Research
Research program
My research lies at the intersection of Hamiltonian dynamical systems, geometric mechanics, bifurcation theory, and mathematical fluid dynamics.
I develop structure-preserving reductions and global geometric descriptions that reveal how invariant structures, singular configurations, and parameter changes organize nonlinear dynamics.
Hamiltonian Systems
I study nonlinear systems whose dynamics are governed by Hamiltonian structure, conserved quantities, and symmetries. A central objective is to identify coordinates and geometric objects that make global dynamics visible without destroying the underlying structure.
Geometric Reduction
Reduction transforms high-dimensional systems into lower-dimensional models while preserving essential invariants. My work emphasizes singularity-free formulations that remain valid across parameter regimes and clarify the topology of the reduced phase space.
Bifurcation Theory
I investigate how equilibria, invariant manifolds, and global phase portraits change as physical parameters vary. This leads to bifurcation sets that organize qualitative transitions and provide a unified view of distinct dynamical regimes.
Vortex Dynamics
Point-vortex and vortex-dipole models provide a rich setting where geometry, topology, and fluid mechanics interact. I use these systems to develop reduction techniques and to classify global dynamics, relative equilibria, and bifurcations.