Seminars

Description

This will be an informal learning seminar on cluster algebras, with weekly expository talks given by participants.

Meetings: Tuesdays 11:10am-12pm in Evans 891 beginning January 28.

References

Introduction to cluster algebras by Fomin, Williams, and Zelevinsky:

• Chapters 1-3 

• Chapters 4-5 

• Chapter 6 

• Chapter 7 

Y-systems and generalized associahedra by Fomin and Zelevinsky. Annals of Math. (2003)

Cluster categories survey by Reiten

Total positivity, Grassmannians, and networks by Postnikov

Braid variety cluster structures by Galashin, Lam, Sherman-Bennett, and Speyer

Weekly schedule

• 1/28: Christian Gaetz: Organization and short overview

• 2/4: Christian Gaetz: Cluster algebras basics [FWZ 3.1 & 3.2]

• 2/11: Lizzie Pratt: An off-the-cuff introduction to the amplituhedron

• 2/18: Xiangru Zeng: The Laurent Phenomenon [FWZ 3.3]

• 2/25: Cameron Chang: Cluster structure for Gr(2,n) [FWZ 1.2 & 5.3]

• 3/4: John Lentfer: Zamolodchikov periodicity, generalized associahedra and Catalan numbers ["Y-systems and generalized associahedra"]

• 3/11: John Lentfer: Zamolodchikov periodicity, generalized associahedra and Catalan numbers (continued)

• 3/18: Nicolle Gonzalez: Quiver representations and cluster categories [see Cluster categories survey by Reiten]

• 4/1: Nicolle Gonzalez: Quiver representations and cluster categories (continued)

• 4/8: Pranav Enugandla: Applications of cluster categories

• 4/15: Kaizhe Shen and Christian Gaetz: Plabic graphs, Le diagrams, etc [see Postnikov's paper and FWZ Ch. 7]

• 4/22: Soyeon Kim: Cluster structure for Gr(k,n) and positroid varieties

• 4/29: Melissa Sherman-Bennett: 3D plabic graphs and the cluster structure on braid varieties [see paper of G, L, S-B, S]