International Conference and Workshop on Cluster Algebras and Related Topics

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This proposal aims to support the International Conference and Workshop on Cluster Algebras and Related Topics, to be held in Mexico (Morelia and Mexico City) in December 2008. These activities will be cofunded by the Algebra, Number Theory, and Combinatorics Program and the Office of International Science and Engineering.Cluster algebras provide a unifying algebraic and combinatorial framework for an impressive variety of phenomena in settings as diverse as quiver representations, Teichmuller theory, classical and non-commutative algebraic geometry, tropical calculus, Poisson geometry, Lie theory, and combinatorics of fans and polytopes. The conference and workshop bring together both young and established researchers working on all major lines of inquiry involving cluster algebras and objects derived from them (cluster categories, cluster varieties, quivers with potentials, etc.), with the goal of cross-fertilization and exchange of ideas between the different domains of application. The conference and workshop attracted approximately 100 participants, including a large number of young researchers, most of them from the US and Latin America. The format of the event---a week of introductory mini-courses followed by another week of research talks---is designed to introduce young mathematicians into this exciting field, and facilitate exchange of ideas between established researchers with different mathematical backgrounds.