Games, Graphs and Randomness
My name is Aanjaneya Kumar and I am a PhD student at the Indian Institute of Science Education and Research Pune, working in the group of Prof. M. S. Santhanam. My primary interest is in obtaining insight into practically relevant problems, which could arise in various fields including (but not restricted to) physics, biology, and the social sciences, by first formulating them as mathematical models and then analyzing them using tools from Statistical Physics, Graph Theory and Game Theory. I also like dogs.
A very high-level goal of statistical physics is to provide a low-dimensional representation of high-dimensional complex systems. This is not always an easy task. Ideally, one wants to arrive at a description which captures essential features of the complex system at hand, but one which is also simple enough, so that it is tractable, and further insight into the system can be generated from it. This is where stochastic processes play an important role, which is a unifying theme of my research interests. The general philosophy behind stochastic modelling is that when you are faced with unmanageable complexity, a good first step is to model that with randomness. The pursuit of describing elements of a complex system in the simplest manner possible, and the remarkable success of stochastic modelling in doing so has shaped my research interests significantly.
The general philosophy described above, in fact, goes much beyond statistical physics and can be thought of as a guiding principle for fruitful research across disciplines. I try my best to keep this approach in mind while tackling research problems. Some of my research endeavours end up in the form of publications and they can be found here or from some of the links in the sidebar (please feel free to contact me if you would like access to any of the papers). A lot of things that I gain from my research do not end up being part of the final research paper that I write but I would be very happy to talk to you about them. I strongly believe in science being a collective and collaborative effort and I look forward to discussing ideas with you.