Speaker: Erik Schreyer

Title: Chains of Spheres and Excluded Volume

Abstract: The inclusion of a notion of excluded volume of linear molecules spearheaded a breakthrough in polymer science. Extensive research to mathematically model excluded volume phenomena has been conducted in particular in the area of geometric knot theory. There the classical notion of thickness and ropelength of a knot have gained much attention. In my talk we will explore the ball number of a knot - the smallest number of tangentially touching non-intersecting equal sized spheres that is necessary to tie a knot. As the spheres are non-intersecting such chains of spheres inherently include a notion of excluded volume. We will concentrate on the open question of the ball number of the trefoil knot, or in other words, how many balls are neccessary to tie a knot at all. The smallest example is a fifteen-ball trefoil knot.