I am interested in a wide range of problems in applied mathematics. Most of my work in the past ten years was motivated by the ubiquity of self-similarity and renormalization in fluid mechanics, materials science and physical chemistry. "Universal" scaling laws bring order to disparate phenomena such as the kinetics of phase transitions, turbulence in fluids, and transport properties of polymers.

My main goal (inspired by Felix Otto and Bob Pego ) was to rigorously pin down some of these deceptively simple laws. This led to some interesting mathematics even if it originated in some "messy" applications. I am particularly pleased with a Lax pair that Ravi Srinivasan and I found and the surprising discovery of complete integrability in a stochastic model. The interplay between analysis, probability and geometry in statistical theories of turbulence is fascinating, and while progress is slow, it is fun to chip away at these mysteries.

Recently, I've found myself drifting again, with increasing pleasure, into a variety of problems in the sciences. My complete ignorance of biology has only increased my fascination with the profundity of the mysterious self-replicating chemical process that is life. I am fascinated with the idea that we may use biology as a source of inspiration in nanotechnology (and on a more modest scale, the idea that mathematics may have something to contribute to this enterprise). David Gracias and I have been collaborating on design principles for self-assembling structures.

I have many more problems than I can handle and I am happy to work with students. If you are a student at Brown and would like to work with me, stop by to talk. Here is a short introductory research sketch for prospective and beginning graduate students. I also work with undergrads on independent studies and theses (for example, Andy Furnas wrote an excellent thesis on woven fabric). I am not really a specialist in anything, but I value elegance and simplicity above all else, and I am happy with work that meets these criteria.

Click here for publications, here for press coverage, and here for the full picture.