Research Interests
My research interests are in Hamiltonian dynamics in a broad sense. Specifically, I have been studying the following topics:
- Quantum dynamics, semiclassical mechanics, and quantum control
- Nonholonomic dynamics (dynamics of mechanical systems under non-integrable constraints, e.g., rolling and sliding constraints)
- optimal control theory
- 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
- Development of structure-preserving numerical integrators
Talks and Posters
PDF files of some of my talks and posters:
- Symplectic Semiclassical Mechanics, Talk given at Differential Equations Seminar, North Carolina State University, Raleigh, November 2012
- Nonholonomic Hamilton–Jacobi Theory via Chaplygin Hamiltonization, Poster given at Oberwolfach Workshop on Applied Dynamics and Geometric Mechanics, August 2011
- Discrete Hamilton–Jacobi Theory, Talk given at the minisymposium "Computational Methods for Geometric PDEs", ICIAM, Vancouver, July 2011
- Dirac and Nonholonomic Hamilton–Jacobi Theory, Talk given at Dynamical Systems Seminar, Waseda University, Tokyo, June 2011
- Nonholonomic Hamilton–Jacobi Theory: The Geometry and Dynamics of Rolling and Skating, Talk given at Differential Geometry and Control Seminar, Arizona State University, Tempe, April 2011
