10 problems

Let $\2C$ satisfy the assumptions of Theorem, and let $\2Z_1(\2C)$ be its quantum double. Write $RT(M,\2Z_1(\2C))$ for the surgery invariant and $Tr(M,\2C)$ for the triangulation i…

Finite-group-double conjecture. There is a 3-cocycle $\omega\in Z^3(G;\mathbb{T})$ such that

Let $V$ be a simple current vertex operator algebra with group of simple currents $A$, and let $F\subseteq\operatorname{Aut}(V)$ be a finite group of automorphisms that leaves inva…

Let $V$ be a holomorphic vertex operator algebra admitting a finite group $G$ as a group of automorphisms, and let $D^{\omega}(G)$ be the twisted quantum double associated to a $3$…

The generalised umbral moonshine phenomenon consists of finite umbral groups, twisted-twined functions, and associated mock modular forms. A deformed Drinfel'd double is the quasi-…

The 23 umbral cases are associated with umbral finite groups and their mock modular forms; a deformed Drinfel'd double is the quasi-triangular algebra $D^{\omega}(G)$ determined by…

Phenomenological Arrhenius law. The memory time should satisfy

Flipping criterion. The morphism $\psi$ is invertible if and only if it is flippable and sends the integral of ${\mathcal D}(G)$ to the integral of ${\mathcal D}(H)$.

Twisted realization conjecture. For any $nu=2n+1$ and any set $P$ consisting of an even number of distinct prime divisors of $mu$, possibly empty, the modular data…

Izumi-type realization conjecture. Subfactor realizations of ${\mathcal{D}}^{0}{\rm Hg}_{2n+1}$ should be provided by Izumi's hypothetical generalization of the Haagerup: the const…