If you're considering applying to IITGN for the Ph.D. program and are wondering how your academic goals would align with various potential Ph.D. supervisors, here is some information about my research profile and interests that you may find useful.
Mathematically, the single most important area for my research is Analysis. If you dislike Analysis, we will not be a good fit. Indeed, at the Ph.D. level, in many instances, the fields of (i) Probability Theory and Stochastic Processes, (ii) Differential Equations and Dynamical Systems, (iii) Control Theory, and (iv) Partial Differential Equations, are really just Analysis in disguise. This is certainly true of the way my work overlaps with these areas.
Having prior experience in Probability is not strictly necessary, although undoubtedly helpful. For the problems in which I'm interested, I believe that with a good Analysis background, a student can (relatively easily) learn enough Probability to take a crack at some of these problems.
Applied Mathematics means different things to different people, so it may best if I say that I enjoy working on mathematical problems which have some connection to applications. Most problems that I work on are, at the very least, a simple cartoon toy model of some actual system which arises in science and engineering. I often, but not exclusively, like to work on mathematics problems which are also of interest to people outside Mathematics (typically Engineers).
I sometimes require a little bit of numerical work, although this is very elementary by the standards of mathematical research in numerical analysis. In other words, a general willingness to learn and write some very basic programs (e.g., in MATLAB) is quite desirable.