8 citations · 14 across the 4 of their papers we have counts for
7 papers
A Lattice-Theoretic Perspective on the Persistence Map
Brendan Mallery, Adélie Garin, Justin Curry
We provide a naturally isomorphic description of the persistence map from merge trees to barcodes in terms of a monotone map from the partition lattice to the subset lattice. Our d…
From Trees to Barcodes and Back Again II: Combinatorial and Probabilistic Aspects of a Topological Inverse Problem
Justin Curry, Jordan DeSha, Adélie Garin +3
In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered con…
Decorated Merge Trees for Persistent Topology
Justin Curry, Haibin Hang, Washington Mio +2
This paper introduces decorated merge trees (DMTs) as a novel invariant for persistent spaces. DMTs combine both and information into a single data structure that disti…
A Relative Theory of Interleavings
Magnus Bakke Botnan, Justin Curry, Elizabeth Munch
The interleaving distance, although originally developed for persistent homology, has been generalized to measure the distance between functors modeled on many posets or even small…
Moduli Spaces of Morse Functions for Persistence
Michael J. Catanzaro, Justin Curry, Brittany Terese Fasy +5
We consider different notions of equivalence for Morse functions on the sphere in the context of persistent homology, and introduce new invariants to study these equivalence classe…
Functors on Posets Left Kan Extend to Cosheaves: an Erratum
Justin Curry
In this note we give a self-contained proof of a fundamental statement in the study of cosheaves over a poset. Specifically, if a functor has domain a poset and co-domain a co-comp…