I love exploring science. If any topic from my past work sparks your curiosity, feel free to reach out to me -- we can discuss and maybe together come up with a project that interests you! Here is the slideshow (Keynote file) that I used to introduce my research to people in Claremont, which might give you more information about what I have been thinking of.
If you are looking for a well-defined potential research project this coming Spring, there are a few directions I want to investigate (the list below is very incomplete), beyond what we have already been studying.
Theoretical research:
Robots driven by competing fields -- some attractive, some repulsive -- can self-organize into blobs that together self-propel coherently. However, the blob stability is non-monotonic -- small and large populations stay intact, while intermediate swarm sizes trigger break‑up. Our goal is to chart this size‑dependent stability landscape, which could potentially be a simple analogue model of motile cell-splitting.
Machine learning can discover hidden symmetries, patterns, and structures in data that are otherwise incomprehensible to us. Our goal is to train neural networks that transform complicated dynamics into trivial ones (e.g. intricate motion under a potential to constant motion by adding more dimensions) or ones with elegant geometrical properties (e.g. prey-predator systems to Hamiltonian/Poisson systems defined on symplectic manifolds).
Develop a number-agnostic machine learning approach for data-driven discovery of additive conservation laws. Can we use it to discover hidden interacting agent?
Investigate the dynamics of Patlak-Keller-Segel system -- the “standard model” of bacteria chemotaxis -- for different parameters and inside different geometries.
Experimental research:
Entropy normally goes up as order gives way to disorder, yet a system can always briefly regain order. These rare negative‑entropy events are manifestations of Poincaré recurrence, whose average timescale explodes with increasing degrees of freedom. Our aim is to quantify the temporal-statistics of those curious events as observed on a system of propelled agents.
Statistic of Paper Airplane Flights
We would like to study emergent behavior of robot swarms, so the first thing to do is to design prototypes of robots. I am inviting you to join my lab to learn electronics, develop autonomous robots, and help us come up with a few simple designs that we can manufacture in bulk (on the order of 10–100 units). Some example platforms I’m interested in include:
(i) robots that can generate and detect sound,
(ii) robots that can float and generate vortices on water,
(iii) robots that can glide on an air table, and
(iv) robots that can emit light and sense light.
(v) robots powered by IR light (i.e. the Sun)
The list above is very incomplete, but it should give you some ideas of what I like!