Introduction to cluster algebras, Khrystyna Serhiyenko (University of Kentucky), Lecture 3, 07/28/2024

Cluster algebras are a class of commutative rings with a good combinatorial structure. They were introduced by Fomin and Zelevinsky in 2002 to study total positivity and the canonical basis in Lie theory, but quickly developed into a very active research area with surprising connections to many other branches of mathematics and physics.

In this course, we will introduce cluster algebras and study their basic properties, including positivity and the Laurent phenomenon. We will also discuss two important classes of cluster algebras, namely those arising from surface triangulations and Grassmannian coordinate rings.