Dear Confidants of Hamiltonian Systems,
The next talk at our seminar by Brent Pym, McGill U "Local normal forms in log symplectic geometry" is this coming Tuesday, January 25, 2022 at 12PM EST (8pm in Moscow, 6pm in Europe, 12noon in Toronto, 10am in Tucson, 9am in LA).
Zoom at
https://utoronto.zoom.us/j/99576627828Passcode: 448487
Abstract: 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.
Just a heads up on later talks:
Feb 8 -- Sanjay Ramassamy, CNRS / Institut de Physique Thèorique -- Cross-ratio dynamics and the dimer cluster integrable system
Feb 22 -- Robert McCann, Toronto -- TBA
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