Introduction to Cluster Algebras and Their Types - Lecture 1

Explore the foundations of cluster algebras in this comprehensive lecture by Jacob Matherne. Delve into the abstract combinatoro-algebraic concept introduced by S. Fomin and A. Zelevinsky in 2000. Learn about cluster variables, mutations, and their distribution across clusters. Discover how cluster algebras relate to various mathematical areas, including Grassmannians, Schubert varieties, and homogeneous spaces. Gain insights into the connections between cluster algebras and fields such as string theory, Poisson geometry, algebraic geometry, combinatorics, representation theory, and Teichmuller theory. Follow along as the lecture covers key topics including quivers, mutations, exchange graphs, and fundamental definitions. Ideal for young researchers, postdoctoral fellows, and graduate students interested in this unifying theme across multiple mathematical disciplines.

Introduction
Outline
Quiver
Mutation
Mutations
Ato quiver
Exchange graph
Exercises
Definition
Observations