3 papers
math.AT2026
An Algebraic Introduction to Persistence
Ulrich Bauer, Thomas Brüstle, Luis Scoccola
We introduce persistence with an emphasis on its algebraic foundations, using the representation theory of posets. Linear representations of posets arise in several areas of mathem…
math.RT2025
Counts and end-curves in two-parameter persistence
Thomas Brüstle, Steve Oudot, Luis Scoccola +1
Given a finite dimensional, bigraded module over the polynomial ring in two variables, we define its two-parameter count, a natural number, and its end-curves, a set of plane curve…
math.RT2024
Decomposing zero-dimensional persistent homology over rooted tree quivers
Riju Bindua, Thomas Brüstle, Luis Scoccola
Given a functor from any category into the category of topological spaces, one obtains a linear representation of the category by post-composing the given functor with a homology f…