Iacopo Nonis (University of Leeds) – An Introduction to Cluster Algebras and Cluster Categories

Cluster algebras were introduced in 2002 by Fomin and Zelevinsky in the context of Lie theory as commutative algebras defined combinatorially through an iterated mutation process. Since then, they have appeared in many areas of mathematics, including mathematical physics, algebraic combinatorics, and algebraic geometry. Buan, Marsh, Reineke, Reiten, and Todorov later introduced the cluster category, providing a natural categorical model for the combinatorics of cluster algebras. This talk will be a gentle, pictorial introduction to cluster algebras and their categorification via cluster categories, illustrated with plenty of examples.