Symmetric criticality for ropelength
speaker: Jason Cantarella (University of Georgia)abstract: In this talk, we describe work in progress on a version of symmetric criticality for ropelength. The basic idea is that, given a knot or link K in \(\mathbb{R}^3\) invariant under a finite subgroup G of SO(3), criticality with respect to symmetric variations of K should imply criticality for K. We give some preliminary results along these lines and use them to construct a number of interesting examples of ropelength-critical configurations for knots and links. Main conference: New Computational Approaches to Exploring Polygon and Knot Spaces After devoting a significant effort to finding ropelength-critical configurations of knots using a version of gradient descent, we are ready to face a different question: what is the best way to explore the space of knotted polygons to understand its topology and geometry and search for alternate (or tighter!) critical configurations? In this talk, we discuss some large-scale experiments performed finding critical configurations for more than 500 composite knot types and some new computational approaches motivated by different geometric and topological structures on polygon space. In particular, the symplectic structure proposed by Millson and Kapovich seems to yield a very promising approach to constructing new alternatives to the "crankshaft'' and "folding'' moves now commonly used in exploring polygon spaces.
timetable:
Wed 29 Jun, 16:00 - 17:00, Aula Dini
<< Go back