B.A., Wellesley College; Ph.D., University of Pennsylvania
Megan KerrKatharine and Claudine Malone '63 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 shape. Most of my work involves searching for nice geometries on classes of spaces with a high degree of symmetry: homogeneous and low-cohomogeneity spaces. These are settings where the big questions are about the existence of examples: What kinds of examples can arise? How common, or rare, are they? Are there obstructions, and if so, what are they? This work harnesses the interactions of the analytic notion of curvature with the algebraic structure of Lie groups. I am collaborating on a new project in geometric analysis in which topology plays an important role. I am expanding beyond my comfort zone, which is an exciting development.
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 interests and her major. The mathematics I use regularly is found in our geometry courses, but also in our algebra and analysis courses. I have taught courses in calculus, linear algebra, combinatorics, real analysis, non-Euclidean geometry, differential geometry, topology, knot theory, and on matrix groups (as an introduction to Lie groups).
Doing mathematics is a terrific way to see the world. In 2019, my research has taken me to Australia, Germany and Mexico.
I enjoy running, and I try to keep up with my two children, who get faster each year. I am thankful for a terrific exercise group of faculty friends who keep me tuned up, tuned in, together.