The Universal $\ell^p$-Metric on Merge Trees

no code implementations • 22 Dec 2021 • Robert Cardona, Justin Curry, Tung Lam, Michael Lesnick

Adapting a definition given by Bjerkevik and Lesnick for multiparameter persistence modules, we introduce an $\ell^p$-type extension of the interleaving distance on merge trees.

Discrete Morse theory for computing cellular sheaf cohomology

1 code implementation • 23 Dec 2013 • Justin Curry, Robert Ghrist, Vidit Nanda

Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing persistent homology.

Algebraic Topology 55-04

Sheaves, Cosheaves and Applications

3 code implementations • 13 Mar 2013 • Justin Curry

Inspired to provide fast algorithms for persistence, we prove that the derived category of cellular sheaves over a 1D cell complex is equivalent to a category of graded sheaves.

Algebraic Topology Representation Theory