Ideal knots: The trefoil, analysis and numerics to experiment

John Maddocks (EPF Lausanne)

24-Nov-2020, 18:00-19:00 (3 years ago)

Abstract: 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, onĀ  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.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometrynumerical analysisoptimization and control

Audience: researchers in the topic


Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php

Organizers: Simon Blatt*, Philipp Reiter*, Armin Schikorra*, Guofang Wang
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