My research is in geometric Hamiltonian dynamics with applications to continuum mechanics.

The subjects of my research encompass:

- Hydrodynamics: Hamiltonian techniques in geophysical fluids, complex fluids, Ericksen-Leslie and Eringen models for liquid crystals;

- Elasticity theory: convective and Eulerian variational formulations, geometrically exact models for molecular strands and dendronized polymers;

- Geometric properties of diffeomorphism groups, momentum maps, dual pairs, and the universal Teichmüller space;

- Variational integrators in continuum dynamics: geophysical fluids and geometrically exact models for beams and plates;

- Nonholonomic continuum mechanics: dynamic of interacting elastic rods with rolling contact, reduction of Dirac structures;

- Lagrangian and Hamiltonian techniques in control theory and image registration;

- Reduction in field theories and covariant variational principles.

François Gay-Balmaz

Discussing field theories at Caltech: