The goal of this seminar was to define cluster algebras (at least in a particular setting) and show its connections to other areas of mathematics. We began 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 brought matroids into the picture. We explored the connection of cluster algebras to polytopes (Grassmannians). We ended the seminar with an overview of three papers that tied multiple concepts together: [7], [8], and [9].
The Cluster Algebras + More reading seminar was organized by Daisie Rock.
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].
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.
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].