Abstract or Additional Information
Geometrical knot theory is an area of mathematics that has been growing in activity over the last few decades. It involves the study of specific shapes of knotted curves, rather than their topology, where the specific knot shape is fixed by some criterion, typically minimizing some form of knot energy. In this talk I will introduce some older work of both my collaborators and I, as well as others, on the specific case of ideal, or tightest, knot shapes. I will start by explaining the analytical difficulties, along with some associated theorems. Then I will describe some numerical results concentrating on the specific case of the ideal trefoil. And finally I will describe some very recent experimental results for the ideal trefoil obtained by the group of Pedro Reis at the EPFL.