Linden Disney-Hogg (University of Leeds) – Locations of JNR skyrmions

Skyrmions, topological solitons arising in nonlinear sigma models, have long been proposed as effective models for atomic nuclei. While exact solutions remain unknown, a variety of approximations, often inspired by better understood solitons such as monopoles and instantons, have been developed. In particular, Sutcliffe recently introduced a novel approximation using an ultra-discrete computation of the holonomy of a JNR instanton. In this talk, I will outline the mathematical framework behind this construction, before focusing particularly on the constituent locations of the resulting Skyrmions. I will present new theoretical and computational tools for analysing these locations, reveal their connections to classical geometry and monopole theory, and discuss their potential implications for future research. Based up joint work with Josh Cork.