In this talk, I'll describe ongoing work with Jason Cantarella, the goal of which is to obtain a sharp upper bound for the writhing number in terms of length and thickness of the DNA, and to describe the patterns of coiling which achieve, or come close to, this maximum.
I'll give an overview of the project, including the ideas from electrodynamics which have given us our best hope for a solution, use videos to demonstrate the computer modelling techniques which we have found so helpful, and end by showing how to transform the problem into one which searches for the largest eigenvalues and corresponding eigenfunctions of a family of compact integral operators on Hilbert space.