30 problems

In the exterior region of a black hole, the bulk entropy $S_{bulk}(\rho)$ is regulated by a bulk UV cutoff, while the area term in the quantum extremal surface formula depends on N…

Gluing conjecture. The continuum amplitudes satisfy

Let the vacuum fluctuations of matter fields be the quantum fluctuations of the matter degrees of freedom in the vacuum state. Sakharov's conjecture. General Relativity arises as a…

Let $g_{ik}(x)$ be a spacetime metric, let $dt=dx^0$ be coordinate time, and consider an ideal clock fixed at spatial position $x^i$, $i=1,2,3$. Its proper time satisfies … Let…

Quantum-gravity tensor-structure conjecture. The tensor-product structure above describes the first steps away from the semiclassical approximation toward a full theory of quantum…

Let quantum gravity theories be theories whose gravitational path integrals include sums over spacetime topologies, and let gauge redundancies associated with topology change denot…

Let $\chi^-_\nu$ be the exponent governing the large-area tail of the negative-curvature JT area distribution. Exact negative-curvature exponent conjecture. … This agrees with the…

Let $\rho^-_{\beta_{\mathrm q}}(A)$ be the area distribution of JT gravity with negative curvature $-2/L^2$, coupled to conformal matter with $c\leq0$, and let $\nu$ be the corresp…

Let $\rho^0_{\beta_{\mathrm q}}(A)$ be the area distribution of zero-curvature JT gravity coupled to conformal matter with $c\leq0$, and let $\nu$ be the critical exponent specifie…

Let $\nu$ and $\vartheta$ be the critical exponents governing the continuum limit and the zero-cosmological-constant partition function of the SOP model. SOP critical-exponent conj…

Let a self-overlapping polygon have boundary length $2n$, and let its multiplicity be the number of distinct distorted disks it bounds. Exponential multiplicity conjecture. There e…

Let $w_{2n}$ be the number of self-overlapping polygons of length $2n$ in the SOP model, counted with multiplicity factor $\mu_\gamma$. SOP connective-constant conjecture. The limi…

Ricci flow conjecture. Any Ricci-flow fixed point at infinite distance should be accompanied by an infinite tower of additional fields with a flow-dependent mass threshold…

Let WZW$_4$ plus Mabuchi gravity be the bulk theory on Burns space, and let the large $N$ chiral algebra be the chiral algebra obtained from the compactification…

Let $c9$ be a tangential structure, and suppose a consistent $n$-dimensional theory of quantum gravity sums over spacetime backgrounds carrying a $c9$-structure. The associated bor…

Graviton density-family conjecture. The perturbative expansion with respect to $\mathfrak{h}^{\{\omega\}}_{\mu\nu}$ depends on $\omega$ only through the external-leg structure. Con…

Predictivity conjecture. (Effective) Quantum General Relativity, possibly coupled to matter from the Standard Model, is predictive.

Let $\mathcal{C}_{\mathbf{q}}$ and $\mathcal{C}_{1/\mathbf{q}^\vee}$ be the two Hopf algebras represented on the Hilbert space $\mathscr{H}$ by $mathpi$, with the corresponding ope…

Joint interface-function convergence conjecture. The joint law of both NW/SE and NE/SW interface functions of a random bipolar-oriented planar map converges to the joint law of bot…

Resolution-of-unity conjecture. For sufficiently small $t>0$, the displayed resolution of unity and the stated asymptotic scaling of $C_t$ hold for an arbitrary Lie group $G$. If…

Let $\Gamma_g$ be the group associated to $g\in\mathbb{M}$, and let $T^{(-1)}_{\Gamma_g}$ denote the normalized Rademacher sum attached to $\Gamma_g$. Duncan--Frenkel conjecture. T…

Let $e$ be an exotic $\mathbb{R}^{4}$ belonging to the DeMichelis–Freedman radial family, and let the foliated topological limit of general relativity (FTL of GR) on $e$ be evaluat…

Continuum spectral-triple conjecture. The Kasparov module

Continuum Kasparov-module conjecture. The infinite sequence

Complexifier conjecture. There exists a choice of complexifier giving a sequence $\phi^t=\{\phi_n^t\}$ of semi-classical states satisfying