6 problems

Higher level Zhu algebra conjecture. One has

Let $M_a(1)$ be the Heisenberg vertex operator algebra, let $A_n(M_a(1))$ denote its level-$n$ Zhu algebra, and let $p(n)$ denote the number of unordered partitions of $n$ into non…

Let a diagrammatic category be a monoidal category whose morphism spaces are depicted by string diagrams, with $0$-composition given by horizontal concatenation and $1$-composition…

Khovanov's conjecture. The ring homomorphism $\gamma$ is a ring isomorphism.

The Heisenberg algebra–Grothendieck group conjecture. The map $\gamma$ is an isomorphism.

Let ${\cal F}^{\otimes2}_n$ denote the level $n$ subspace of the tensor-product Fock module, and let ${}_a\langle n;\Xi;{\rm H}|$ be the level $n$ coefficients in the expansion of…