Solving word problems via generalisations of small cancellation

This project is concerned with developing new algorithms for working with finitely-presented groups, and other related mathematical objects. We have developed new mathematical language for describing these objects, and have proved that it captures precisely the notions that we need.

Recently, we have proved that our algorithms will work on the largest possible class of finitely-presented groups upon which one could plausibly expect methods of this type to work, namely "hyperbolic" groups. We are now working on proving that our algorithms work for other mathematical objects than finitely-presented groups, which involves generalising the notion of hyperbolicity to other contexts.

One of the key features of this project is that we aim to produce well-documented, useful, code that can be used by mathematicans and others via the computer programming language GAP, which is based at St Andrews. We have now developed an extensive suite of development code, which is already demonstrating impressive run-times compared to existing methods, and we are about to start the process of transforming this into a publicly-downloadable GAP package.