JARCS SYDNEY 2013 | ||
|
Mini CourseSingularities arising from nilpotent orbits. Among the most-studied singular varieties are the closures of nilpotent orbits in a simple Lie algebra, including the basic type-A example of the closures of similarity classes of nilpotent nxn matrices. The continuing interest in these varieties stems mainly from their connections to representation theory, but they also offer a well-structured context in which to explore examples and methods of singularity theory. In these talks I will start by explaining classical results of Kostant, Brieskorn, Slodowy, Kraft, Procesi, etc. and work gradually towards recent discoveries, omitting proofs in favour of examples. I will focus on the geometry of the singularities but include some comments on their representation-theoretic significance.
|