- Reader, ICTS TIFR 2015-Present
- S. Chowla Research Assistant Professor, Pennsylvania State University 2012-2015
- PhD, Applied Mathematics, University of Washington 2012
- MS, Mechanical Engineering, Arizona State University 2007
- BE, Mechanical Engineering, Anna University 2005
My main interest is in partial differential equations and methods of constructing solutions to these equations. I use a mixture of analytical and numerical techniques in analyzing these equations. Frequently, I supplement these tools with experimental observations of the physical system in question. The kind of problems I am interested in range from more theoretical questions to very applied problems.
From an applications point of view, I focus mainly on the study of surface water waves.The mathematical study of water waves has been a fruitful exercise, revealing many new areas of research. Previously, I have worked on inverse problems associated with bathymetry detection in oceans and wave-height determination, physical modeling of wave systems, developing new means of solving the associated equations of motion and finding special solutions to these equations. Given the nature of the work I do, almost every mathematical tool may be useful and of course, the tools developed here are also useful elsewhere in other physical situations. Finally, I also conduct experiments in fluid mechanics that complement our mathematical investigations to both validate and refine our understanding.
- Introduction to perturbation methods [Updated: 14 May 2019] In May 2019, I gave four lectures introducing perturbation methods for nonlinear partial differential equations. These lectures cover a subset topics from the notes. Lecture 1 Lecture 2 Lecture 3 Lecture4 I gave a related lecture on the derivation of the quasi-geostrophic equations using the same ideas as part of a discussion meeting on Air-Sea interaction in the Bay of Bengal Quasi-geostrophic equations