My mathematical research lies in the general area of nonlinear Partial Differential Equations(PDEs) and infinite dimensional Riemannian Geometry. In particular, I study equations that are related with incompressible Euler’s equation for ideal fluid; Camassa-Holm, Quasi-Geostrophic equations, etc. Also, I study the Riemannian Geometry of the group of diffeomorphisms to solve the PDEs, to gain insights about the properties of PDEs using the geometric interpretations, or to understand its geometry in its own right.


[1] Local well-posedness of the Camassa-Holm equation on the real line, with Stephen C. Preston, in DCDS-A 37-6 June 2017 [journal], [arXiv]

[2] Global Lagrangian Solutions of the Camassa-Holm equation, [arXiv]