Packing, curvature, and tangling of filaments

Prof. Jonathan Simon

Department of Mathematics
University of Iowa

March 16, 2005
202 Madison Hall
2:30 PM (Coffee and Cookies at 2:00)

Abstract

How much knotting, or other topological entanglement, is possible with a given piece of string? It is intuitively "obvious" that if a person is given a short, thick piece of rope, then it is impossible to tie complicated knots. But turning this into mathematics has taken some time and effort by a number of researchers.

In this talk, we will consider several theorems that help explain how length, thickness, and stiffness of filaments can limit the possible tangling.

If time permits, we also will discuss a particularly simple model of random, packed filaments designed to help clarify the question of whether "average crossing number" is a fair measure of entanglement in random filament processes.