Petersen opens the door to his office in the new Albano complex at Stockholm University. Just ten years ago this was nothing more than a sprawling expanse of gravel. The complex now houses 70,000 square meters of university facilities and a thousand student and researcher apartments.

Behind the modern facades lie open areas and corridors lined with study facilities. Not many of them are vacant; the air is filled with the murmur of discussion. But when Petersen closes the door behind him, calm descends, giving him the peace and quiet he needs to work.

Like the majority of mathematical researchers, he makes most of his progress with the help of pen and paper. But rarely alone.

“Being in the right place at the right time can be crucial. You need to get around and be curious about what other people are working on.”

Progress in Petersen’s field is achieved through intensive teamwork. The findings that attracted most attention are the result of his collaboration with six international co-authors.

“The ideal situation is when we manage to find time to work together. It’s much easier to get an idea across on a white- or blackboard. So we often invite each other over to work at our respective universities. The Scholar grant has made it much easier for me to host meetings with my colleagues,” he says.

Keeping abreast of developments

Petersen stresses the importance of keeping up to date in the subject. Every day he scans the Arxiv website for articles on algebraic geometry and algebraic topology. Arxiv is a forum for sharing scientific articles that have not yet been accepted by a scientific journal. It has also become a site that brings researchers together.

“It would be virtually impossible to gain a similar overview using the printed journals. I often see things on Arxiv that give me new ideas.”

My branch of mathematics requires me to peruse scientific articles from many different fields. I then have to identify the links between apparently disparate subjects and findings.

His research centers on the mathematical properties of moduli spaces of Riemann surfaces. Riemann surfaces were introduced in the 19th century by the German mathematician Bernhard Riemann as a tool for linking together different fields of mathematics and physics. Nowadays they play a key role in many scientific fields, such as number theory in mathematics and string theory in physics.

“As a mathematician I think it’s an unusually interesting field. It brings me into contact with many branches of the subject. Even though I’m researching in pure mathematics, the work is interdisciplinary.”

A Riemann surface may be described as a two-dimensional surface on which it is possible to measure angles but not distances. The moduli space is in turn a mathematical structure that is used as a kind of map of the landscape of all Riemann surfaces. By studying the moduli space it is possible to gain a deeper understanding of how Riemann surfaces behave.

“Since the map is an indirectly defined space, it is difficult to understand geometrically. Many people have long wondered what that space could look like.”

Mathematics without counting

Petersen fell for mathematics during one of his first courses in engineering physics at university. There was a trial project offering a special course in more advanced mathematics.

“The assignments we were given on the course did not entail calculating different solutions; it was a question of proving why a given postulation was true. I thought that was much more fun than all the other courses and it was also something I was good at.”

He soon began to look forward to each assignment so much that he started working on them already on the subway home from university.

His interest led him to a PhD. Around that time he became a father for the first time, and was looking forward to some paternity leave after defending his thesis. But shortly before he was due to go on leave he received an e-mail from a professor at ETH Zurich.

“He made me an offer that was too good to pass up. So we moved to Switzerland for six months. Mathematically speaking, it was a very productive time that put me in touch with people I still collaborate with.”

Collaboration vital

Cross-border collaboration is vital in mathematics. The first ideas behind the article mentioned earlier were formed at Stockholm University. But by sharing them with other mathematicians throughout the world, the pieces gradually came together in a real breakthrough.

“Everyone contributed their specialist expertise, enabling us to create a more comprehensive understanding of a certain mathematical assumption than had ever been achieved before.”

The results attracted attention within the world of mathematics. Following publication, Petersen and a co-author were invited to give a series of lectures at the Institute for Advanced Study (IAS) at Princeton in the U.S. Additionally, the research findings will be the topic of a forthcoming Bourbaki seminar in Paris. Each year around ten of these seminars are held, with a prominent expert being invited to present someone else’s work.

“The seminar is highly prestigious. The idea is to draw attention to the most interesting recently proven findings in mathematics. And if it’s not held in French only, I’ll probably attend.”

Text Magnus Trogen Pahlén
Translation Maxwell Arding
Photo Magnus Bergström