Symmetries of Riemann Surfaces and Magnetic Monopoles

This repository contains code giving calculations from my PhD thesis. The files are split according to which of the two main chapters the code is relevant for. One section of the thesis is based upon Bring's Curve: Old and New by H. W. Braden and Linden Disney-Hogg, and the code relevant for that section is available here.

Requirements

I shall not give a complete list of system requirements, but as a rough guideline:

• the bulk of the code was written in Sage version 9.4,
• the code training a classifier on theta characteristic orbit data used Python and the additional packages numpy, pandas and scikit-learn,
• additional python packages were required for the plotting of monopole energy density isosurfaces; the corresponding packages may be deduced by reading the imported functions,
• (optional) and further functionality can be added with a licensed copy of Maple which can be ran via Sage,

Acknowledgements

Not all the code contained in this repository is entirely written by me, there are two execptions.

• I had no part in writing grupos_que_actuan.sage and polyB.sage; these were programmed by Antonino Behn and Anita Rojas for the papers Adapted hyperbolic polygons and symplectic representations for group actions on Riemann surfaces by Antonio Behn, Rubí E. Rodríguez and Anita M. Rojas, and A SAGE package for equisymmetric stratification in Mg by A. Behn, A. M. Rojas, M. Tello-Carrera. I have included them here for ease of access, as I use them to compute data on orbits of theta characteristics on which a classifier is trained.
• The files monopole_plotting.py, V4_nahmdata.py and minimal_plotting_from_file.ipynb were developed from an initial source provided to me by Paul Sutcliffe.