13 problems

Fidkowski's conjecture. $Y$ is a nontrivial QCA if the invertible phase it entangles has a nontrivial partition function on some orientable manifold.

Let $\mathcal H=\ell^2(\mathbb Z^2)$ and let $P$ be the Fermi projection of a gapped Hamiltonian $H$ satisfying exponential locality. Let $\omega_P$ be the associated quasi-free st…

Boundary-map classification conjecture. All maps $B$ satisfying

Let $\mathcal{C}$ be a fusion 2-category and let $2\operatorname{Vec}$ be the 2-category of finite semisimple 1-categories. A fiber 2-functor is a tensor 2-functor…

Let $\mathcal{C}$ be a fusion category, let $\mathcal{M}$ be a $\mathcal{C}$-module category, and denote the corresponding gapped phase by $\mathcal{T}_{\mathcal{M}}^{\mathcal{C}}$…

The 16-fold way conjecture. Every super-modular category $\mathcal{B}$ admits a minimal modular extension, and it has exactly 16 minimal modular extensions up to braided monoidal e…

Generalized-cohomology conjecture. The spaces $\Theta_d$ can be chosen to satisfy

Internal-symmetry classification conjecture. The classification of SPT or SET topological phases in $d$ dimensions with internal symmetry $G$ is given by homotopy classes of maps

Let $Z$ be the partition function of a unitary $(3+1)$-dimensional topological quantum field theory. Homotopy-invariance conjecture. The partition function of any unitary $(3+1)$-T…

A chiral topological phase of matter (TPM) is a TPM whose topological order is a chiral unitary modular category. A CLP Hamiltonian is a commuting local-projector Hamiltonian. Chir…

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 a $2D$ topological phase of matter (TPM) be an equivalence class of connected stable topological Hamiltonian schemas, and let its topological order be the unitary modular categ…

Let $\mathcal{A}_i$ and $\mathcal{A}_j$ be Lagrangian algebras, and let $\tau_{ij}$ denote a boundary defect between them. Let $t_i$ be a simple object of the boundary fusion categ…