The goal of this seminar is to define cluster algebras (at least in a particular setting) and show its connections to other areas of mathematics. We begin with cluster algebras from surfaces and then study representations of quivers. The representations of quivers allows us to read the famous BMRRT paper that links quiver representations to cluster algebras by constructing a cluster category. After quiver representations we will bring matroids into the picture. We will then explore the connection of cluster algebras to polytopes (Grassmannians). Using our combined knowledge thus far, we will look at the connection between quiver reprsentations and some of the possible polytopes and matroids associated to a cluster algebra. Time permitting at the end of the Spring 2026 term, we will loop back to surfaces and connect them to the cluster categories from quiver representaitons.
The Cluster Algebras + More reading seminar is organized by Daisie Rock.
Unless noted otherwise below, we meet on Wednesdays from 12:30 to 13:30 in B02.18.
Sections 6 and 7 in reference [5].
Sections 8 and 9 in reference [5].
Sections 15 and 16 in reference [5].
Sections 17 and 18 in reference [5].
Section 2 in reference [6].
Sections 3 and 4 in reference [7].
Section 5 in reference [7].
Reference [8].
Topic TBD.
Conclusion of Seminar.
Party! 🎉
Introductions, orientation. Begin Chapter 1 in [1].
Finish Chapter 1 in [1].
Chapter 2 in [1].
Begin Chapter 3 in [1].
Finish Chapter 3 in [1].
Chapter 4 in [1].
Reorientation. Section 1 in [2].
Organization. Sections 2 and 3 in [2].
Sections 4 and 5 in [2].
Sections 6 and 7 in [2].
Introduction and Section 1 in [3].
Some more details from [3].
Reorganization
Statrt lecture 1 from reference [4].
Finish lecture 1 from reference [4]. Start lecture 2 from reference [4].
Finish lecture 2 from reference [4].
Meeting cancelled due to illnesses.
Start lecture 3 from reference [4].
Finish lecture 3 from reference [4].
Sections 2 and 3 in reference [5].
Sections 4 and 5 in reference [5] by Bruno Jaoquín Giordano
Bonus lecture "Dimer model on a hexagon (introduction)" by Arno Kuijlaars.