Seminar

Geometric knot theory studies how geometric properties of space curves relate to their topological knot type.  One of the earliest results is the Fáry/Milnor theorem relating total curvature to bridge number.  Recent work has been partly motivated by applications to the shapes of knotted polymers like DNA molecules.  One interesting problem with some surprising answers asks for the shapes of knots and links tied tight in rope of fixed thickness.  We will consider this ropelength problem, a variant of it for ribbons around knot diagrams, as well as Gromov's notion of distortion for knots.