Computable Invariants of Quiver Representations

Over the past decade, topological data analysis (TDA) has emerged as a powerful tool for extracting structure from complex data. While the classical theory of TDA, centered on one-parameter persistence, is well understood and computationally effective, many real-world data sources naturally lead to generalizations with significantly more intricate algebraic structure. At its core, this brings TDA into the realm of quiver representation theory. This workshop aims to advance both the theoretical and computational foundations of quiver representations motivated by TDA. Key goals include: (1) developing new computational methods and software tools for structured quiver representations; (2) furthering the theory of representations over continuous indexing categories, informed by insights from TDA; and (3) exploring the role of cluster categories at the interface of TDA and representation theory. Through tutorials, invited talks, and problem-driven working groups, the workshop seeks to spark lasting interdisciplinary collaborations and produce tangible theoretical and computational outcomes.