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Description:

A cluster algebra is a kind of commutative algebra with a distinguished set of generators organized into overlapping finite subsets called clusters. Though the definition of a cluster algebra seems strange at first encounter, these algebras appear naturally in many areas of mathematics. In the two decades since they were first discovered, cluster algebras have been used to study topics as seemingly different as Grassmannians, Teichmüller spaces, and the representation theory of finite-dimensional algebras. This course will give an introduction to cluster algebras, focusing on examples from several different areas of mathematics.

Prerequisite:

Basic algebra and topology