6 problems

Directional combinatorial curvature conjecture. This type of curvature information is encoded in direction-dependent combinatorial quantities of the three-cells: any statistically…

Let a polytope be resistance-positive when its resistance curvature is positive at every vertex. Finiteness conjecture for resistance-positive simple 3-polytopes. There are finitel…

Let $P$ be a polytope, and call it Forman–Ricci-positive when its Forman–Ricci curvature satisfies $\kappa_F(e)>0$ for every edge $e$. Finiteness conjecture for Forman–Ricci-positi…

Let $\Omega$ be a finite unweighted graph and consider the stochastic matrix $P$ associated with the simple random walk on this graph, $\tilde{P} = \frac{P+I}{2}$ associated to the…

Let $K_n$ be a complete graph with an even number of vertices, and let the action be the sum of the edge curvatures. A perfect-matching minimum-action conjecture states that the mi…

Let a triangle or square lattice graph be equipped with edge lengths, and consider the action obtained by summing the Ollivier-Ricci curvatures over its edges. The maximum-action c…