Time: 3:20-3:28pm

Speaker: Ethan Ross

Title: Stratified Quantization

Abstract: Symplectic stratified spaces are a natural class of singular spaces which emerge when a symplectic space has a proper group action on it. There are a few different schemes for quantizing these spaces which have been proposed. In this talk, I give a new one by essentially extending the theory of vector bundles to stratified spaces and giving "stratified" versions of all the usual flora and fauna of geometric quantization. This includes stratified versions of prequantum line bundles, polarizations, and polarized sections.

Time: 3:34-3:42pm

Speaker: Hyunmoon Kim

Title: Basis theorems and quantization

Abstract: Geometric quantization requires passing to the complex numbers, and making additional choices over the symplectic manifold. We will view the complex Lagrangian Grassmannian as a parameter space for quantization, describe a stratification on it, and sketch the topological structure of each stratum.

Time: 3:48-3:56pm

Speaker: Leopold Zoller

Title: On integral Chang-Skjelbred computations

Abstract: The Chang-Skjelbred method provides a powerful tool to compute the equivariant cohomology of a torus action from the one-skeleton. When applied to integral cohomology, some control on the disconnected isotropy groups becomes necessary. In the case of Hamiltonian actions on manifolds with torsion free cohomology, we describe a procedure that computes the integral equivariant cohomology from the one-skeleton even in the presence of arbitrary disconnected isotropy groups. In particular we extend the GKM formula to this case.

Time: 4:02-4:10pm

Speaker: Rei Henigman

Title: Invariants of symplectic non-Hamiltonian circle actions on 4-manifolds

Abstract: Famously, Karshon gave a full classification of Hamiltonian circle actions on compact connected symplectic 4-manifolds up to equivariant symplectomorphisms. In this talk, we tackle the non-Hamiltonian case. We describe a set of invariants for symplectic non-Hamiltonian circle actions on compact connected symplectic 4-manifolds that admit circle-valued Hamiltonians. If the first cohomology of the quotient space $M/S^1$ is one-dimensional, we show that the action must admit a circle-valued Hamiltonian, and that our invariants provide a complete classification up to equivariant symplectomorphism. We also discuss results for spaces with higher dimensional first cohomologies.