Symplectic Varieties, Orbifolds and Contact Homology of Toric Manifolds

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

Abstract Award: DMS-0603892 Principal Investigator: Eugene M. Lerman Lerman proposes to carry out three interrelated projects on the interface of geometry topology and category theory. The first project aims to classify singular symplectic toric varieties. This necessitates a development of a satisfactory set-up for such spaces. The second project studies periodic orbits of Hamiltonian systems on orbifolds and on symplectic stratified spaces. The third project studies infinite dimensional Lie 2-groups arising as symmetries of orbifolds. The projects contribute to the mathematics underpinning classical mechanics, the science governing the motion of satellites and the like. They also have links with important theoretical problems of high energy physics, higher gauge theory in particular.