794 citations · 879 across the 24 of their papers we have counts for
28 papers
Harder-Narasimhan Filtrations of Persistence Modules
Marc Fersztand, Emile Jacquard, Vidit Nanda +1
The Harder-Narasimhan type of a quiver representation is a discrete invariant parameterised by a real-valued function (called a central charge) defined on the vertices of the quive…
Multiscale topology classifies and quantifies cell types in subcellular spatial transcriptomics
Katherine Benjamin, Aneesha Bhandari, Zhouchun Shang +7
Spatial transcriptomics has the potential to transform our understanding of RNA expression in tissues. Classical array-based technologies produce multiple-cell-scale measurements r…
Homology stability for asymptotic monopole moduli spaces
Martin Palmer, Ulrike Tillmann
We prove homological stability for two different flavours of asymptotic monopole moduli spaces, namely moduli spaces of framed Dirac monopoles and moduli spaces of ideal monopoles.…
Harder-Narasimhan Filtrations and Zigzag Persistence
Marc Fersztand, Vidit Nanda, Ulrike Tillmann
We introduce a sheaf-theoretic stability condition for finite acyclic quivers. Our main result establishes that for representations of affine type quivers,…
Grounded persistent path homology: a stable, topological descriptor for weighted digraphs
Thomas Chaplin, Heather A. Harrington, Ulrike Tillmann
Weighted digraphs are used to model a variety of natural systems and can exhibit interesting structure across a range of scales. In order to understand and compare these systems, w…
Homology of homologous knotted proteins
Katherine Benjamin, Lamisah Mukta, Gabriel Moryoussef +4
Quantification and classification of protein structures, such as knotted proteins, often requires noise-free and complete data. Here we develop a mathematical pipeline that systema…