This Presidential Young Investigator will work on a nonlinear harmonic theory for representations of the fundamental group of ordinary differential equations. He will also work on the relationship between the two algebraic structures on the space representations, in particular the behavior at infinity. This project falls into the general area of modern geometry -a subject that blends two of the oldest areas of mathematics: algebra and geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many application are to gauge theories in physics and dynamical systems in mechanics.
