EVENT DETAILS AND ABSTRACT

Title: Star products and quantization of manifolds with symmetry
Speaker: Professor Ranee Brylinski
Speaker Info: PennState
Brief Description:
Special Note:
Abstract:

Poisson manifolds (smooth or algebraic) are manifolds where the algebra of functions has an intrinsic bracket operation. Key examples are cotangent bundles, the dual of a Lie algebra and coadjoint orbits. These all have symmetry groups. A star product on functions deforms the Poisson bracket in a precise way. The first example is the Moyal star product on flat space, and this is equivariant under the symplectic group.

The problem of constructing equivariant star products on curved spaces is still wide open. The main reason is that to get equivariance one is often forced to use "pseudo-differential" operators. I will illustrate this with an example in algebraic geometry: the SL(n+1,C)-equivariant star product on regular functions on the cotangent bundle of n-dimensional complex projective space.