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Vertex Distortions of Lattice Knots
Student-Run Research Seminar| Speaker: | Nicholas Cazet, UC Davis |
| Location: | Zoom |
| Start time: | Thu, Apr 16 2020, 12:10PM |
The vertex distortion of a lattice knot is the supremum of the ratio of the distance between a pair of vertices along the knot and their distance in the `1-norm. We show analogous results of Gromov, Pardon and Blair-Campisi-Taylor-Tomova about the distortion of smooth knots hold for vertex distortion, the vertex distortion of a lattice knot is 1 only if it is the unknot, and that there are minimal lattice-stick number knot conformations with arbitrarily high distortion.
This project has an application to Biology and enjoyable to those in combinatorics.