School of Mathematics & Statistics

Symplectic singularities

Symplectic singularities lie at the interface of algebraic geometry, symplectic geometry and geometric representation theory. This rich class of singularities includes many commonly studied examples in algebraic geometry such as the famous Kleinian singularities. The symplectic structure allows one to studies the singularities via their Poisson deformations or their crepant resolutions. At the University of Glasgow we are interested in understanding symplectic singularities both from the algebraic geometry perspective - existence of crepant resolutions etc. and with a view to geometric representation theory. The latter involves understanding quantizations of symplectic singularities.