Back to Departmental Colloquium: Spring 2005
Departmental Colloquium
Date: Monday, Feb 14, 2005
Time: 4:15PM
Location: JWB 335
Special Colloquium Monday
Formulas for Quiver Varieties
Title |
Formulas for Quiver Varieties |
Abstract |
A quiver variety is a general type of degeneracy locus associated to a quiver of vector bundles and bundle maps over a variety. Examples include Schubert varieties in flag manifolds and determinantal varieties. I have proved a formula for the Grothendieck class of a quiver variety when the underlying quiver is equioriented of type A. This formula is stated in terms of integers called quiver coefficients, which are generalizations of Littlewood-Richardson coefficients. Knutson, Miller, and Shimozono have shown that the lowest degree coefficients, which describe the cohomology class of the quiver variety, are non-negative. I will speak about a proof that general quiver coefficients have signs that alternate with codimension. I will also explain a cohomology formula for non-equioriented quiver varieties, which I have recently proved with R. Rimanyi. |
Algebraic Geometry
Topology