# Mathematics student Alex Colling: ‘Bachelor’s thesis was highlight of my time in Leiden’

Alex Colling himself calls his bachelor's thesis ‘the highlight of his time in Leiden’. And according to his supervisors, that resulted in an outstanding thesis, with great attention to detail. The Mathematics and Physics student worked on a mathematical description of monopoles: hypothetical particles that can tell us more about the origin of the universe. Alex has been nominated for the Science Young Talent Award 2022.

‘A magnetic monopole, if we can ever find one, could give us invaluable information about how our universe came to be,’ Alex says. ‘Monopoles are hypothetical particles with a magnetic charge,’ he explains. ‘Think of a magnet with only a north or south pole. Certain physical theories predict that such particles were formed in the early universe.'

## Using math to describe physics

In addition to mathematics, Alex also studied physics. And that came in handy for this topic. ‘I also covered physical aspects in my thesis,’ he says. ‘Such as what exactly is “magnetic” about a magnetic monopole. In physics, monopoles are a well-known topic. I wanted to treat this subject mathematically as rigorously as possible. This was not always easy: the literature often lacked precisely formulated mathematical theorems and proofs.’

Alex relied mainly on ‘topology’: a branch of mathematics concerned with the deformations of objects (see box). ‘In my research, for example, I used topology to show that there are no deformations that cause a monopole to decay: in other words, they could still be somewhere around us.’

'I had to learn a lot of theory before I even understood what the subject was about.'

### What am I actually investigating?

The first few weeks were the biggest challenge for Alex. ‘Mainly because I had to learn a lot of theory before I could understand what the subject was about in the first place.’ Once that penny started to drop, I loved that I was given so much freedom and that I had the chance to combine ideas from different fields. Not only did I learn a lot about the subject, but I also gained a lot of experience in presenting and writing a thesis. All in all, this period has definitely been the highlight of my time in Leiden.’

## A bachelor's project at a PhD level

According to supervisor Robin de Jong, Alex has more than earned his nomination. ‘Steadily my colleague Ana Achúcarro and I watched the thesis grow into a beautiful piece of mathematical physics. Even the interim versions were all perfectly in order. We had literally zero corrections, cumulative across all the versions we saw. That’s extraordinary. In fact, his undergraduate research and work ethic are already at a PhD level.’ In addition, De Jong praises Alex’s sparkling final presentation and independence. ‘But also his enthusiasm and eye for detail. All in all, it was a pleasure to supervise Alex.’

## On to find a place in academia

Alex is now doing a master’s degree in Mathematics at Cambridge. During his Bachelor’s research, he discovered that the combination of mathematics and theoretical physics really appealed to him. Alex: ‘I am therefore still following both mathematics and physics courses. After my master’s I want to do a PhD and I hope to eventually find my place in academia. In any case, this nomination is a great start.’

### Is a doughnut the same as a coffee cup?

Topology is the subfield of mathematics that studies how spaces are connected. Topology is also called rubber-band geometry. In two-dimensional topology, there is no difference is between a circle and a square. In fact, a circle made of a rubber band can be stretched into a square. However, there is a difference between a circle and the figure eight. In fact, you cannot stretch a figure eight into a circle without tearing the joint in the middle. Similarly, mathematicians often joke that a doughnut is the same as a coffee cup.