Yiyan Shou – GMA Seminar

Title: Symplectic Toric Orbifolds

Abstract: Toric varieties are a special class of algebraic T-varieties whose geometry is encoded in convex polytopes. In addition to being interesting in its own right, toric geometry often serves as a source simple examples where even very abstract geometric concepts manifest in concrete and explicit ways. For example, the cohomology ring and usual characteristic classes of a smooth complete toric variety admit simple descriptions in terms of the combinatorics of the associated polytope. This talk concerns a subset of toric varieties with extremely mild singularities that appear in both algebraic and differential symplectic geometry. The main result is Delzant’s theorem, which establishes a correspondence between symplectic toric manifolds and Delzant polytopes. The talk focuses on the differential side of the story, so no knowledge of algebraic geometry will be assumed. Basic manifold theory will be taken for granted, but relevant concepts from symplectic geometry will be summarized. While prior knowledge of symplectic geometry and orbifolds would be helpful, none will be assumed.