- 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 the theoretical and numerical analysis of partial differential equations as well as their applications. The application domains include large-scale atmospheric and ocean dynamics, Bose-Einstein condensates and cold atoms, water waves and coastal engineering, growth and its regulation in biological tissues among others. I tend to take a dynamical systems perspective and the tools I use include scientific computing, rigorous analysis and formal asymptotics. Often it is a healthy mix of them all.
My research presently consists of two broad themes.
Dynamical systems & Data. The broad aim of this research theme is to establish the data-driven viewpoint of dynamical systems from a theoretical perspective. We seek results that firmly establish inference principles for the state and parameters of a dynamical system from partial noisy observations.
Analysis & Computation. This theme is concerned with developing numerical algorithms and their analysis to establish guarantees on error, convergence and computational cost. The algorithms are strongly motivated by applications and influenced by the theoretical understanding of the mathematical models.
- 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.