B.A., Wellesley College; Ph.D., University of Pennsylvania
Professor of Mathematics
Research in global Riemannian geometry, especially the interplay of curvature constraints in the context of large symmetry groups.
I work in the area of global differential geometry. Geometry is the study of the shapes of manifolds, which are generalized surfaces. I consider a special class of manifolds with a high degree of symmetry, called homogeneous and low-cohomogeneity spaces. My work involves varying the shape of a given manifold so that the symmetries, or most of them, remain. This work harnesses the interactions of the analytic notion of curvature with the algebraic structure of Lie groups. Most of my results involve finding new examples in settings where the “big questions” are about the existence of examples: What kinds of examples arise? Why are they rare? What are the obstructions?
An alumna of Wellesley College, I am especially interested in encouraging women in mathematics. I enjoy teaching students at all levels. Greater mathematical understanding and confidence in mathematical skills—these benefit every student, whatever her major and her interests. The mathematics I use regularly is found not only in the geometry courses, it also straddles Algebra and Analysis. I have taught courses in calculus, linear algebra, combinatorics, real analysis, non-Euclidean geometry, differential geometry, topology, knot theory, and a special topics course on matrix groups: introduction to lie groups.
I am an active member of the Association for Women in Mathematics (recently served terms on the Schafer prize selection committee and JMM workshop organizing committee). Through the AWM I have enjoyed meeting and working with successful women mathematicians in a broad range of research areas and at a variety of universities and colleges. Doing mathematics is a terrific way to see the world. Recent conferences have taken me to San Francisco, Middlebury, Aspen, Rio de Janeiro, and Cuernavaca.
I try to keep up with my two children, who get faster each year. I am thankful for a terrific running group; they keep me tuned up, tuned in, together.