# Andreas Greven is the Kloosterman Professor 2020

German mathematician Andreas Greven is the Kloosterman Professor 2020 at the Mathematical Institute in Leiden. He held the Kloosterman Lecture on 6 February and will give three more in-depth lectures in the weeks after that. ‘I’m really looking forward to this month.’

## A longstanding connection

Greven was the Chair of Mathematical Stochastics at the Friedrich-Alexander University Erlangen-Nürnberg (FAU) but retired in October last year. However, he is still active as a mathematician. Greven will spend February 2020 at Frank den Hollander’s Chair in Leiden as visiting Kloosterman Professor. The Dutch and German mathematicians go way back. ‘For the past thirty years, we’ve been each other’s main co-author. We’ve collaborated a lot, and currently supervise Leiden PhD candidate Margiet Oomen together,’ Greven says.

## How to mathematically describe family trees

In his lectures, Greven will talk about the mathematics of genealogy – the study of families and the tracing of their lineages. ‘It will be about the mathematical treatment of genealogies of populations that evolve randomly. If you have a population, it will have a genealogy – some sort of family three. For any two individuals, each has its ancestors, and maybe they even have a common ancestor. Studying the structure of these genealogies can be interesting, but also challenging.’

As the population evolves in time stochastically, for instance, because the number of children is varying or parts become extinct, the family trees evolve in time. ‘The founding father stays, but what comes after that changes. It’s interesting to study this, for instance for a virus population. In that case, you have an innumerous number of individuals, who have very rapid changes in generations. You need a mathematical description where you can describe an infinite amount of individuals. I will explain how to study and describe this, and how you can model the evolutions of the genealogies.’

‘It’s always better to physically be in the same room and use the same blackboard. It intensifies and improves collaboration.’

Greven is happy to be in Leiden for a month. ‘Twice a year I come here to work with Frank, but that’s usually only for a week or so. Now, we can work together for a longer period of time. I’m really looking forward to that. And I also like to speak to other members of the team, and work intensively together with Margriet.’ Being in the same room is really important in mathematics, he says. ‘Despite the possibilities with new technologies, such as Skype, it’s always better to physically be in the same room and use the same blackboard. It intensifies and improves collaboration.’

### Kloosterman Chair

Every year, a distinguished mathematician is appointed as a visiting professor at the Mathematical Institute, usually for one or two months. This Chair is named after Hendrik Douwe Kloosterman, who was born on 9 April 1900. After studying in Leiden, Copenhagen, Oxford, Göttingen, and Hamburg, he was appointed ‘lector’ in Leiden in 1930 and full professor in 1947. He is mostly known for his work in analytic number theory on what we now call ‘Kloosterman sums’. For more information on the Kloosterman Chair, see here