11 problems

A super-modular category is a premodular category whose Müger center is equivalent to $\sVec$. A spin modular category is a modular category containing a fermion. For a fusion cate…

A super modular category (SMC) is a modular tensor category with the fermionic structure appropriate to spin or fermionic rational conformal field theories; its data are defined by…

Classification conjecture. The quantum group categories in Proposition 3.9 are all the s-simple non-split transitive super-modular categories, up to Galois conjugates and spherical…

Let $\mathcal{B}$ be a super-modular category, and let $\widehat{S}$ be its corresponding reduced $S$-matrix. Suppose that $\widehat{S}$ is the $S$-matrix of some modular category.…

Minimal modular extension conjecture. Every super-modular category $\mathcal{B}$ can be embedded in a modular category $\mathcal{C}$ with

Splitness conjecture. Then $\mathcal{B}$ is split super-modular.

Consider the subgroup generated by the matrices $\hat{S}$ and $\hat{T}^2$ associated with $\operatorname{PSU}(2)_{4m+2}$. 2-group order conjecture. If $m+1=2^k$ for some integer…

Let $A_m$ be the subgroup of $\operatorname{SU}(k)$ generated by $\hat{S}$ and $\hat{T}^2$ associated with the super-modular category $\operatorname{PSU}(2)_{4m+2}$. Let…

Let $\mathcal{B}$ be a super-modular category of rank $2k$, and let $\hat{S}$ and $\hat{T}^2$ be the corresponding matrices. Let…

16-fold way conjecture. Let $\mathcal{B}$ be super-modular. Then $\mathcal{B}$ has precisely $16$ minimal unitary modular extensions up to ribbon equivalence.

Sixteenfold minimal-extension conjecture. A minimal modular extension always exists, and there are exactly $16$ such minimal extensions of every super-modular category.