37 citations · 56 across the 10 of their papers we have counts for
14 papers
Homology-based Morphometry of Brain Atrophy: Methods and Applications
Donato Quiccione, Mariam Pirashvili, Nathan Broomhead +1
Understanding the structure of the brain, and how it changes with time and disease, is a core goal of structural neuroimaging. Contemporary approaches to structural brain analysis…
An isometry theorem for persistent homology of circle-valued functions
Nathan Broomhead, Mariam Pirashvili
This paper explores persistence modules for circle-valued functions, presenting a new extension of the interleaving and bottleneck distances in this setting. We propose a natural g…
Simple tilts of length hearts and simple-minded mutation
Nathan Broomhead, Raquel Coelho Simoes, David Pauksztello +1
We characterise when a simple Happel-Reiten-Smalo tilt of a length heart is again a length heart in terms of approximation theory and the existence of a stability condition with a…
The heart fan of an abelian category
Nathan Broomhead, David Pauksztello, David Ploog +1
We apply convex geometry (cones, fans) to homological input (abelian categories, hearts of bounded t-structures) to construct a new invariant of an abelian category, its heart fan.…
Partial compactification of stability manifolds via massless semistable objects
Nathan Broomhead, David Pauksztello, David Ploog +1
We introduce two extensions of the space of Bridgeland stability conditions of a triangulated category. First we consider lax stability conditions where semistable objects are allo…
Thick Subcategories of Discrete Derived Categories
Nathan T Broomhead
We classify the thick subcategories of discrete derived categories. To do this we introduce certain generating sets called arc-collections which correspond to configurations of non…