Research 

Our world is not linear - which, roughly speaking, is like saying that we should not expect anything to evolve "monotonically". For example, the Moon revolves around the Earth almost periodically, the price of a given stock can oscillate sharply, the motion of a water particle can spiral inside a whirlpool - only to be ejected out and then return again, and while two colors can be mixed to form another color they "cannot be unmixed". One can easily think of many other such examples - if only because such nonlinear evolution laws, i.e., "nonlinearities", occur all around us.

It should therefore come as no surprise that many natural phenomena that can be modeled mathematically include non-linear components - and it is precisely such nonlinearities I am fascinated by. To quote the words of the greatest mathematician in the 20th century, V.I. Arnold, "mathematics is the part of science where experiments are cheap" (see here for the context of this quote) - and in this spirit, I strive to analyze nonlinearities using the cheapest means possible :)  

More seriously, despite being a theoretical mathematician, my belief is that in order to understand nonlinearities mathematically one must study nonlinear systems which arises through the modeling of a natural phenomena. The reason for that is my belief that mathematical results are not invented, but rather discovered. Consequently, the best way to realize new mathematical truths is to observe nature, and see how these ideas "play out" in real life. For the more technical details which explain how I actually study non-linear phenomena, please see my research statement below.