- 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 (PDEs), their applications and methods of constructing solutions (both analytical and numerical). Most of my work has come with a very applied motivation to solve concrete problems in engineering or geophysics, often in the form of an inverse problem. The tools I use include scientific computing, rigorous analysis and formal asymptotics. Often it is a healthy mix of them all.
The PDEs I study arise in a variety of applications including water-waves, Bose-Einstein condensates and atmospheric science. I tend to take a dynamical systems perspective and am interested in questions related to state estimation/inference via observations.
I am part of the ICTS monsoon dynamics group devoted to understanding the mathematics of the Indian monsoon. We look at the problem from a number of perspectives including multi-scale dynamical models, probabilistic models of meteorological data and the motion of cloud particles.
Recently I've developed an interest in applying control-theoretic ideas to investigate pattern-formation and -regulation in biological tissues. I'm particularly excited about building new mathematical tools specifically motivated by questions in biology.
A very wise man once said to write down what you've done. And make it available. To that end, here is a (hopefully) growing list of notes that may or may not be useful to someone.
- Nonlinear systems of ordinary differential equations A very quick introduction to nonlinear ODEs (only two dimensional) covering the very basics of equilibrium points, jacobians and associated stability. These notes are written for undergraduate students with little-to-no-background in linear algebra and some knowledge of calculus. The notes do NOT contain any proofs as they were intended for engineering students taking a course on differential equations. These were written when I was a graduate student, so excuse the informal nature.
- 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
Prospective project students/visiting researchers
I take students through the SN Bhatt summer program or the long term visiting student program only. Interested students should apply to either https://www.icts.res.in/academic/summer-research-program or https://www.icts.res.in/academic/ltvsp and not email me directly.