8 problems

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

For each spatial dimension $d$, let $\mathcal I(\mathbb Z^d)$ be the abelian group of invertible gapped phases, and let $\mathrm{IP}(\mathbb Z^d)$ denote a proposed space-level con…

Microscopic index conjecture. The index $omega_N$ provides a microscopic definition of the chiral central charge modulo $24$.

Twist-defect invariant conjecture. The resulting invariant $\theta_N$ is fine enough to capture $c_-$ as a real number, not only $c_- \bmod 24$.

Refined invariant conjecture. There exists a $\boldsymbol{Z}$-valued invariant for 2d invertible phases which, under special circumstances involving the emergence of conformal symm…

Distinct-phase conjecture. States $\Psi_{\tau}$ associated with holomorphic vertex operator algebras having different values of $c$ are in different invertible phases.

Cobrordism-invariant conjecture. For invertible topological orders in branch-independent bosonic systems, the topological invariant $Z^\text{top}(M)$ is a cobordism invariant.

A topological quantum field theory is a quantum field theory whose observables depend only on topological bordism data, and an invertible phase is an invertible field theory, equiv…