6 problems

Let $X$ be a quasi-projective surface. For each $n$, let $H^*(X^{[n]})$ be expressed in the Heisenberg monomial basis $(\mathfrak h_\mu(n))$. Constant Conjecture. The structure con…

Decategorification isomorphism conjecture. The injective algebra homomorphism above is always an isomorphism.

Symmetric-power criterion conjecture. If the canonical morphism above is an isomorphism, then $\pi$ is an isomorphism.

Converse categorification conjecture. If $\bicat{F}_{{\cat V}}$ categorifies $F_{{\cat V}}$, then $\pi$ is an isomorphism.

Let $Q$ be a quiver with one vertex and $m$ arrows. For even $m$, let $Cl_c$ denote the infinite Clifford algebra with generators $\xi_n^{+}$ and $\xi_n^{-}$ for…

For each $n\geq 1$, let $R_0$ denote the remainder of the element $D_0$ in the construction of the minimal relation for ${\mathcal H}(n)^{O(n)}$. Nonvanishing remainder conjecture.…