6 problems

Let $\textbf{Ising}$ be the Ising fusion category, and consider its Deligne product $\textbf{Ising}\boxtimes\textbf{Ising}$ together with a $\mathds{Z}_2$-crossed extension contain…

Let $G$ act on a braided fusion category, let $X_g$ be a defect fixed by the $G$-action, and let $\rho_{X_g,n}$ be the associated projective representation of the braid group…

Let $\mathcal{C}$ be a unitary braided fusion category, and let $X\in\mathcal{C}$ be simple. Localization conjecture. The object $X$ can be localized if and only if … The source sa…

Let a Levin–Wen (LW) model be the Hamiltonian model determined by a unitary fusion category, and consider its ground-state subspace. Levin–Wen error-correction conjecture. The grou…

Let $V$ be a unitary topological modular functor (UTMF), and let $\mathcal{B}$ be its associated unitary modular category. Let $\mathcal{C}$ be a unitary fusion category. UTMF real…

Let $X$ be a simple object in a modular category, and let $d_X$ denote its quantum dimension. Property $F$ conjecture. The braid group representations afforded by $X$ have finite i…