Algebraic Geometry Seminar Spring 2012

The seminar meets on Fridays at 2:25 pm in Van Vleck B215.

The schedule for the previous semester is here.

Spring 2012

date	speaker	title	host(s)
January 27	Sukhendu Mehrotra (Madison)	Generalized deformations of K3 surfaces	(local)
February 3	Travis Schedler (MIT)	Symplectic resolutions and Poisson-de Rham homology	Andrei
February 17	Arend Bayer (UConn)	TBD	Andrei
February 24	Laurentiu Maxim (UW-Madison)	TBD	local
March 2	Marti Lahoz (Bonn)	TBD	Sukhendu
March 9	Shilin Yu (Penn State)	TBD	Andrei
March 16	Weizhe Zheng (Columbia)	TBD	Tonghai
March 23	Ryan Grady (Notre Dame)	Twisted differential operators as observables in QFT.	Andrei
April 27	Ursula Whitcher (UW-Eau Claire)	TBA	Andrei
May 4	Mark Andrea de Cataldo (Stony Brook)	TBA	Laurentiu

Abstracts

Sukhendu Mehrotra

Generalized deformations of K3 surfaces

Travis Schedler

Symplectic resolutions and Poisson-de Rham homology

Abstract: A symplectic resolution is a resolution of singularities of a singular variety by a symplectic algebraic variety. Examples include symmetric powers of Kleinian (or du Val) singularities, resolved by Hilbert schemes of the minimal resolutions of Kleinian singularities, and the Springer resolution of the nilpotent cone of semisimple Lie algebras. Based on joint work with P. Etingof, I define a new homology theory on the singular variety, called Poisson-de Rham homology, which conjecturally coincides with the de Rham cohomology of the symplectic resolution. Its definition is based on "derived solutions" of Hamiltonian flow, using the algebraic theory of D-modules. I will give applications to the representation theory of noncommutative deformations of the algebra of functions of the singular variety. In the examples above, these are the spherical symplectic reflection algebras and finite W-algebras (modulo their center).