Title: A glimpse into the world of cluster algebras

Date: 12/06/2016

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

Cluster algebras were introduced by Fomin and Zelevinsky to axiomatize a remarkable relation they observed among special coordinate systems on Lie groups. Since then, this same pattern has been discovered in many other algebras in many other contexts. This talk will explore the fundamental examples of this phenomenon, and demonstrate how the general definition unifies and generalizes these examples.
This naturally leads to the consideration of cluster algebras in the abstract, where many surprises await. One surprise is the existence of pathological cluster algebras, with such horrors as non-Noetherian singularities. I will survey the theory of `locally acyclic cluster algebras', a sub-class of cluster algebras which eliminates the horrible examples while containing all known well-behaved examples.