
## 5. Others

1. #### Problem 5.1.

A theorem of Morton-Samuelson connected the Elliptic Hall algebra at $q=t$ to the Skein algebra of the torus. Categorify this result.
• #### Problem 5.2.

Are there simplifications of the above problem for the $\mathfrak{sl}_n$-quotient invariant?
• #### Problem 5.3.

Is there an equivalence of categories between DAHA representations and a suitable extension of the Fukaya category of the character variety of a single punctured torus?
• #### Problem 5.4.

Is there a braid invariant extension of HHH which replaces bigraded vector spaces with bigraded $S_n$-modules suitably compatible with the action of $R=\mathbb{Q}[x_1, \dots, x_n]$ and the action of $\mathbb{Q}[y_1, \dots, y_n]$ coming from $y$-ification?
• #### Problem 5.5.

Can one describe HHH$^{a>0}$ using HHH$^{a=0}$ after tensoring with a suitable central complex?
• #### Problem 5.6.

How does one describe the Procesi bundle in the other settings, like K$^b(\mathbb{S}\text{Bim}_{\text{fin}})$?

Cite this as: AimPL: Categorified Hecke algebras, link homology, and Hilbert schemes, available at http://aimpl.org/catheckehilbert.