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Cluster Algebras ProgramMonth: August 2012 Date: August 20--December 21 Name: Cluster Algebras Program Location: Mathematical Sciences Research Institute, Berkeley, California. DescriptionCluster algebras were conceived in the Spring of 2000 as a tool for studying dual canonical bases and total positivity in semisimple Lie groups. They are constructively defined commutative algebras with a distinguished set of generators (cluster variables) grouped into overlapping subsets (clusters) of fixed cardinality. Both the generators and the relations among them are not given from the outset, but are produced by an iterative process of successive mutations. The program will focus on links between cluster algebras and other areas, such as: polyhedral combinatorics; triangulations of surfaces; Y, Q, and T-systems; additive categorification via quiver representations; quivers with potentials and Donaldson-Thomas invariants; Lie theory and monoidal categorification; Poisson geometry and Teichmueller theory. Information
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