by A. Oblomkov, L. Rozansky. [OR]
(Physics). Knot homology and refined Chern-Simons index by M. Aganagic, S. Shakirov.
(Physics). Mirror symmetry and line operators by T. Dimofte, N. Garner, M. Geracie, J. Hilburn.