| Speaker: | Travis Schedler (Imperial College London) |
|---|---|
| Title: | Towards classification of symplectic singularities and their resolutions |
| Date (JST): | Tue, Oct 21, 2025, 13:30 - 15:00 |
| Place: | Seminar Room A |
| Abstract: |
There is a growing program to classify symplectic singularities and their resolutions, generalising the Springer resolution of the nilpotent cone, which famously encodes (via quantization) the representation theory of semisimple Lie algebras. Recently Namikawa produced new examples of Hamiltonian reductions of vector spaces by tori (singular toric hyperkaehler varieties) with trivial local fundamental group. I will explain how to generalise his result to quotients by nonabelian groups. This allows one to construct such examples which are additionally Q-factorial. These can be considered as the fundamental building blocks of conical symplectic singularities, which cannot be resolved or simplified. Given a general symplectic singularity, one also wishes to understand all its crepant (partial) resolutions. This is closely related to the study of the Cox ring of the resolution. I will explain recent tools to compute this. Finally, I will explain a conjectural program to use Cox rings of deformations to construct all symplectic singularities from the Q-factorial terminal ones via Hamiltonian reduction by tori. |
