Ella Kirschner & Jakob Heidrich
To make use of knot theory in astrophysics, I will introduce a modified version of the three-body problem, the so-called CR3BP. To classify orbit families, I will define the Alexander polynomial, a knot invariant.
The paper "Application and implication of knot theory to the circular restricted three-body problem" by Mason R. Mill and Robert A. Bettinger, which my talk is based on, is the first paper to identify non-trivial knots in the CR3BP trajectories.
My talk is based primarily on the essay "A Short History of an Elusive Yet Ubiquitous Structure in Chemistry, Materials, and Mathematics" by Stephen T. Hyde, Michael O'Keeffe and Davide M. Proserpio.
I will introduce the concepts of tilings and of symmetries in nets and crystal structures in order to understand the properties of the srs net. Throughout the talk, I will provide insight into the history of research on the srs net, in particular how it came to be studied independently in different branches of science. Finally, I will present examples of occurrences of the srs net or its corresponding minimal surface, the gyroid, in materials, crystals and in nature.
