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)