Contemporary Mathematics- Cluster Algebras, Hall Algebras and Representation Theory

Proceedings from an AMS Spring Central Session on Cluster Algebras, Hall Algebras, and Representation Theory reveal innovative studies in algebra and representation theories. Explore research on canonical bases, queer Lie superalgebras, radical Weyl algebras, and topological data analysis applications in Hall algebras. This volume contains the proceedings of the AMS Spring Central Sectional Meeting Special Session on Cluster Algebras, Hall Algebras, and Representation Theory, held at the University of Wisconsin-Milwaukee, WI, from April 20-21, 2024. This volume contains original research articles and survey papers in algebra and representation theory. The contributions address topics including canonical bases and their duals in both cluster algebra and representation-theoretic contexts, representation theory related to the queer Lie superalgebra $\mathbf{Q}(2)$, radical Weyl algebras, and finite-dimensional algebras. The volume also includes a study of Hall algebras under edge contractions allowing edge loops, as well as a survey on applications of representation theory to topological data analysis.