9 problems

Let $k$ be a field, let $\mathbf Q(\mathbb Z^3)$ be the QCA space in dimension three, and let $\mathrm{Witt}_k$ denote the Witt group of braided fusion $k$-linear categories. The Q…

Let $\mathcal{E}$ be a finite symmetric tensor category. Let $\mathrm{Mor}_2^{\mathrm{fin}}(\mathbf{Pr}_{\mathcal{E}})$ be the symmetric monoidal sub-4-category whose objects are f…

Let $(B_*,\beta)$ be a chain bundle with algebraic Wu class $\widehat v_{2k}(\beta)$, and let $\operatorname{ev}$ denote evaluation on homology. Let $\Sigma$, $\Sigma_8$, $\Lambda$…

Let $(B_*,\beta)$ be a chain bundle, let $q\geq0$, and let $\eta_\beta\colon W_0(Q_\beta(q))\to L^{2q}(B_*,\beta)$ be the natural homomorphism. Conjecture on $\eta_\beta$. If…

Let $Q$ be a form parameter, and let a nonsingular full $Q$-form be a nonsingular $Q$-form whose linearisation is surjective. Write $H_{b\epsilon_Q}(\mathbb{Z}^m)$ for the standard…

Disentangling-QCA conjecture. For every such Hamiltonian $H$, there exists a QCA that disentangles its ground state. A pair of disentangling QCAs are equivalent if and only if the…

FDQC equivalence conjecture. The Hamiltonians $H$ and $H'$ are FDQC equivalent if and only if their surface topological orders in the presence of a gapped boundary are Witt equival…

Let $\mathcal{W}$ be the Witt group of non-degenerate braided fusion categories, let $s\mathcal{W}$ be the corresponding group of slightly degenerate braided fusion categories, and…

Witt-realization conjecture. There is at least one unitary vertex operator algebra (VOA) $V$ of central charge $c$ such that $\operatorname{Mod}_V$ is a UMTC Witt equivalent to…