7 problems

Let $h$ range over the hinges of an $n$-dimensional triangulation. For each hinge, let $W_{\alpha}(h)$ be the holonomy around its dual Voronoi plaquette, let…

Let $g$ be a smooth metric, let $\theta$ be a tensor field with the regularity assumed in Theorem, and let $B$ belong to the test-tensor space $\mathring{\mathcal{B}}$. The quantit…

Diffeomorphism-invariance conjecture. QRC measures with $p=1$ should be diffeomorphism-invariant measures.

Large-$L$ approximation conjecture. For large $L$,

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 Kasner cosmology is a vacuum, homogeneous, anisotropic solution of the Einstein equations with topology $R\times T^3$, whose metric has Kasner exponents $p_1,p_2,p_3$ satisfyin…

Existence conjecture. Non-equihedral constant scalar curvature metrics exist in every conformal class.