I am interested in Morse theory and its applications. In my work, I am primarily concerned with situations where the Morse Theorems can be proven by studying a modified gradient vector field. Much of this work centers on manifolds with corners. These spaces give rise to interesting results, and appear naturally in applications. I have been using these results to study billiard path problems. Specifically, I am looking at billiard paths that reflect off a compact manifold embedded in Euclidean space. Other areas of application may include the study of configuration spaces of distinct points in a smooth manifold, the path space of a manifold with boundary and the configuration space of a planar linkage.

As a teacher, I am developing a curriculum for differential equations that emphasizes the use of computer technology. The important point is to help students see computer techniques as an extension of more traditional methods, rather than a substitute. The way to achieve this is to emphasize understanding the behavior of a system, rather than simply computing solutions. In this way they see how analytical, numerical and qualitative techniques may be used in conjunction with each other.