# Researcher profile: Cecilia Holmgren

## Going to the roots of mathematical trees

**When Cecilia Holmgren was twelve years old, she spent a tedious aeroplane trip inventing a new number series. She had always been driven by a strong desire to solve problems and by the time she was a teenager had already decided to become a scientist. Today, she is breaking ground in the mathematical field of probability theory. **

“I’ve always been rather stubborn,” says Cecilia. “I sat on that plane for maybe fifteen hours and decided to invent something new, and that number series was what I came up with.”

Cecilia Holmgren was happy about her discovery and gave the number series to a family friend as a birthday gift. Later, she also showed it to a professor in mathematics, but to her disappointment, was told that the number series was already known. Despite this, her desire to create new mathematics continued to grow.

**Cecilia Holmgren became interested** in mathematics as soon as she encountered the subject in school. She progressed rapidly and by fifteen, had already completed upper secondary school maths. During her time at upper secondary, she studied university courses at Chalmers with the ambition to become a scientist.

“I was actually interested in two things. I couldn’t decide if I wanted to be a veterinarian or a mathematician.”

Cecilia’s interest in animals was just as strong as her interest in mathematics. When she was three, she found out where meat came from and immediately vowed to become a vegetarian. But what finally made her decide on mathematics was that she wasn’t sure she’d be able to handle cutting into animals. She’d also already taken a large number of university courses in mathematics and wanted to continue.

**When Cecilia finished** her undergraduate studies at Chalmers, she wanted to do a Ph.D. under one of the best mathematicians in Sweden. She searched online and found Uppsala mathematician Svante Janson, a leading researcher in combinatorial probability theory.

“I’d taken several postgraduate courses in combinatorics and probability theory and worked with percolation in my master’s thesis, but it was really just a coincidence that this was precisely what Svante was working with. I was interested in many areas and mostly just wanted to know who was good in general.“

Cecilia contacted Svante Janson and began a Ph.D. under his supervision at Uppsala University. Her doctoral thesis investigated a special type of random tree, so-called split trees. Split trees were a completely new class of random trees and when Cecilia began her doctoral thesis, no one knew their properties.

“My thesis was not applied, but many of the random trees I studied in the thesis come from data algorithms. The most famous example is the binary search tree. It comes from the search algorithm Quicksort, which is used to sort data. Previously, all such data algorithms were studied one at a time, but there was a mathematician in Canada, Luc Devroye (who I incidentally collaborate with now), who had colligated all of these trees into one class and called them split trees.

Once the split trees were brought together, they could be studied at the general level to obtain results that applied to all trees in the class. Cecilia was the first to prove theorems that describe the split trees’ general properties.

When her doctoral thesis was completed, Cecilia went to Cambridge and worked with Béla Bollobás, a world-renowned pioneer in the field of random graphs. Later on, at just 27 years of age, she got a permanent position as a senior lecturer at Stockholm University.

**How did you end up back in Uppsala?**

“I’ve always liked Uppsala and the mathematics department here very much since my doctoral studies and kept my residence here while I was working abroad and in Stockholm. The valuable research collaboration I continue to have with Svante Janson has also been a major influencing factor.”

**Today, Cecilia is a researcher** who loves working on several projects concurrently. She is currently involved in a large number of projects with collaborators in several different countries. She says that it is rewarding to work on several problems in parallel.

“Often, you can be working on a problem and the method you’re using isn’t working, and then discover that a completely different method that you’re using on another problem can be applied in the first problem. That’s why it can be a good idea to work in several different areas at the same time because it can allow you link the areas together.”

**Cecilia finds inspiration** in discussions with other researchers. She likes going to conferences and workshops and to discuss unsolved problems with mathematician colleagues around the world.

“I’ve been going for many years now to a workshop in Barbados that is amazingly rewarding. We discuss various open problems that we’re working on, and suddenly you can see connections – the methods I’m working on might fit in here.”

**Finding new and exciting problems - is that what drives you forward?**

“Yes, exactly. It is through new problems that I learn best. I often get interested in areas that I may have previously thought were a bit boring when I discover that I can use them in my research.”

**What do you do when you get stuck on a problem?**

“Just keep working. Sometimes I come up with the solution when I’m least expecting it. I’ve been out riding my horse, for example, when I realised the solution to a problem. Sometimes I’m not even aware that I’m thinking about it, but I am.”

Cecilia adds that there are no shortcuts to becoming a skilled mathematician. Even if it can seem so, the solutions never come on their own. There is a lot of hard work and knowledge behind them.

**It can be easy to think that someone like you, who has always been good at maths, could solve everything immediately.**

“No, that’s absolutely not true. It takes hard work. The more you work with different things, the better you get at solving problems more quickly and seeing bigger connections.

*Alma Kirlic*

## Postgraduate Studies in Mathematics

If you want to do research in mathematics, then a postgraduate programme is a first step in the right direction. To enter our programme, you need a master's degree in mathematics, or a master's degree in engineering physics. On our website, we usually advertise vacant PhD positions which all eligible candidates are welcome to apply. The advert will be posted in February.

The photo shows Marta Leniec who received her doctoral degree in financial mathematics at CIM last year. Today, she works for Swedbank as quantitative analyst.