**Academic Profile**

- 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

**Research Interests**

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.

**Notes**

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.