5 problems

Geometric Realisation Conjecture. Every $f$ whose Jacobi algebra satisfies

Let $B=\mathbb C\widehat{Q}'$ be the path algebra of $\widehat{Q}'$ with potential $W'$, let $A=\operatorname{Jac}(B,W')$, and let $\omega\in A$ be central. Define the partition fu…

Minimal $W$-algebra Jacobi-algebra conjecture. The Zhu $C_2$ algebra is isomorphic to a Jacobi algebra associated with a hypersurface singularity $F$ of type

Jacobi-algebra conjecture. The $C_2$ algebra is isomorphic to a Jacobi algebra associated with a quasi-homogeneous hypersurface singularity.

Fix a homogeneous degree $d$ superpotential $W$ in $m$ non-commuting variables, let $R_W$ be its Jacobi algebra, and write … for the associated motivic Donaldson–Thomas series. Let…