BIMSA > BIMSA Topology Seminar Persistence of directed graphs via Hochschild and reachability homology
Persistence of directed graphs via Hochschild and reachability homology
Organizers
Matthew Burfitt , Jingyan Li , Jie Wu
Speaker
Henri Riihimaki
Time
Thursday, November 27, 2025 2:00 PM - 3:00 PM
Venue
A3-4-101
Online
Zoom 928 682 9093 (BIMSA)
Abstract
There is currently an active interest in homotopy and homology theories in the world of graphs and directed graphs; discrete homotopy theory, magnitude homology and path homology are few prominent themes. Many of these also have incarnations in topological data analysis and persistent homology as tools for network analysis. We extend the use of Hochschild homology of directed graphs in persistence setting. We "lift" Hochschild homology to higher degrees via so called connectivity structures, of which I will present functorial examples. To get an efficiently computable pipeline we have to resort to non-functorial constructions. To remedy this leads to defining the reachability category of a directed graph, and associated persistent reachability homology. Our recent machine learning results on epilepsy detection show that this pipeline performs better than traditional simplicial homology of the directed flag complexes. This is a joint work with Luigi Caputi and Nicholas Meadows.