Combinatorial surface models for cluster algebras and cluster categories - Lecture 1

Surface combinatorics have been instrumental in describing algebraic structures such as cluster algebras and cluster categories, gentle algebras, etc. In this course, I will show how triangulations give rise to cluster algebras and to cluster categories. We will also study the combinatorial approach to Grassmannian cluster algebras and cluster categories. Time permitted, we will also discuss how tilings of surfaces give gentle algebras and module categories.