Welcome to MATH 292: Cluster Algebras and Cluster Varieties

Location: Science Ctr 411 (FAS)
Meeting Time: Tue, Thurs: 9-10:15am

Lecture note:

There is another cluster algebras class in MIT on MWF 1-2 pm at Room 2-147. People who are interested in cluster algebras are highly recommended to attend!
MIT class website

Reference:

References for cluster algebras:

References for cluster varieties:

  • M. Gross, P. Hacking, and S. Keel. Birational geometry of cluster algebras.Algebraic Geometry,2(2):137-175, 2015
  • Gross, M., Hacking, P., Keel, S. and Kontsevich, M., 2018. Canonical bases for cluster algebras. Journal of the American Mathematical Society, 31(2), pp.497-608.
  • Fulton, W., 1993. Introduction to toric varieties (No. 131). Princeton University Press.
  • M. Gross. Tropical geometry and mirror symmetry, volume 114 of CBMS Regional Conference Seriesin Mathematics. Published for the Conference Board of the Mathematical Sciences, Washington,DC, 2011

References for quiver representations:

  • Keller, B., 2012. Cluster algebras and derived categories. arXiv preprint arXiv:1202.4161.
  • Schiffler, Ralf. Quiver representations. Berlin: Springer, 2014.
  • Derksen, Harm, and Jerzy Weyman. An Introduction to Quiver Representations. Vol. 184. American Mathematical Soc., 2017.

Schedule of the class:

Sept 5: Definition of cluster algebras without frozen variables
Sept 11: Cluster algebras with frozen variables, triangulation of polygon
Sept 13: Cone and fan in toric geometry
Sept 18: Defining cluster varieties by gluing tori
Sept 20: Relating the A and X cluster varieties
Sept 25: Revision
Sept 27: Continue revision, Langlands duality, Y-system
Oct 2: c, g vectors, F polynomials, 'Tomoki Nakanishi and Andrei Zelevinsky. On tropical dualities in cluster algebras'
Oct 4: Cluster algebras from quivers
Oct 9: Caldero-Chapton formula
Oct 11: Simple, projective and injective representations
Oct 16: Auslander-Reiten theory
Oct 18: Cluster category
Oct 23: Guest lecture - Tim Magee: Crash course in toric geometry
Oct 25: Guest lecture - Tim Magee
Oct 30: Scattering diagram
Nov 1: Scattering diagram continue
Nov 6: Computation of scattering diagram
Nov 8: NO Class!
Nov 13: Mutation invariance of the scattering diagram
Nov 15: NO Class!
Nov 20: Broken lines and theta functions
Nov 26: Theta functions (continued)