Simon Crawford, Department of Pure Mathematics, University of Waterloo
"Deformations of Quantum Kleinian Singularities"
In recent work, Chan--Kirkman--Walton--Zhang defined a family of noncommutative rings which they call quantum Kleinian singularities, which may be thought of as noncommutative analogues of (the coordinate rings of) Kleinian singularities. Crawley-Boevey and Holland showed how to deform Kleinian singularities, and in this talk I will show that the same is possible for quantum Kleinian singularities. I will discuss some of the properties of these deformations, and compare the behaviours of the deformations in the quantum and non-quantum cases. I will also define a family of algebras called deformed quantum preprojective algebras, and show that these are Morita equivalent to deformed quantum Kleinian singularities.