Title: An Introduction to Cluster Algebras

Abstract: Cluster algebras are commutative algebras with a special combinatorial structure. They were introduced in 2002 by Sergey Fomin and Andrei Zelevinsky in the context of canonical bases in Lie theory and have quickly developed deep connections to other areas of mathematics and physics, including combinatorics, representation theory, hyperbolic geometry, elementary number theory, knot theory and many more. In this talk, I will explain the combinatorial structure of cluster algebras and give an overview of some of the connections.