14 problems

Zeghib's conjecture. All compact quotients are standard.

Kaigorodov duality conjecture. For a string/M-theory on the Kaigorodov spaces, a compact manifold is dual to a conformal field theory in an infinitely boosted frame with constant m…

Let $d$ be the spacetime dimension. An asymptotically Anti-de Sitter spacetime is a spacetime that asymptotes to Anti-de Sitter space in $d$ dimensions, and let a conformal field t…

Anti-de Sitter (AdS) space is the solution of the vacuum Einstein equations with negative cosmological constant, with reflective boundary conditions imposed at the conformal bounda…

Let $W_0$ denote the universal cover of anti-de Sitter space, and let $Z$ be the invariant anti-de Sitter quantity appearing in the Gegenbauer kernels. For the relevant parameter…

Let anti-de Sitter space be a solution of the Einstein–Klein–Gordon system, and consider small perturbations of this solution arising from initial data. Bizoń–Rostworowski islands-…

In three-dimensional gravity with $\mu^2\ell^2=1$, one of the two central charges vanishes; this theory is called chiral gravity. Chiral gravity conjecture. Chiral gravity makes se…

Homogeneous Yang–Baxter deformations of anti-de Sitter space are associated with twists of the conformal algebra. Correspondence conjecture. Homogeneous Yang–Baxter deformations of…

In asymptotically anti-de Sitter gravity, consider the sets of non-collapsing solutions at finite amplitude and their behavior as the amplitude tends to zero. Stability island conj…

Let anti-de Sitter spacetime be the maximally symmetric solution of the vacuum Einstein equations with negative cosmological constant. Consider perturbations of anti-de Sitter spac…

Let $\operatorname{AdS}_3$ denote three-dimensional Anti-de Sitter space, and consider small smooth perturbations whose spatial dependence admits a radius of analyticity $\rho(t)$,…

Let $\phi_{[0]}(t,\mathbf{x})$ be the massless-graviton component of the gravitational wave, and let $\phi_2(t,\mathbf{x})$ denote the corresponding comparison field. For a functio…

Let anti-de Sitter space be perturbed by arbitrarily small generic perturbations, and consider the resulting nonlinear evolution of the spherically symmetric Einstein–massless-scal…

Brink–Metsaev–Vasiliev conjecture. An irreducible massless field in $AdS_d$ decomposes in the flat limit into a collection of irreducible massless fields in Minkowski spacetime.