Dr. Pillai is an interdisciplinary scientist working on problems lying at the interface of applied mathematics, probability and statistics,with a particular research focus on statistical inference for data coming from dynamical systems, partial differential equations (often representing physical processes) and diffusions. Another central theme of his research is studying the efficiency of Markov Chain algorithms in statistical problems.
Dr. Pillai's broad interests and genuine curiosity in different fields of mathematics and statistics gives him a chance to talk to and learn from other scientists. Applied mathematics is concerned with developing models which yield both qualitative and quantitative insight into the physical phenomena being modeled. Statistics is data-driven and is aimed at the development of methodologies to understand and account for the uncertainty in the information derived from the data. The main motivation for his research is the prospect of combining the increasingly complex physical phenomena that scientists and engineers observe and wish to model, together with the plethora of modern statistical techniques developed to understand uncertainty. This exciting aspect requires these two subjects to work in conjunction in order to significantly improve our knowledge with beneficial impacts on both the disciplines.
His current research interests may be broadly classified into the following three complementary themes:
1. Statistical inference for inverse problems from diffusions and dynamical systems.
2. Stability of Markov Chain Monte Carlo (MCMC) algorithms in high dimensions.
3. Ergodic theory for Markov (and Non-Markovian) processes.