Sophie Raynor

I am a theoretical mathematician whose work seeks to understand the most fundamental (abstract) features of structures and systems in nature, information, and mathematics.

In a world full of pressing problems, the value of pure (as opposed to applied) mathematics is not always obvious. Yet most of my work has been motivated by real-word scientific questions like: “how does global data about the brain (e.g. from fMRI scans) relate to microscopic local information about individual neurons and their connections?”. Or, more generally: “can we find general theoretical principles that underly inter-scale relationships and emergent properties in complex networked systems?”.

My research has developed novel methods to solve a long-standing foundational problem related to the mathematics underlying networks with cycles. Current research builds on those foundations to investigate the algebra and geometry of such systems. By investigating the fundamental mathematics underlying complex networks, we can hope to develop new solutions to a range of (environmental, social and technological) challenges: for example, towards improving efficiency and interpretability of AI algorithms.

Inspired by JCU’s unique location and local expertise, I have recently started projects – in collaboration with reef scientists (at JCU and at the Museum of Tropical Queensland) -- to develop new geometric tools for coral classification and reef conservation.

If you are a student interested in learning more any of these themes, or fascinated by shapes, patterns or abstract maths in general, then please get in touch.

I subscribe to Frederico Ardila’s Axioms for Mathematics and recognise the high concentration of mathematical talent -- that is independent of previous mathematical experiences -- among our student cohort. As a teacher, my main focus is on creating genuine opportunities for all students to participate and excel. I welcome questions and conversations on all aspects of inclusion in mathematics.