Title: Holonomic Poisson geometry of Hilbert schemes
Speaker: Brent Pym (McGill University)
Abstract: The Hilbert scheme of a complex surface parameterizes finite
sets of points in the surface, and the various ways they can collide.
If the surface carries a Poisson structure, its Hilbert scheme does,
too, as explained by Beauville, Bottacin, and Mukai. The geometry of
these Poisson structures turns out to have rich connections with other
parts of mathematics. For instance, their symplectic leaves are
classified by Young diagrams; their symplectic groupoids can be
constructed using derived geometry and the theory of syzygies; they
locally admit toric degenerations, built using a combinatorial game of
dominoes; and properties of their deformation theory (Poisson
cohomology) can be established using a classical dynamical system known
as the interval exchange transformation. I will give an overview of
these ideas, based on joint work with Mykola Matviichuk and Travis Schedler.