Sympletic reduction and quantization: algebraic and geometric aspects

• Grant number: 14/00250-0
• Support Opportunities: Research Grants - Young Investigators Grants
• Start date: September 01, 2014
• End date: February 28, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Hans-Christian Herbig
• Grantee: Hans-Christian Herbig
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• City of the host institution: São Carlos
• Associated researchers: Carlos Henrique Grossi Ferreira ; Daniel Levcovitz ; Igor Mencattini
• Associated scholarship(s): 14/20191-8 - Sympletic reduction and quantization: algebraic and geometric aspects, BP.JP

Abstract

The procedure of symplectic reduction is an important operation in symplectic geometry. The basic idea is to exploit the symmetries of a mechanical system to reduce the number of degrees of freedom. In Hamiltonian mechanics, the symmetries are incorporated in the so-called moment map. It is particularly interesting to see what happens if we take the symplectic quotient at a singular value of the moment map. In this case the symplectic quotient is not a manifold, but a stratified symplectic space, and as such much more intricate. For this reason, here many problems that are well understood in the regular case are open or only partially solved. (AU)