Gareth Boreland

Current research project

Information theoretic parameters for graphs and operator systems

This project brings together topics in graph theory and information theory, both classical and quantum.  We survey how many information theoretic ideas can be formulated in terms of graphs.  In quantum information, objects known as operator systems or non-commutative graphs can be thought of as generalisations of graphs.  We explore how various parameters can be defined for a given operator system, and see how these extend the analogy between non-commutative graphs and graphs.  Concepts such as graph entropy and convex corners are generalised to the quantum information setting.

Biography

After graduating in theoretical physics, I worked as a mathematics teacher in a County Down school for a number of years.  I completed a part-time master’s degree in mathematics in 2014, which included a dissertation in graph theory.  This led me to explore the opportunities for further research, and I began this PhD project in 2016, having taken a career break from my teaching job. 

Research interests

• Information theory

• Graph theory

• Linear algebra

• Functional analysis