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Grenfell Matters: Mathematicians in Mexico

Robert Bailey
Robert Bailey - Contributed

Being a research mathematician is, in some respects, the ultimate “ivory tower” profession.

Essentially, it involves being paid to sit in a room and think, but it’s not always that way. It’s a very international business, with researchers in one field being scattered in many countries across the world.

So, it is not all that surprising that, for a week in September, I got to travel to the Casa Matemática Oaxaca (CMO) in Oaxaca, Mexico.

The CMO is an institute set up in 2015, as an affiliate of the existing Banff International Research Station, set up in 2003 in Banff, Alta.

The two institutes (which receive Canadian, American and Mexican government funding) each host week-long themed workshops throughout the year, each of which attract groups of researchers from around the world, providing them with an ideal environment to hear presentations on new research results, make contact with potential collaborators, discuss new research ideas, and actually make progress on their work. Proposals for workshops are invited from anywhere in the world.

In our case, the workshop was “Symmetry Breaking in Discrete Structures,” organized by myself and two colleagues, one from Austria and one from the U.S. In layman’s terms, the idea of “symmetry breaking” can be explained like this: a cube is a very symmetrical shape, but if you were to start painting its six faces with different colours, this symmetry would be “broken.” But, what is the most efficient way of doing this? And how can we measure what “efficient” even means?

Remarkably, when considering structures much more sophisticated than a cube, there are many open research problems on questions of this type. There were 35 of us attending the workshop, not just from Mexico, Canada and the U.S., but also the UK, Poland, Slovakia, Iran, and as far away as Australia and New Zealand. Many languages were spoken around the dinner table!

A question that pure mathematicians are always asked is, “What use is it?” and this is not easy to answer, as the work is often not motivated by immediate practical applications. However, these applications often come along much later. Some famous examples include the mathematics behind many modern data security techniques (such as those used in online banking or biometric passports), which date from the 19th century, or the original PageRank algorithm which made Google its fortune, which is dependent on the Perron–Frobenius theorem obtained in 1912, long before anyone had imagined internet search engines. Maybe, in 100 years’ time, someone will find an important application of symmetry breaking.

The other question we are asked is “How does this contribute to the community?” Readers may wonder what value such seemingly esoteric material adds to the local economy. However, it is important to note that this research is being done not just anywhere but here, in western Newfoundland. A postdoctoral researcher recently relocated to Corner Brook all the way from Australia to work in mathematical research at Grenfell Campus, and his income is spent here, supporting local businesses.

In a region with a declining and aging population, even small contributions help.

Robert Bailey is an assistant professor at Grenfell Campus, Memorial University of Newfoundland.

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