"The hardest thing of all is to find a black cat in a dark room, especially if there is no cat." Confucius
Currently, my research interests are primarily focussed on the following four topics.
Sub-Riemannian structures, especially on Lie groups: classification, isometries and isometry groups, geodesics, conjugate and cut loci, totally geodesic submanifolds, submersions and immersions.
Control sytems & optimal control problems, especially on Lie groups: equivalence and classification, explicit calculation of extremals, differential geometric links.
Linear Poisson spaces, and especially quadratic Hamilton–Poisson systems on such low-dimensional spaces: equivalence and classification, geometric and topological invariants, stability of equilibria, explicit integration.
Lie groups and Lie algebras: classification of distinguished classes of groups, algebras, and various substructures.
2nd Mini-Symposium: Geometry, Groups and Control, Rhodes University, South Africa.
Research visit to Geometry of Metric Groups group (ERC Project), Jyväskylä University, Finland.
1st Mini-Symposium: Geometry, Groups and Control, Rhodes University, South Africa.
61th Annual Congress of the South African Mathematical Society, Rhodes University, South Africa.
Research visit to Rhodes University
60th Annual Congress of the South African Mathematical Society, Potchefstroom, South Africa.
Two research visits to Rhodes University.
7th European Congress of Mathematics, Berlin, Germany.
13th International Conference on Differential Geometry and its Applications, Brno, Czech Republic.
4th International Conference on Lie groups, Differential Equations and Geometry, Modica, Italy.
Research visit to the University of Palermo.
Workshop on Geometry, Lie Groups and Number Theory, University of Ostrava, Czech Republic.
Research visit to University of Ostrava, Óbuda University, and the University of Debrecen.
13th European Control Conference, Strasbourg, France.
2nd International Conference on Lie Groups, Differential Equations and Geometry, University of Palermo, Italy.
Research visit to Óbuda University, the University of Debrecen and the University of Palermo.