Ana Rita Pires

Title: Origami Manifolds
Date: Tuesday, April 6, 2010
10:00am, Room 66-168
Committee: Victor Guillemin (thesis advisor), Tom Mrowka,
Ana Cannas da Silva (Princeton University), Eva Miranda (Universitat Politécnica de Catalunya)

Abstract

An origami manifold is a manifold equipped with a closed 2-form which is symplectic everywhere except on a hypersurface, where it is a folded form whose kernel defines a circle fibration. In this talk I will explain how an origami manifold can be unfolded into a collection of symplectic pieces and conversely, how a collection of symplectic pieces can be folded (modulo compatibility conditions) into an origami manifold. Using equivariant versions of these operations, I will show how classic symplectic results of convexity and classification of toric manifolds translate to the origami world. There will be pictures resembling paper origami, and possibly instructions on how to fold a paper crane.