Rutherford Fellowship for mathematics research

Researcher Dr Nick Brettell will be joining the University’s School of Mathematics and Statistics to undertake research on mathematical structures called matroids, supported by a Rutherford Foundation Fellowship. Dr Brettell is currently at Durham University in the United Kingdom.

Nick Brettell headshot

“Matroids are abstract mathematical structures that can be used to describe the geometry underlying discrete objects,” Dr Brettell says. “Any network, including computer networks, subway networks, and even networks of friends have an underlying discrete geometry that is described by a matroid.”

Dr Brettell will be investigating a particular class of matroids—those underlying efficient algorithms and practical networks—that exhibit more structure.

“Matroids in this class can be described by an array of numbers which belong to a finite set with particular properties, known as a field,” Dr Brettell says. “An example of such a finite field is the binary field that consists of only the numbers one and zero, which underpins the binary arithmetic of computers.”

Dr Brettell will be working with the University’s Professor Geoff Whittle, who leads a large research project in matroid theory.

“Characterising these classes of matroids is recognised as a notoriously difficult problem, so the successful completion of this project would be an achievement, and a vital step towards future research in this area,” he says.

Rutherford Foundation Fellowships are awarded to early career researchers in New Zealand to help them establish the foundations for an independent research career. The fellowships support these researchers for two years.

The Fellowships are administered by Royal Society Te Apārangi. Support for this programme comes from MBIE, the Freemasons New Zealand and the Cambridge Commonwealth, and European and International Trust.

Royal Society Te Apārangi President and Chair of the Rutherford Foundation Trust, Professor Wendy Larner FRSNZ, said the Society was pleased to award fellowships and scholarships to these outstanding early-career researchers.

“The Society seeks to support all New Zealanders to explore, discover and share new knowledge. We look forward to hearing what these talented researchers uncover with their research.”