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.
|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|
|May 4||Mark Andrea de Cataldo (Stony Brook)||TBA||Laurentiu|
Generalized deformations of K3 surfaces
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).