143 citations · 581 across the 51 of their papers we have counts for
16 papers · 1 filter
Evasion paths by homotopy limits
Gunnar Carlsson, Benjamin Filippenko, Wyatt Mackey
The evasion paths problem asks when a dynamically changing space can be navigated: imagine guards are patrolling a region, for instance, and we need to stay outside their view. We…
The space of sections of a smooth function
Gunnar Carlsson, Benjamin Filippenko
Given a compact manifold with boundary and a submersion whose restriction to the boundary of has isolated critical points with distinct critical value…
Persistent Homology and Applied Homotopy Theory
Gunnar Carlsson
This paper is a survey of persistent homology, primarily as it is used in topological data analysis. It includes the theory of persistence modules, as well as stability theorems fo…
Persistent and Zigzag Homology: A Matrix Factorization Viewpoint
Gunnar Carlsson, Anjan Dwaraknath, Bradley J. Nelson
Over the past two decades, topological data analysis has emerged as a field of applied mathematics with new applications and algorithmic developments appearing rapidly. Two fundame…
Persistent homology of the sum metric
Gunnar Carlsson, Benjamin Filippenko
Given finite metric spaces and , we investigate the persistent homology of the Cartesian product equipped with the sum metric $…
Parametrized Homology via Zigzag Persistence
Gunnar Carlsson, Vin de Silva, Sara Kalisnik +1
This paper develops the idea of homology for 1-parameter families of topological spaces. We express parametrized homology as a collection of real intervals with each corresponding…