6 problems

Bjerkevik's conjecture. On persistence modules of bounded pointwise dimension, the pruning distance is stable and Lipschitz equivalent to the interleaving distance. More precisely,…

Let $c\geq 1$ be an odd integer, and let $(P,Q)$ be a compatible-inclusion problem, with its $c$-weakening defined by retaining directed edges represented by paths of length at mos…

Let $M$ and $N$ be upset decomposable persistence modules, where an upset decomposable module is a direct sum of upset modules. The upset matching conjecture. There is a constant…

Let $M$ and $N$ be persistence modules that are $\epsilon$-interleaved, with $\epsilon\geq 0$. Let … Here $B(M)$ is the relevant neighborhood of $M$ defined in the paper, and an…

Cubic Betti-number bound. We have

Let $n\geq 1$ be fixed, and let $d^p_{\mathcal{M}}$ and $d^p_{\mathcal I}$ denote the corresponding distances on finitely presented $n$-parameter persistence modules, with…