8 problems

Hypercube spectral conjecture. The simple random walk $P^s$ is unstable, all eigenvalues of the corresponding linearized curvature-flow matrix are real, and

Complete-graph spectral conjecture. The simple random walk $P^s$ is asymptotically stable, and the eigenvalues of $DF(P^s)$ are

Octahedral curvature-flow conjecture. The normalized curvature flow on the octahedron converges to a limit described by the stated classification of totally degenerate non-lazy cur…

Non-degenerate-subgraph conjecture. The subgraph $G_W$ coincides with the subgraph of $G$ induced by $W$, all transition rates from $W$ to $V\setminus W$ are zero, and $(G_W,P_W)$…

Curvature flow convergence conjecture. The curvature flow converges for any initial condition $(G,P_0)$, that is, $(G,P(t))$ has a well-defined limit

Let $\mathcal M$ be a cone and let a closed curve on $\mathcal M$ be not homotopic to a point on $\mathcal M$. Elliott's conjecture. Under geodesic curvature flow, the curve will c…

Let $\hat{\Omega}$ be curvature flow on embedded graphs in $\mathbb{R}^n$, rescaled so that a characteristic length scale remains equal to one, and let $\mathcal{G}^n$ be the class…

Let $\mathcal{G}^n$ be the class of embedded graphs in $\mathbb{R}^n$. Suppose $G\in\mathcal{G}^n$ is an embedded graph with a homogeneous topological cloth and a well-defined time…