Cluster algebras: notes for 2004 IMCC (Chonju, Korea, August 2004)

Abstract

This is an expanded version of the notes for the two lectures at the 2004 International Mathematics Conference (Chonbuk National University, August 4-6, 2004). The first lecture discusses the origins of cluster algebras, with the focus on total positivity and geometry of double Bruhat cells in semisimple groups. The second lecture introduces cluster algebras and discusses some basic results, open questions and conjectures.

14 pages

References in corpus (7)

• Cluster ensembles, quantization and the dilogarithm
• Tilting theory and cluster combinatorics
• The tropical totally positive Grassmannian
• The Cube Recurrence
• Cluster algebras and Weil-Petersson forms
• Orbits of groups generated by transvections over $\FF_2$
• Simply-laced Coxeter groups and groups generated by symplectic transvections

Cited by in corpus (2)

• Cluster mutation via quiver representations
• Cluster Structure on Generalized Weyl Algebras