April 24, 2014

Gongfest conference a quantum leap in fundamental maths

When Austrian mathematician Johann Radon came up with a series of calculations in 1917 that would later bear his name, he would have had no idea they would one day be used in everyday medical imaging.

Yet, such is the nature of fundamental mathematics - the study of fundamental mathematical structures without knowing their application or impact. 

Fundamental mathematics has led to many of the developments that drive the modern world, from medical imaging to computer science and high finance.

This week the University of Wollongong hosted a gathering of local and visiting mathematicians who are tackling the fundamental problems in operator algebras and non-commutative geometry.

The gathering, called ‘Gongfest III: Beyond Thundergong’, is now in its third year and is fast becoming an Easter tradition.

Associate Professor Adam Rennie, from the School of Mathematics and Applied Statistics (SMAS) in the Faculty of Engineering and Information Sciences, said Gongfest started three years ago when he moved to UOW from the Australian National University and an informal meet and greet, based on conversations about maths, was held.

It has grown from there, building interest from the Australian mathematics research community.

“Everyone attending is engaged in fundamental research,” Professor Rennie said. “The sorts of problems we are working on often have long-term applications. Look at the transistor and what impact it has had on the world of computers, yet it’s a form of quantum mechanics that was once very fundamental mathematics.” 

Professor Aidan Sims from SMAS said operator algebras and non-commutative geometry were mathematical models for quantum-scale variables. 

“They extend geometric ideas - such as position and speed - to the quantum world, allowing a new kind of geometric intuition to replace faulty large-scale physical intuition.

“Our physical intuition is based on what we can see,” he said. “At this scale, it seems we can precisely measure a few variables, such as position or speed, and then predict how they’ll behave. But that’s not how the universe works: measuring one quantum variable affects the values of the others.

“We don’t see this day to day for the same reason that if we randomly coloured each pixel of a football-field-sized screen a million times a second and watched it across Sydney Harbour, we’d see a predictable shade of grey rather than each individual colour change. But it matters enormously if we want to develop quantum-scale technology.”

Professor Rennie said a key part of the now annual conference was to form research collaborations with leaders in the field.

“UOW’s research in non-commutative geometry and operator algebras is constantly expanding the boundaries of these research fields, and GongFest provides a relaxed forum for scientific interaction with other world leaders,” he said.