Cluster Algebras + More

Reading Seminar 2025-2026

Information - Resources - Meetings

Information

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.

Resources

In progress / upcoming

  1. Tilting theory and cluster combinatorics by Aslak Bakke Buan, Bethany Rose Marsh, Markus Reineke, Idun Reiten, Gordana Todorov [link]
  2. Lectures on Matroids and Oriented Matroids by Victor Reiner [link]
  3. Totally nonnegative Grassmannian and Grassmann polytopes by Thomas Lam [link]
  4. ABHY Associahedra and Newton polytopes of F-polynomials for cluster algebras of simply laced finite type by Véronique Bazier-Matte, Nathan Chapelier-Laget, Guillaume Douville, Kaveh Mousavand, Hugh Thomas, and Emine Yıldırım [link]

Completed

  1. Cluster algebras from surfaces by Ralf Schiffler [link]
  2. Lectures on Representations of Quivers by Bill Crawley-Boevey [link]

Meetings

Upcoming

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