# ASML Graduation Prize for mathematics student Pim Spelier – Incentive Prize for first-year student Jorre The

Alumnus Pim Spelier is one of the two winners of the ASML Graduation prizes for mathematics students. He used a new method to solve single polynomial equations. Bachelor student Jorre The wins one of the ORTEC Incentive prizes for the best study results during the first year. On 30 November, the Royal Holland Society of Sciences and Humanities (KHMW) awarded the prizes via a live stream.

## Exceptionally talented

Supervisor Bas Edixhoven calls Spelier ‘exceptionally talented’. The 21-year-old obtained his master’s degree summa cum laude, and according to Edixhoven, also his thesis is of an exceptionally high level. ‘I have never seen a master’s student participate in ongoing research at an international level in such a way,’ he says. ‘I am therefore very pleased that Pim is staying in Leiden as a PhD. With my colleague David Holmes, he is going to research a very exciting and ambitious subject.’

## Fixed number of outcomes

For his thesis, Spelier looked into a very old unsolved problem: proving how many solutions there are to a single polynomial equation (see box). Spelier: ‘Under a few conditions there is only a finite number of solutions but finding them all and giving proof that you haven't missed any can be quite tricky.’ Nevertheless, Spelier managed to elaborate on an old method and write an algorithm on the computer. ‘The Chabauty method I used reduces the problem to simple linear algebra,’ he explains. ‘In the end, I succeeded in proving that my equation has exactly four rational solutions!’

The mathematical problem Spelier has worked on is as follows: describe all solutions of a polynomial equation in 2 variables with rational coefficients. A polynomial is a function that is the sum of multiples of positively integer power functions. The latter are functions such as xk. A polynomial therefore combines several of these power functions.

Spelier has worked on the equation: y2 = x6+ 8x5+ 22x4+ 22x3+ 5x2+ 6x+1

## PhD research

Spelier is pleased with the prize. ‘It is very special and nice to win! I've been to a lot of interesting graduation talks, just from my own field in Leiden. So that the jury decide to choose my thesis from all the studies, feels like a real honour.’

As mentioned before, Spelier will stay in Leiden. He will continue in geometry, but will change subjects. ‘My PhD thesis is about geometric objects that are parameterised, in other words: described in parameters. We know fairly well what happens when there is one parameter, but in the case of multiple parameters, new techniques are needed to better understand what happens.’

## Incentive Prize for Jorre The

On 30 November, the KHMV also awarded the ORTEC Incentive Prizes for Mathematics and Technical Mathematics. These prizes are intended for the best study results in the first year of study. Jorre The is one of the winners of the prize and 500 euro. We have many talented students, says student advisor and assistant professor Onno van Gaans. ‘But even we are occasionally surprised by exceptionally high achievements. Last year our first-year student Jorre achieved the exceptionally high average of 9.7! He completed five courses with a ten. For a ten, you cannot make one single mistake – or maybe just a small miscalculation – in a three-hour examination. And he has succeeded in this five times!’ Also the lockdown and the online education didn't cause Jorres' enthusiasm and working spirit to collapse. As a student assistant he now helps the new first year students.

Van Gaans emphasises that Jorre himself is very modest. ‘So, all the better, that this Incentive Prize puts him in the spotlight and gives him the appreciation he deserves!’

### KHMW Young Talent Awards

On 30 November the Koninklijke Hollandsche Maatschappij der Wetenschappen (Royal Dutch Science Society) presented the so-called Young Talent Awards. In three sessions, 22 graduation prizes, 57 encouragement prizes, 3 research prizes and the ET Outreach Award were presented. The award ceremony could be followed live on the KHMW website.