For Dr Pierre Portal, the tools of his trade are “a pen, paper and a whiteboard” combined with “a lot of staring out the window.”

Dr Portal is a mathematician with the ANU Mathematical Sciences Institute who spends his working days contemplating the problems of harmonic analysis.

“It’s the general phenomenon that various complicated mathematical objects can be written as sums of simple objects.

“The objects you’re looking at could be coming from any science, like physics, chemistry or biology.”

Dr Portal looks at “the type of mathematical analysis which provides a model for finding the most relevant information in signals, such as sounds or images, or even economical and financial data.”

Specifically, Dr Portal deals with “roughness”, a term used to describe a lack of regularity that makes mathematical analysis substantially more difficult.

“With economics, for instance, if we’re talking about purely rational agents having purely rational information then all the mathematics works quite well.

“But if you’re trying to be more realistic, and acknowledge we don’t live in a vacuum and we never have access to all the information, there are all sorts of things we can only measure very imprecisely.

“Mathematically, this means dealing with the effects of random noises, which is quite hard if one wants to do a full harmonic analysis.

“In the last 20 years or so, we’ve realised that we can nonetheless apply harmonic analysis to data which are more irregular than what was thought possible before. This is exciting because it brings us a lot closer to the real world.”

Dr Portal does himself leave his windowsill contemplation for the real world, teaching Mathematics of Finance in the Master of Mathematical Sciences.

“A solid mathematical foundation is increasingly useful in finance because things change ridiculously fast these days.

“The more grounded in pure mathematics your foundations are, the more prepared you are for all the changes that are bound to be made to the mathematical models in the future.”

The ANU Mathematical Sciences Institute is ranked number one in Australia for maths teaching and research. We host some of the best mathematicians in Australia, including 14 fellows of the Australian Academy of Sciences, two fellows of the Royal Society, and ten recipients of the Medal of the Australian Mathematical Society. The Institute offers researchers up-to-date computing facilities including access to the National Computational Infrastructure supercomputer.

We fulfil both a national and international role as a “research institute” in mathematical sciences, working cooperatively with the Australian Mathematical Sciences Institute (AMSI) and international centres. Our students enjoy small class sizes and a personal teaching environment.