Ezra Miller, Duke University

Bar codes for quiver representations

At the turn of the millenium, algebraic geometers developing combinatorics to describe cohomology classes associated to representations of quivers happened upon the same "bar codes" that the nascent applied topology community was independently inventing for the purpose of summarizing topological information extracted from data via persistent homology. This is a historical overview of multiple views on bar codes, drawing connections to topology, representation theory, algebraic geometry, combinatorics, and commutative algebra.