A (complex) log symplectic manifold is a holomorphic symplectic manifold whose symplectic form is allowed to have simple poles on a hypersurface. Examples arise naturally in many contexts, e.g. from various moduli spaces in gauge theory and algebraic geometry. In contrast with ordinary symplectic geometry -- where Darboux's theorem implies that all symplectic structures are locally equivalent -- log symplectic forms can have quite complicated singularities along the polar hypersurface, so their local classification is subtle. I will give an overview of what's currently known about the local classification, based on some older work of mine on the basic theory and the role of elliptic curves, and some more recent joint work with Matviichuk and Schedler on deformation theory.

The talk will be via Zoom at: https://utoronto.zoom.us/j/99576627828

Passcode: 448487

https://arxiv.org/abs/1507.05668