Broadly speaking, my research is about Partial Differential Equations and Riemannian geometry. I study nonlinear PDEs in geometric perspective which was pioneered by V. Arnold in 1966. He demonstrated that Euler’s equation for an ideal fluid describes the geodesic equation on the group of volume preserving diffeomorphisms, which is an infinite dimensional Riemannian manifold. Then we can use geometric data to understand qualitative information about the fluid.
- 2017: ‘Local well-posedness of the Camassa-Holm equation on the real line,’ with Stephen C. Preston, in DCDS-A 37-6 June 2017