School of Mathematics & Statistics

Symplectic singularities

Though geometric objects, symplectic singularities play a crucial role in geometric representation theory. Their quantizations realise many of the most commonly studied algebras in geometric representation theory such as primitive quotients of enveloping algebras, W-algebras, rational Cherednik algebras or quantized Nakajima quiver varieties. The study of geometric properties of these singularities, such as their Poisson deformations or crepant resolutions, provides important information on the representation theory of their quantizations.