An introduction to cluster algebras

Cluster algebras are commutative algebras with a special combinatorial structure. They originated in Lie theory in the context of canonical bases and total positivity, but are now connected to a number of areas including combinatorics, representation theory, knot theory, integrable systems and algebraic geometry. In this talk, we give an overview of the theory and highlight a recent connection to the joint spectrum of representations of the symmetric group.Non UBCUnreviewedAuthor affiliation: University of ConnecticutFacult