Friezes, Syzygies, and Connections to Cluster Algebras

Cluster algebras were introduced by Fomin and Zelevinsky in 2001, and since then there have been numerous connections established to seemingly unrelated areas of mathematics and theoretical physics. Cluster algebras provide an intricate combinatorial framework that describes various mathematical phenomena. They allow one to build bridges between the different research areas that lead to some fascinating discoveries in the past two decades. The proposed project is in a highly active research area at the intersection of algebra and combinatorics with close connections to cluster algebras. The PI intends to answer fundamental questions about SL_k tilings and friezes as well as category of syzygies of dimer algebras. The main techniques involve the development and use of combinatorial models as well as their representation theoretic interpretations.