# Honouring a mathematical legacy: Edixhoven fellow tries to understand millennia-old problems

Not all problems are easy to solve, but with enough bright minds, you make progress step by step. ‘The kind of problems I am interested in have been occupying mathematicians for over two millennia,’ says theoretical mathematician David Lilienfeldt. In September, he started at the Mathematical Institute (MI) as the first Edixhoven Postdoctoral Fellow. The fellowship was set up to honour Professor Bas Edixhoven, who passed away in January 2022.

‘The conjecture I will be working on was first formulated 40 years ago,’ tells Lilienfieldt. ‘Yet, it remains wide open. The Beilinson-Bloch conjecture predicts a beautiful connection between the realm of Algebra and the realm of Analysis.’

## Driven by the desire to solve problems

A better understanding of the conjecture will have important consequences for several fields within mathematics. In theoretical mathematics, research is not necessarily motivated by applications to the real world, Lilienfeldt stretches. ‘It is rather driven by curiosity and the desire to solve problems, simply because they have puzzled mathematicians for centuries or maybe even millennia. However, if my work ends up being useful for practical purposes by other scientists, then I would be more than happy! Perhaps in the field of cryptography.’

## Edixhoven always had time for maths

This mindset is fully in line with Bas Edixhoven’s legacy. ‘Because you couldn’t make Bas happier with anything than a mathematical problem,’ former colleague and professor in Mathematics Ronald van Luijk says. ‘No matter how busy he was: if you came in with a question about maths, his eyes started to sparkle, and he would put his fountain pen down. Maths, there was always time for that.’

## A renowed mathematician with two feet on the ground

Edixhoven was a world-renowned mathematician and one of the best in his field of algebraic geometry. ‘Everyone in that world knows his name,’ says Van Luijk. ‘Before you had finished your question, he already knew the answer. Leiden professor Hendrik Lenstra always says it seemed like he got his answers from the stars. Bas lived and breathed mathematics.’

Yet Edixhoven was anything but unworldly. He was actively working for a better world. For instance, as an energy coach to make his neighbourhood the Merenwijk more sustainable. He sang in a choir and had a great affinity for art. Van Luijk: ‘In which he, of course, also saw mathematics. And besides all of that, he was just a very nice and sociable person.’

## Filling the math teacher gap

He was also concerned with education, especially the shortage of maths teachers in the Netherlands. As chairman of the organisation Wisk4all, Edixhoven dedicated himself to tutoring aspiring math teachers from other professions in mathematics.

‘Bas was dedicated to everyone and the whole institute.’

### A tribute in the form of a fellowship

The MI had been wanting to set up a postdoc fellowship for some time. ‘And it’s very fitting that we can now do that in honour of Bas,’ Van Luijk says. The fellowship is not dedicated to one particular field. ‘Because Bas was committed to everyone and the whole institute. So mathematicians from any field can apply. Although Lilienfeldt happens to have a nice interface with Bas’ work.’

## Honouring a mathematical legacy

Lilienfeldt met Edixhoven during his time as a PhD candidate at McGill University in Montréal, Canada. ‘I was a member of his research project group at the Arizona Winter School in 2020. Under his guidance, fueled by his striking enthusiasm and mathematical generosity, I wrote a joint paper generalising the geometric approach of Bas and his then PhD student Guido Lido. From that moment on we kept in contact, as I was interested in coming to Leiden to work with Bas.’

‘Like everyone else in the mathematical community, I was shocked and saddened to learn of Bas’ sudden and untimely passing. I am grateful to have been awarded the inaugural Edixhoven Postdoctoral Fellowship, which offers me a unique opportunity to honour his mathematical legacy.’

### About David Lilienfeldt

David Lilienfeldt (29 years old) is originally from Denmark. His mathematical education started in Switzerland, where he obtained his bachelor’s and master's degrees in mathematics from the École Polytechnique Fédérale de Lausanne. Lilienfeldt wrote his master’s thesis during an exchange semester at Harvard University.

Encouraged by his overseas experience, Lilienfeldt moved to Canada to pursue a PhD in number theory with Henri Darmon at McGill University, which he completed in 2021. In this period, he was awarded a Graduate Scholarship and a Scholarship for Outstanding PhD Candidates from the Institut des Sciences Mathématiques du Québec. Lilienfeldt also received a Pelletier Fellowship by the Faculty of Science of McGill University. Upon completion of his PhD, he received an Emily Erskine Postdoctoral Fellowship to work with Ari Shnidman for two years at the Einstein Institute of Mathematics of the Hebrew University of Jerusalem.

Since September 2023, Lilienfeldt has been the inaugural Edixhoven Postdoctoral Fellow at the Mathematical Institute of Leiden University.