Applied analysis. Mathematical problems in fluid mechanics, materials science and physical chemistry.
My recent work has been on dynamic scaling. The ideas of self similarity and renormalization are central to many problems in fluid mechanics, materials science and physical chemistry. Robust scaling laws are observed in the kinetics of phase transitions, "universal" statistics in turbulent flows, and the transport properties of polymers. My main goal is to rigorously pin down some of these deceptively simple laws.
Here is a short introductory research sketch for prospective and beginning graduate students.
Click here for publications, and here for press coverage.
The 2004 IMA program on the mathematics of materials and macromolecules is a good overview (and argument for) mathematical work in these areas.