Cluster algebras were conceived by Fomin and Zelevinsky (1) in the spring of 2000 as a tool for studying dual canonical bases and total positivity in semisimple Lie groups. However, the theory of cluster algebras has since taken on a life of its own, as connections and applications have been discovered in diverse areas of mathematics, including representation theory of quivers and finite dimensional algebras, cf., for example, refs. 2–15; Poisson geometry (16– 19); Teichmüller theory (20–24); string theory (25–31); discrete dynamical systems and integrability (6, 32–38); and combinatorics (39–47).
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