7 problems

Let $(X,d,A)$ be a separable metric pair, let $E$ be a complex Banach space, and let $f\colon K(X,A)\to E$ be Lipschitz. Lipschitz extension spectral synthesis conjecture. Every su…

Geodesic-space conjecture. Under mild assumptions, the space of persistence diagrams with the PPD induces a geodesic space structure that is computationally tractable and topologic…

A persistence diagram records homology classes by their birth and death times; for a class, its persistence ratio is the death-to-birth ratio. The noise consists of the features in…

Let $X$) be a compact Riemannian manifold of dimension $d$, and let $f\in C^{r+\alpha}(X)$, with the persistence quantity $\Pers_p(H_k(X,f))$ defined as the $p$-persistence of the…

Distance-threshold conjecture. The interactions between points in a persistence diagram rely on distance thresholds that are considered to be appropriate.

Let $\mathcal D_\infty=\varinjlim \mathcal D_n$, where each $\mathcal D_n$ is endowed with a Wasserstein metric; one may also consider the Wasserstein $p,q$ metric. Wasserstein asy…

Let $X_1,\ldots,X_m$ be persistence diagrams with only finitely many off-diagonal points. For a persistence diagram $Y$, define … For each optimal pairing from $W=\{w_j\}$ to $X_i$…