24 problems

Let $k$ be a field of characteristic different from $2$. The fundamental ideal $\mathbf{I}(k)$ is the ideal in the Witt group $\mathbf{W}(k)$ generated by even-dimensional inner pr…

Let $G$ be a symmetry group, let $d$ be the spatial dimension, and let $\mathrm{Witt}(G\text{-TQFT}_d)$ be the Witt group of $d$-dimensional $G$-TQFTs. Let…

Gersten–Witt exactness conjecture. This complex is exact when $A$ is a regular local ring.

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…

Let $\mathcal W$ denote the Witt group of $(2+1)$-dimensional topological quantum field theories, identified in the source with the Witt group of nondegenerate braided fusion categ…

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 the Witt group classify topological orders in spatial dimension ${\mathsf{d}}=3$. Johnson–Freyd's conjecture. The Witt group of topological orders in ${\mathsf{d}}=3$ is isomor…

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 $\mathcal S_\text{UV}$ be the surviving pre-modular fusion category and $\mathcal S_\text{IR}$ be its image pre-modular fusion subcategory in the infrared diagonal rational con…

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…

Classical Witt-group conjecture. The group of such QCAs is isomorphic to the classical Witt group.

2-primary QCA group conjecture. The QCAs presented in this work generate a group isomorphic to

Generator conjecture. The QCA $b1_1$ generates the $a95_8$ subgroup, and $b1_1b1_2^{-1}$ generates the $a95_2$ subgroup.

Categorical Witt-group classification conjecture. This subgroup is improper; equivalently, the group of three-dimensional QCAs is isomorphic to the categorical Witt group.

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…

For each integer $r\geq 1$, let $\mathcal{C}_r=\mathfrak{so}(2r+1)_{2r+1}$ be the quantum group modular category from the source, let $[\mathcal{C}_r]$ denote its Witt class, and l…

Let $s\mathcal{W}$ be the Witt group of completely anisotropic s-simple braided fusion categories of finite order, and let $s\mathcal{W}_2$ be its subgroup generated by their Witt…

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…

Let $S$ be a smooth real surface, and write $W(S)$ for its Witt group and $WR(S)$ for its real Witt group. Witt–real Witt equality conjecture. One conjectures that … This conjectur…

Moore–Seiberg conjecture. The Witt group $W_M$ should be generated by the classes

Let $\mathcal{C}(so(2n+1),2n+1)$ denote the braided fusion category associated with $so(2n+1)$ at level $2n+1$, and let $S$ be the homomorphism sending a Witt class to its product…