Doctor of Philosophy (PhD)
This dissertation describes a general setting for dimer models on cylinders over Dynkin diagrams which in type A reduces to the well-studied case of dimer models on a disc. We prove that all Berenstein--Fomin--Zelevinsky quivers for Schubert cells in a symmetric Kac--Moody algebra give rise to dimer models on the cylinder over the corresponding Dynkin diagram. We also give an independent proof of a result of Buan, Iyama, Reiten and Smith that the corresponding superpotentials are rigid using the dimer model structure of the quivers.
Kulkarni, Maitreyee Chandramohan, "Dimers on Cylinders over Dynkin Diagrams and Cluster Algebras" (2018). LSU Doctoral Dissertations. 4642.