Polynomial knots (Led by Alan Durfee and Donal O'Shea).
The students were:
- Sarah Croog (Mount Holyoke College '01)
- Peter Kim (MIT '01)
- Suzanne Reichel (University of Wisconsin, '01)
- Lee Stemkoski (Boston University '01)
- Oichi (Cornelia) Yuen (UC Berkeley '01)
Three of the students investigated knots in three-space parameterized by polynomials. They found the topological structure of the space of these knots of degree five, thus improving results of Vassiliev. The paper that they wrote is no longer available on the Web site. (A version of this paper has already appeared in the MIT undergraduate mathematics journal.) Suzanne Reichel used methods of A'Campo to find local equations for polynomial knots, and Sara Croog investigated limits of tangent sets to plane curves.