This research is concerned with new applications of topology to molecular biology and chemistry, and consists of three projects. The first is knot theory and DNA, in which the analytical ability of knot theory and the precise new experimental techniques of molecular biology (gel electrophoresis and rec A enhanced electron microscopy) are combined to study enzyme mechanism and substrate configuration. The second is the topological modelling of rotating spiral wave phenomena in excitable media. The techniques of differential topology can be combined with the algebraic topology of knot theory to quantize these wave patterns, and to describe the time evolution of these patterns. The third is polymers and the statistical mechanics of knots, in which knot theory and self-avoiding random walk statistics are used to model volume exclusion effects for polymers of high molecular weight in dilute solution. Some computer computation, simulation and graphics will be required on these projects.
