Cluster Structures in the North II
Date:
A short meeting gathering the experts in cluster theory in the North of England.
I gave the following talk:
Finite type LP cluster structures
Laurent phenomenon (LP) algebras are one possible extension of cluster algebras introduced by Thomas Lam and Pavlo Pylyavskyy. In this framework a seed may have arbitrary irreducible exchange polynomials, providing a substantial course of new examples of cluster structures. However, owing to their complexity, understanding when these cluster structures are of finite type is a very difficult problem in general. In this talk I will introduce these algebras, their basic properties, and some prominent examples of finite type LP cluster structures. In addition, we will discuss some progress on a conjecture of Lam and Pylyavskyy, and demonstrate a computer-assisted classification result.