Research Interests
My research interests are in Hamiltonian dynamics in a broad sense. Specifically, I have been studying the following topics:
- Shape Dynamics of Vortices
Funded by NSF grant DMS-2006736
- Stabilization of mechanical systems with broken symmetry
Funded by NSF grant CMMI-1824798
- Quantum and semiclassical dynamics
- Optimal control theory
- Nonholonomic dynamics (dynamics of mechanical systems under non-integrable constraints, e.g., rolling and sliding constraints)
- Symplectic, Poisson, and contact geometry associated with the above systems
- Hamilton–Jacobi theory and its generalization to constrained dynamics
- Dirac structures and their applications to constrained dynamics
- Reduction by symmetry
- Structure-preserving numerical integrators