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Quiver representations and persistent homology

Abstract

Topological data analysis via persistent homology has been an active area of research over the past 20 years. In short, it probes data using tools from algebraic topology. Surprisingly, this approach has not only made a significant impact at the level of applications, but also found connections to other areas of mathematics at the theoretical level. Here we mainly introduce the relationship between persistent homology and quiver representation theory, following Steve Y. Oudot.