ABSTRACT: Cluster algebras are commutative algebras of a special kind introduced by Sergey Fomin and myself in an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups. The main structural result of the theory so far is a classification of cluster algebras of finite type which turns out to be yet another instance of the Cartan - Killing classification. We shall discuss main structural properties of cluster algebras and the main ingredients of the proof of the classification theorem.

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For further information visit the Seminar web site at http://www.northeastern.edu/martsinkovsky/p/rtrt.html  or contact Alex Martsinkovsky <alexmart@neu.edu>