Location: Science Ctr 411 (FAS)
Meeting Time: Tue, Thurs: 9-10:15am
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:
- Fomin, Williams, and Zelevinsky, Introduction to cluster algebras. Chapters 1-3.
- Fomin, Williams, and Zelevinsky, Introduction to cluster algebras. Chapters 4-5.
- Williams, Cluster algebras: an introduction.
- Fomin and Zelevinsky, Cluster algebras: Notes for the CDM-03 conferences, International Press, 2004.
- Cluster Algebras Portal
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 variablesSept 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)