Research Topics

Geometric Quantization

Quantization of symplectic manifolds with applications to the quantization of general classical mechanical systems and the geometric realisation of representations of Lie groups. My recent work has been on properties of star products. Prior to that I worked on the quantization of Kaehler manifolds.

 

Deformation Quantization

Construction and classification of star products and comparison with other methods of quantization. Symmetries of star products.

 

Geometry of Symplectic Manifolds

Construction of symplectic connections with special properties and applications.

 

Differential Geometry of Homogeneous Spaces

The extension of methods and results from symmetric spaces to other classes of homogeneous spaces.

 

Twistor Theory

Development of twistor theories for even-dimensional manifolds, in particular symplectic manifolds.