9 problems

A spin foam is a two-dimensional cell complex whose faces are labelled by group representations and whose edges are labelled by intertwiners. The Riemannian Barrett--Crane model is…

Gluing conjecture. The continuum amplitudes satisfy

Let $\mathfrak{J}_{\text{EL}}$ be the set of equilateral configurations and let $\mathfrak{J}_{\text{EL}}^{S}$ denote the subset of configurations for which the relevant $6J$-symbo…

Consider four-dimensional Regge-type discretizations of gravity, in which triangle areas and suitable dihedral angles are used as independent variables. These models implement simp…

The $SU(2)$ $6j$ symbol is considered in the large-spin asymptotic regime, with spins $j_i$ and corresponding dihedral angles $\theta_i$. Let … The coefficients $A_n$ denote consec…

Let $z_1,z_2,\ldots$ be the coefficients governing the large-$N$ perturbative corrections, and suppose that for some $p$ one has … Let…

Fix a positive integer $n$ and a three-dimensional manifold $M$. For a triangulation $\Delta$ of $M$, let $K$ be the number of tetrahedra in an $n$-grasping $\mathcal G$, and let…

Non-vanishing second-order coefficient conjecture. The value of $z_2$ is non-zero and is independent of the triangulation $\Delta$ and the manifold $M$. This conjecture concerns th…

In the dilute gas expansion, let a perturbative configuration be a configuration obtained by inserting perturbations into a triangulation, and fix its perturbation-theory order. Fi…