You go to the closet to pull out that extension cord that has been buried under years of memories. It is a big tangled mess which takes you ten minutes to untangle. You are the victim of random knotting.
Some knots are easier to tie and, thus, more likely to occur in your extension cord. This is one of many ways to measure the complexity of a knot. Another strategy is to find the position of a certain knot that is optimal in some regard (e.g. it takes the fewest number of "sticks" or the least amount of rope to tie). We will explore some measures of complexity, the relationships between these measures, and an application of optimal knots to molecular biology.
This talk is intended for a general audience.