Integrable systems and applications to differential geometry
Specific research interests
Many problems in geometry have a loop group formulation, that is they come as one parameter families which correspond to maps into certain loop groups. The list of known examples includes constant mean curvature surfaces in 3 dimensional space forms, isometric immersions between space forms, other immersions with special properties, and pluriharmonic maps into symmetric spaces. The study of loop groups themselves has led to techniques for producing solutions to these problems. I am interested both in developing these techniques as well as in the issue of identifying the special geometric problems which fall within this framework.