Kirill Mackenzie

Biography

I work in differential geometry - Lie algebroids, Poisson geometry, connection theory, double and multiple structures. Most of my work at present involves aspects of multiple Lie algebroids. In the same way that a Lie algebroid generalizes the notion of tangent bundle, multiple Lie algebroids abstract the notion of higher-order tangent bundles. Despite their complexity, these objects are more tractable than other approaches to higher-order differential geometry: in place of, for example, a second-order jet bundle or a Courant algebroid, a double Lie algebroid has two simple bracket structures, the relations between which embody the second-order features.  Lie algebroids are intimately related to Poisson structures and none of my recent work would have been achieved without the use of Poisson methods. Reciprocally, Lie algebroid and double Lie algebroid methods are allowing difficult questions involving Poisson groupoid actions to be resolved in a simple and conceptual fashion.  More detail about my work can be found by following the links on my home page.

Research Interest

Differential geometry -- Lie groupoids and Lie algebroids, connection theory, Poisson geometry, multiple structures