7 problems

Let $T$ be a merge tree, and let a path be a 1-dimensional simplicial complex with no cycles. A discrete Morse function on a path induces a merge tree by filtering the path through…

Bounded barcode-chain conjecture. There exists a number $M(n)$ such that for any $y_0,y_1\in\mathrm{MT}_n$, there exist $x_0,\ldots,x_k$ with $k<M(n)$, $y_0=x_0$, and $y_1=x_1$ sat…

Restricted interleaving metric conjecture. When $n=1,2$,

Let an appropriate higher-dimensional analogue of a merge tree be given, and consider the authors' algorithm for finding cancellations of critical cells using generalized merge tre…

A discrete Morse function (dMf) is a function on a graph satisfying the discrete Morse conditions; an Ml tree and an Mo tree are the merge-tree constructions associated with the un…

Branching-tree non-realizability conjecture. If $T$ contains a vertex with degree greater than $2$, then there exists a merge tree that cannot be realized by any discrete Morse fun…

Bottleneck–interleaving intrinsic distance conjecture. The intrinsic distance $\hat{d}_B$ induced by $d_B$ is equivalent to $\hat{d}_I$ (and hence to $d_I$).