Research

My research develops geometric and qualitative methods for Hamiltonian systems with symmetry. A central focus is the point-vortex problem, where symmetry reduction transforms a high-dimensional dynamical system into a lower-dimensional phase space whose geometry reveals relative equilibria, invariant manifolds, bifurcations, and global transitions.

In recent work, I developed and analyzed singularity-free reductions of the three-vortex problem using Jacobi coordinates together with Nambu-bracket and Lie–Poisson formulations. These approaches produce a unified phase-space description across circulation regimes and clarify when the reduced space is spherical or hyperbolic.

Current and future directions include higher-vortex systems, non-integrable Hamiltonian dynamics, structure-preserving numerical methods, and applications of geometric reduction to scattering and coherent structures in fluids.