Research Interests

My research interests originate from my fascination with the interplay between mathematics and physics. In particular, I study geometric mechanics, which can most easily be described as mechanics on manifolds.

A particularly interesting related field is that of nonholonomic mechanics. These are mechanical systems subjected to non-integrable constraints on the velocities of the system. Some familiar examples of nonholonomic systems are cars and bowling balls. It turns out that these systems are not Hamiltonian. However, under certain conditions they can be embedded in a larger Hamiltonian system. Much of my research to date has been focused on finding different ways to do this. Lately I have been exploring the applications of these results to questions like the integrability and quantization of nonholonomic systems.