Mathematical Research
Persistence Module and Quiver Representation
The algebraic structure of persistent homology was originally understood via modules on a polynomial ring with one variable. Recent theoretical progress generalizes persistent homology as representations on quivers (more generally on associative algebras). This extension enables us to apply TDA to much wider problems, e.g., spatiotemporal analysis, multi- parameter persistence, etc.
literatureE. Escolar and Y. Hiraoka. Persistence Modules on Commutative Ladders of Finite Type.
Discrete & Computational Geometry, 55 (2016), 100-157.
H. Asashiba, E.G. Escolar, Y. Hiraoka, H. Takeuchi. Matrix Method for Persistence Modules on Commutative Ladders of Finite Type.
