[Last updated March 29, 2001]

Some of the themes of my work are described in the following abstracts of research proposals funded by the National Science Foundation.- The abstracts "Knot Theory and Algebraic Geometry in the Large" and "Problems in Knot Theory and Low- Dimensional Topology: Applications of Quasipositive Knots and Surfaces" describe topological research I've been engaged in for many years. Links to several papers based on that research can be found on the page listing my publications.
- The abstract "Looking Into Mathematics: A Visual Invitation to Mathematical Thinking" describes research in mathematics education and visualization; I was a consultant on that project, and my fall 1997 First-Year Seminar (Math 108, "Looking Into Mathematics") was one of the pilot sections described in the abstract. Some of the "new visual tools" mentioned were developed by my fellow consultant Jeff Weeks (holder of a MacArthur Foundation "genius grant" for 1999-2000) and can be explored at his Topology and Geometry Software web page.