9 problems

Lifted toroidal-cycle conjecture. All cycles in $K$ which are trivial in $G$ can be written in terms of lifts of toroidal cycles.

Root-of-unity conjecture. The eigenvalues of $M_i$ must be roots of unity.

Total-persistence conjecture. The extremal filtrations described in Section 4 achieve the maximal total persistence over any edgewise filtration of flag complexes in homology degre…

Polynomial relationship conjecture. For any triply-periodic minimal surface $M$, there exists a polynomial $P \in \mathbb{R}[t]$ such that

Left-skewed Gumbel conjecture. The universal limiting distribution is

Let $\mathbb{S}$ be a sampling model in the class $\mathcal{U}$. For a complex type $\mathcal{T}$ and homological degree $k\geq 1$, let $\mathcal{L}_n$ be the empirical measure of…

Steinhaus–Čech equivalence conjecture. The Čech filtration constructed from $X$ is isomorphic to the cover filtration on $X$ constructed from $\check{C}_R(X)$.

Let $X$ be a topological space and let $f:X\to[0,\infty)$ be a continuous function. For $p\in(0,\infty]$, let $\operatorname{{\bf ucat}}^p(f)$ denote the minimum number of unimodal…

Interleaving optimality conjecture. For any field $k$ and $i\in\mathbb Z_{\geq 0}$, $d_I$ is $i$-optimal.