A retreat to nature that stimulates new mathematical thinking

Brainstorming, deep discussions and collaborations at the University of Melbourne’s forestry campus foster new ways to tackle mathematical problems, including modelling COVID-19 and the mathematics of string theory.

In the small town of Creswick, an hour and a half drive west of Melbourne, groups of mathematicians and statisticians from around the world are taking up residence on the forest science campus of the University of Melbourne for MATRIX residential research programs and workshops.

The MATRIX institute is a partnership between the Australian National University, Monash University and the University of Melbourne that provides key infrastructure for facilitating and supporting research in the mathematical sciences in Australia and the broader Asia-Pacific region. The Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS) and the University of Queensland are associate members.

Researchers in all scientific fields regularly gather for conferences, but MATRIX research programs are different. Professor James McCaw, a mathematical biologist from the University of Melbourne, says while conferences allow people to hear from other people, they don’t have much unstructured time for discussion and dedicated interaction time that leads to deep collaboration.

Sometimes these conversations lead to dead ends, and sometimes they spark a plan that will take decades to complete. Other times, the outcomes are more immediate, perhaps unexpectedly so.

Following the research program that Professor McCaw co-led with Associate Professor Jennifer Flegg in July 2019, it was not long before some of the outcomes were put to the test in rather dramatic circumstances.

Professor McCaw has, alongside colleagues around the world, studied and developed epidemiological models for over fifteen years, including at research institutes like MATRIX. When the COVID-19 pandemic struck his group was prepared and ready.

“At MATRIX we explored new ways to model and analyse data on household transmission of disease from so-called First Few Hundred (FFx) studies,” he says.

These studies involve rapid data collection in the early stages of a pandemic from the first few hundred cases and their close contacts.

“These data and the newly developed analysis methods in applied probability were put to the test in 2020,” says Professor McCaw.

“Australian researchers, many of whom attended the MATRIX research program, led the design of the World Health Organization's FFx studies, which were deployed in Australia to learn more about COVID-19 transmission dynamics.”

Professor Jan de Gier, who has been the director of MATRIX since it formed in 2015, points to examples like this of the importance of continued research in the mathematical sciences, and the effectiveness of residential research programs at international research institutes.

“In MATRIX, Australia now has such an advanced mathematical research institute of international calibre, with the obvious added benefits of developing new knowledge and educating new generations on home soil,” he says.

Professor de Gier believes the interaction not just between internationally renowned researchers, but also younger, early career researchers, drives further innovation.

Recent DECRA awardees Dr Sasha Garbali and Dr Yaping Yang attended a MATRIX research program on Geometric R-matrices in 2017. R-matrices have their origin in statistical physics and are key ingredients to mathematical models that describe features of a wide variety of systems such as ice crystals, freeway traffic or quantum spin chains.

A recently developed connection between R-matrices and symplectic geometry (the mathematical structure behind dynamical systems such as those used to forecast weather, epidemics, and used in more abstract areas like quantum cohomology, an important tool for string theory) has created a buzz for this type of mathematics.

R-matrices research is highly abstract and deep, and currently developed by a relatively small field of experts, so being able to spend a week mixing with 20 of the top researchers in this field internationally was a formative experience for these young academics.

Dr Garbali says the location, amongst nature and away from distractions, was inspiring.

“The surrounding nature of the institute creates a pleasant atmosphere, helps the attendees to forget their usual distractions and better focus on solving common problems.”

Gatherings of intellectuals to stimulate discussion and collaboration is not a new phenomenon.

Professor Arun Ram, Chair of Pure Mathematics at the University of Melbourne, has long been fascinated by the 19th century ‘Mendelssohn Salons’, gatherings of physicists, mathematicians and musicians at the home of Abraham and Lea Mendelssohn, for evenings of music, science and deep discussion. He sees similarities in the MATRIX research programs but says that these modern programs are “so much more intense”.

“You go on a hike and chat about things, then there might be an official planned brainstorming session, then there is dinner with the same group where you can spend the evening talking about what you’d like to prove in 10 years. You see the whole group the next morning at breakfast and everybody has new, exciting, thoughts on the problems that only came into focus during the night.

Professor de Gier is keen for MATRIX to continue to innovate and create spaces for new kinds of collaborations. He is excited to get back to in-person research programs after moving to virtual workshops in 2020. In November 2021, the institute ran its first in-person women-only research program, on the topic of Analysis and Topology.

First published on 15 February 2022.

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