December 8, 2017

New frontiers in maths research leads to international award

From the waves that rhythmically lap our shores to gravitational waves that have intrigued scientists for decades, Dr Glen Wheeler is using maths to understand nature.

Dr Glen Wheeler, from UOW’s School of Mathematics and Applied Statistics (SMAS), studies nonlinear partial differential equations, with a specific interest in the motion of surfaces through their curvatures (called curvature flow), which has been one of the cutting-edge areas of contemporary mathematics for many years.

While curvature flow is grounded in complex maths and could seem a world away from the people who are steeped in the world of fundamental maths, his work is helping to predict bushfire movement, offer clues for the treatment of blood disease and new developments in materials science.

“In this type of fundamental maths, we take something we observe in nature, use abstraction to make mathematical models that we can manipulate and interpret back to the real world,” Dr Wheeler said.

“I’m really interested in transition states. For example, when a block of ice melts, that surface area where the solid and fluid transition from one state to the other is really fascinating.

The same fundamental maths that describes transition states can be applied to fire fronts. Where two fire fronts travelling toward each other join they become incredibly intense and the speed of the front increases.

“Yet in the transition state a curve is formed and the curvature of that curve can actually predict the jump velocity or speed of the fire,” Dr Wheeler said.

“During extreme fires such as the Canberra fires in 2003, the movement of front was said to be unpredictable but data and the right models can predict the movement quite accurately.

“The key is to develop a useable model. It’s no good having a model that is impossible to implement and integrate into existing systems.”

Usable insights continue to drive Dr Wheeler. As well as its intrinsic mathematical development, his research has led to substantial advances in the theory underpinning semiconductor design, image processing and relativity.

His interest in how things in the physical world work at a mathematical level began long before he became an academic.

Dr Wheeler was a self-taught programmer who at age two was tapping away on a Commodore 64.

He studied a Bachelor of Computer Science and a Bachelor of Maths (Advanced) and entered industry for a time but was drawn back to academia and completed his PhD at UOW in 2010.

"I want to make a difference, to inspire people to think more about the world around them." - Dr Glen Wheeler

“We really don’t understand that much about the universe. We can’t yet accurately describe how a tree might grow,” he said.

“When you look at what the mathematical models predict and what actually happens in nature they can be very different and the challenge is to continually refine our understanding to reconcile that difference.

“Our job as researchers is to push the edge of what is known, to create new knowledge and understanding. I want to make a difference, to inspire people to think more about the world around them.”

During his career he has been awarded fellowships in Germany, including an Alexander von Humboldt Fellowship in 2010, and visiting fellowships in the US, China and South Korea.

In 2015 he received $450,000 in funding from the Australian Research Council as part of a team to further investigate curvature flow.

He recently won the 2017 Peter Schwerdtfeger Award, which recognises the academic and professional achievement of members of the Australian Association of von Humboldt Fellows (AAvHF).

The Humboldt Foundation is a global academic organisation spanning multiple disciplines that takes its name from the famous German thinker Alexander von Humboldt (1769 - 1859).

The 2017 award, presented at a formal dinner event at Te Papa, the National Museum in New Zealand by the German ambassador to New Zealand, is given once every two years and spans all scientific disciplines. It is the first time the award has gone to mathematics.

“The award is wonderful recognition that I’ve been doing good work in my field, particularly because it’s the first time it’s been awarded to a mathematician,” Dr Wheeler said.

“Math underpins everything we do and is so important in an increasingly technology-driven world. For example, you don’t get to develop Wifi without the maths underpinning signal processing.”

Faculty of Engineering and Information Sciences Executive Dean Professor Chris Cook said: “This award is a great achievement for Glen and also a great outcome for maths as a discipline, as well as for maths at UOW.”