Arunima Ray, Brandeis University (SUNY Geneseo, Class of 2009)
Is the Set of Knots Fractal?
Knots are everywhere - in your shoelaces, neckties, and usually your earphones. The field of knot theory is devoted to the study of questions like: Are there infinitely many knots? When are two knots the same? How can we tell if one knot is more or less knotted than another? I will discuss the basics of knot theory along with a family of natural functions on the set of all knots. We will then investigate a recent conjecture that this family of functions gives the set of knots (modulo an equivalence relation) the structure of a fractal.