University of Toronto's Symplectic Geometry Seminar

Abstract: Toric varieties provide an interesting class of examples in algebraic and symplectic geometry. From the symplectic point of view, toric varieties are symplectic reductions of a complex vector space by a linear torus action. In this talk, I will discuss the topology of symplectic (and other) quotients. I will briefly review Kirwan's techniques for proving that the restriction map from the equivariant cohomology of the originial space to the ordinary cohomology of the symplectic reduction is a surjection. I will show how this result can be used to understand various aspects of the topology of quotients, touching on such themes as real loci, orbifolds and orbifold cohomology. Throughout, I will illustrate the main results with examples of toric varieties.