Home

Publications and Preprints

Theses

Research Interests

Talks and Presentations

I work in an area of mathematics called noncommutative geometry. Here one views differential geometry as a distinguished sub-field of commutative algebra, and then searches for noncommutative generalisations of commutative objects.

I am interested in whether or not noncommutative Riemannian geometry contains subfields generalising complex and symplectic geometry, and whether there exists a notion of noncommutative Kähler geometry in their intersection. I feel that this should be done in such a way as to generalise classical symmetries of each area, and so I am work in the context of quantum groups, which can be viewed as the noncommutative analogues of symmetry groups.

For these reasons I am lead to the noncommutaive geometry of the quantum flag manifolds, which are the motivating family of noncommutative Kahler manifolds with quantum group symmetries.