09/11 & 09/18 at 17:30 in 507

Sam DeHority

Title:  Noncommutative surfaces and toroidal algebras

Abstract: Poisson structures on algebraic varieties can be seen as first order noncommutative deformations which sometimes integrate to give noncommutative varieties. In the case of algebraic surfaces, moduli spaces of sheaves on noncommutative surfaces are generalizations of the Calogero-Moser spaces which deform the Hilbert schemes of points in the plane.  At least since Slodowy's approach to Springer theory, it is often possible to use deformations of maps from holomorphic symplectic varieties to prove results in geometric representation theory. In our situation, after an introduction to the required noncommutative geometry, such deformations will be used to provide geometric realizations of representations of extensions of toroidal algebras with applications to the enumerative geometry of Lagrangian fibrations.