Undergraduate Research Projects

The Relation of Chemistry to Knot Theory
Elizabeth M. Joslyn, Spring 2001

This project investigates the applications of knot theory to chemistry and in particular, whether a moelcule is achiral or chiral, that is whether or not it can be deformed into its mirror image. Roughly speaking, we can think of a molecule as being represented by a graph, and the same applies to knots, so it is possible to apply knot theory to the problem of chirality of molecules. Also to study chirality of molecules, the generalization of knots to links is required at some points.

Note: some figures are missing in the pdf-file.

Discrete Hyperbolic Transformations as Unique Product Groups
Steven M. Hair, Fall 2001

This paper uses the action of groups acting on hyperbolic 2 and 3-space to prove that certain groups are unique product groups. Specifically it is proved that torsion free Fuchsian groups and torsion free subgroups of Picard's group are unique product groups. Though these results can be obtained from the known structure of these groups, it would seem reasonable that the techniques used in this paper will give new examples of unique product groups.