Associate Teaching Professor
6214 Wean Hall
Department of Mathematical Sciences
Carnegie Mellon University
5000 Forbes Avenue
Pittsburgh, PA 15213
Ph.D., Rice University
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.
Handron, David G.C. (2002). Generalized Billiard Paths and Morse Theory for Manifolds with Corners. Topology and its Applications, 126, 83-118.