In Spring '14 the second year graduate students will be organizing a graduate student seminar on symplectic geometry, torus actions, and equivariant cohomology. We meet from 10-11 AM on Mondays in DL 431. Our canonical reference will be the book "Torus Actions on Symplectic Manifolds" by Michele Audin. Our goal will be to get through Chapters I-IV the first half of the semester, and Chapters V-VII in the second half. 
On localization: A short 1-page overview of what localization is, here. "The Moment Map and Equivariant Cohomology" by Atiyah and Bott. (A seminal paper on localization theorems, with powerful results. Link here.) "A residue formula for holomorphic vector field" by Bott. (A prequel to the one above.) "Localization of virtual classes" by Graber and Pandharipande. (A state-of-the-art formulation of localization in Gromov-Witten theory. Link here.) Other References: "Lectures on Symplectic Geometry" by Ana Cannas da Silva. (Seems to be available here.) "Symplectic Toric Manifolds" by Ana Cannas da Silva. (Seems to be available here.) "Introduction to Toric Varieties" by Bill Fulton. (For the algebraic perspective. The canonical reference.) "Lecture Notes on Equivariant Cohomology" by Matvei Libine. (From a course taught at Yale. Available here.) |