July 2012 till date: My research activitites at IIT Jodhpur can be broadly categorized as:
Differential equations, applied functional analysis, scientific computations, applied mathematics
Wave-matter interactions, mathematical physics
Data analytics and data sciences
Technology foresight and policy
November 2010 till July 2012: Researcher at Computational Nano-optics group in Department of Numerical Analysis and Modelling at Zuse Institute Berlin (ZIB). Here my research area was numerical solution of Maxwell's equations by finite element based methods. Especially I was looking into solution of time dependent Maxwell's equations using discontinuous Galerkin FEM (for various material models). This has a lot of applications in plasmonics and nano-optics. I was involved in a project "Theory of spatio-temporally resolved optical dynamics in hybrid-nano-structures", which was a part of DFG Schwerpunktprogramm 1391 "Ultra-fast Nano-optics". This was in collaboration with a group of Prof. Dr. Andreas Knorr at Institute for Theoretical Physics at Technical University at Berlin.
February 2008 to October 2010: Scientific co-worker at Institute for Applied and Numerical Mathematics, and (from November 2008) DFG (German Research Foundation) post-doctoral research fellow at Research Training Group Analysis, Simulation and Design of Nano-technological Processes, Department of Mathematics, Karlsruhe Institute of Technology. Here I worked on mathematical and computational aspects of optics. I was on a project "Numerical Simulation of ring resonators by wavelet collocation in the time domain" with Prof. Dr. Andreas Rieder and Haojun Li. Accurate representation of curved interfaces and reliable resolution of narrow coupling regions are some of the numerical difficulties for simulation of ring resonators. Wavelets are well known for efficient multi-resolution representation of data. The above project explored the application of this property of the wavelets for spatial mesh adaptivity for simulation of ring resonators.
December 2006 to January 2008: Post-doctoral researcher at Optoelectronics Center, University of North Carolina at Charlotte. There I worked on modeling and simulation of light propagation in photonic microstructures (e.g. microresonators, microspheres, layered media), and effects of perturbations on the propagation of light. The work involved building mathematical models for those optical devices, and then analyzing the underlying physics with those models, which required mathematical analysis and use of numerics (finite difference time domain method, beam propagation method, analytical methods). My collaborators were Prof. Vasily Astratov, Prof. Eric G. Johnson and Prof. Tsing-Hua Her.
March 2000 to August 2001: Junior research fellow, senior research fellow at Industrial Mathematics Group of Department of Mathematics, IIT Bombay for Department of Science and Technology sponsored project "Doing Industrial Mathematics via Genetic Algorithms, Differential Algebraic Equations, Online Optimization, Computer Aided Geometric Design and Market Forecasting". This work was focused on scientific computing, numerical analysis of partial differential equations, conservation laws, Hyperbolic integro-differential equation (with Prof. A. K. Pani).
I worked on industry sponsored problem of emulsion polymerisation. The modeling of emulsion polymerisation process involves hyperbolic integro differential equation. It poses difficulty in the numerical computation. We tried to apply semi implicit finite difference method to it. The work was presented at International Conference on Nonlinearity: Modeling, Simulations and Application held at Nanded, Maharashtra in December, 2000.
May 1999 to February 2000: Junior research fellow in Microwave Remote Sensing Lab of Center for Studies in Resource Engineering (CSRE), IIT Bombay, for Indian Space Research Organization (ISRO) -IITB sponsored project of "SAR Interferometry and Earth Crust Movement" under the guidance of Dr. K. S. Rao.
The work was focused on mathematical modeling of Synthetic Aperture Radar (SAR) and Baseline Estimation. The programming was done in C, C++. I also worked as a system administrator of the same lab. I gave several workshop talks on the above mentioned topic in the courses and seminar conducted by CSRE. I visited Department of Science and Technology (DST) of Government of India, Delhi for technical consultancy.