We begin with the loose observation that in many complex real-world systems, dynamics seem to settle into some relatively simple behaviors, rather than remaining completely chaotic. Think of planets solidifying out of a chaotically moving gas, sand-dunes forming with reproducible shapes and sizes, debris on a river getting trapped near the shores, active colloids accumulating in corners, or DNA reliably copying itself via proofreading mechanisms. While vastly different mechanisms account for each of these phenomena, the emergence of simplicity seems to be a common thread. So: how general is this phenomenon? How easy is it to break? Is there some common mathematical framework that can capture some of it? To begin a discussion of these questions, I will restrict to non-equilibrium dynamical systems with two strongly separated time-scales - which is another common feature of the above examples. In this context, the structures from field theory prove relevant, and we derive that under fairly general conditions, slow variables will settle into configurations where fast dynamics become least stochastic. Illustrating the relevance of the framework on a toy example, I will then talk about the steps for extending it to broader contexts.

If you are interested in meeting with Pavel after his talk, please email him directly at pchvykov@mit.edu