Jan-Willem van Ittersum

Stieltjesprijs 2020-2021

Day 1 (April 19) @ 15:30 – 16:00

The jury for the Stieltjes Prize met on Friday 17 December 2021 to award the prize for the best mathematical dissertation published in the academic year 2020-2021. A total of 76 dissertations were assessed this time. External advice was obtained at various stages of the assessment. After an initial selection, a shortlist of 13 dissertations was drawn up.

Once again the jury was impressed by the high level of the dissertations. After the first round of discussion, 4 dissertations remained; all 4 of those candidates would have been worthy winners of the Stieltjes Prize. There was, however, one dissertation out of these four of outstanding quality, written by a PhD student who has shown that he has many other qualities as well. The jury therefore awarded the Stieltjesprijs 2020-2021 to Jan-Willem van Ittersum.

Jan-Willem van Ittersum wrote his thesis  “Partitions and quasimodular forms: Variations on the Bloch–Okounkov theorem” at Utrecht University under the supervision of Gunther Cornelissen and Don Zagier (Bonn). In this well-written thesis he investigates how functions of partitions of integers, by way of a statistical physics inspired averaging operation, lead constructively to quasi-modular forms.

The concept of quasi-modular form originates in the work of Ramanujan, but the definition used here is due to Kaneko and Zagier. The thesis addresses three natural fundamental questions:

  1. which collections of functions lead to such forms ?
  2. which forms do arise in this manner ?
  3. when does a classical modular form arise ?

The answers take the form of eight results about properties of such functions and their application. The approach is highly original and far reaching. The results provide new insights in a broad range of subjects, including combinatorics and enumerative geometry. Experts are (pleasantly) surprised by these results. The thesis combines methods from analysis, number theory, algebraic geometry and mathematical physics. A referee wrote: “his thesis is one of the nicest I have ever seen”. 

Already at an early age Jan-Willem van Ittersum demonstrated extraordinary mathematical intuition and comprehension. Both his bachelor thesis and his master thesis contained original work generalizing results of well-known mathematicians. He converted each into a paper that was accepted right away (i.e., without substantial revision) by a journal.

Jan-Willem shows remarkable independence: he formulated the proposal for the thesis topic himself and managed to win a grant to perform the research. In his research he often went his own way, departing from the road suggested (or even recommended) by his advisors.

 Alongside the research for his thesis, he initiated collaborations on other topics, which led to yet another publication as well as three almost finished preprints.