An introduction to cluster algebras I

Abstract: Cluster algebras are commutative algebras equipped with remarkable combinatorial structures. Since its inception in 2000, the theory of cluster algebras has found numerous exciting applications in mathematics and physics. This series of lectures aim to provide an accessible introduction to cluster algebras for a general mathematical audience. In particular, we will investigate the following topics.

Lecture 1: Cluster algebras of rank 2: positive Laurent Phenomenon and greedy bases $\newline$ This lecture will focus on cluster algebras of rank 2. Using elementary combinatorial tools, we will prove the positive Laurent Phenomenon and construct greedy bases for cluster algebras of rank 2.

algebraic geometrycombinatoricsdifferential geometrygeometric topologyquantum algebrarepresentation theorysymplectic geometry

Audience: researchers in the topic

Legendrians, Cluster algebras, and Mirror symmetry

Series comments: Schedule
School: January 4–8, 2021
Conference: January 11–15, 2021