10 problems

Marckert–Mokkadem conjecture. The scaling limit of random quadrangulations should be given by the Brownian map.

Angel–Kolesnik–Miermont's conjecture.

Miermont's conjecture. There exist $k$-star points for $1\leq k\leq 4$, and there do not exist $k$-star points for $k\geq 6$.

A planar map is an embedding of a finite connected graph into the two-dimensional sphere, considered up to orientation-preserving homeomorphisms. The Brownian map is the random met…

Let $\mathcal{C}_n$ be a circle-packing embedding of a uniformly distributed simple triangulation with $n$ faces, let $V(\mathcal{C}_n)\subset\mathbb{S}^2$ be its vertex set, and l…

Canonical-embedding conjecture. This canonical embedding would be related to the approach to two-dimensional quantum gravity developed by Duplantier and Sheffield via the Gaussian…

Le Gall–Miermont's subcritical gasket conjecture. There exists $h_c(N)$ such that, if $h<h_c(N)$, the scaling limits of random planar decorated triangulations and of their gaskets…

Universality conjecture for p-angulations. The scaling limit of uniformly distributed $p$-angulations with $n$ faces, when $n$ tends to infinity (or, equivalently, when the number…

Let $p$ be a positive integer, and let $({\bf m}_\infty,D)$ be a Brownian map obtained as a subsequential Gromov–Hausdorff limit of rescaled uniform $2p$-angulations, with the subs…

The Brownian map is the random compact metric space obtained as a scaling limit of rescaled random planar maps. Universality conjecture. The Brownian map should be the universal sc…