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Organizers |
Elastic knots
by
Philipp Reiter
University of Georgia
Coauthors: Heiko von der Mosel; Henryk Gerlach; Sören Bartels
It is an interesting experiment to form a knot in a piece of springy wire, stick the endpoints together, and release the configuration. Can we predict the resulting shape?
In this talk we will present an outline on this question which goes back to the work of Joel Langer and David Singer in the 1980s and report on recent developments.
Considering an elementary model which only relies on the bending energy of the centerline of the wire, the answer should only depend on the respective knot class.
We face a free obstacle problem that involves techniques at the interface of geometric analysis, low-dimensional topology, modeling, numerical analysis, and nonlinear optimization.
Date received: November 17, 2018
Copyright © 2018 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbpq-16.