Order from Disorder
What is it that causes organization to come from disorganized or even random things? Randomly moving air molecules develop into tornadoes under the right conditions. Proteins can start as chains of randomly vibrating atoms, but quickly organize into their predefined shapes so that they can function like machines. Individual stock traders make decisions to buy or sell, and together create a reasonably behaved market (well, maybe not lately, but usually). Individual neurons communicate between themselves, and together implement a brain that can learn and make decisions. Life, remarkably, evolves into ever more complex organisms.
While I don't claim that there is a single organizing principle behind these examples, they are all ways in which Nature develops high organized systems with disparate, random, and unorganized components. These are the sorts of problems that interest me. Using physical principals, mathematics, and computer simulations, I try to learn about the ways in which Nature uses random components to develop powerful machinery.