3 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…

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…

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 $X_i$…