Research 

Our world is not linear - which, roughly speaking, is like saying that we should not expect anything to evolve "in a straight line". 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. Two colors can be mixed to form another color, but "cannot be unmixed". One can easily think of other such examples - mostly because such examples. i.e., "nonlinearities", are 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 non-linear behaviors I am fascinated by. To rephrase the words my mathematical idol, 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 understand non-linear behavior using the cheapest means possible :)  

More seriously, despite being a theoretical mathematician, my belief is that in order to understand non-linearities mathematically one most study non-linear behavior which arises through the modeling of a natural phenomena. The reason I believe this is the case is because in my opinion, mathematical results are not invented - but rather discovered. Consequentially, 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.