Stieltjes Prize Award 2023-2024
Day 2 (Wednesday 23 April) @ 15:30–16:15
The jury for the Stieltjes Prize met on 18 December 2024 to award the prize for the best mathematical dissertation published in the academic year 2023-2024. A total of 87 dissertations were assessed. The jury was impressed by the high quality of the dissertations, the number of publications resulting from the PhD candidates’ research, and the independence demonstrated by the PhD candidates. After an intensive discussion, two dissertations remained in entirely different fields of mathematics, both of impressive quality, great originality and extremely well written. The jury concluded that there were no distinguishing elements on which a winner could be decided, hence they decided on two winners:
- Pim Spelier from Leiden University for his thesis “Counting curves and their rational points”
- Leonardo Garcia-Heveling from Radboud University for his thesis entitled “Causality and Time in Non-smooth Lorentzian Geometry”
Pim Spelier
The thesis of Pim Spelier is marked by unusual breadth, depth, and originality. The contributions around moduli spaces address both foundational questions and questions of applications and computations. Similarly, the contributions around rational points both build new tools to control rational points and provide explicit computations. In his work two different topics related to algebraic curves are considered. The first topic is counting curves and intersection theory on moduli spaces of curves. The thesis takes a logarithmic geometry approach, focussing on log moduli spaces and their intersection theoretical properties. The second topic is on finding rational points on curves, using a general principle called Chabauty’s method.
The chapter “Polynomiality of the double ramification cycle” provides a natural, and explicitly computable proof of the polynomiality property. What makes the proof very natural is that it relies inductively on the structure of the moduli spaces in question. In particular one proves polynomiality for all building blocks and all substructures of the underlying structures (the moduli spaces associated to specific graphs). Thus the proof of this particular result follows by putting it in a sufficiently general framework, where the general result follows because the general structure is so very rich.
Rational points on algebraic curves are the source of some of the most important challenges in number theory and algebraic geometry, and Pim’s contributions are remarkable. The improvement on Chabauty-Coleman provided in Theorem 6 is a surprising result. The result of Theorem H which does the same for quadratic Chabauty is certain to find numerous computational applications.
Leonardo Garcia-Heveling
Leonardo’s thesis is exceptionally broad in its scope, ranging from the analysis of concrete models of general relativity to questions of quantum gravity, and from low regularity space-time geometry to full fledged synthetic Lorentzian geometry. This topical broadness is matched by the variety of techniques he has used including Lorentzian geometry, causality theory, cobordism, and the newly emerging field of synthetic Lorentzian geometry. Throughout, the exposition is excellent, with the main ideas always laid out very clearly at the beginning of the papers and a lucid and readable exposition even of the technically more involved aspects. The choice of topics and the highly original approaches Leonardo takes, combined with the expert use of mathematically sophisticated techniques show his impressive mastery of the subject matter.
The works included in his thesis have been published in leading journals, such as Annales Henri Poincare and Communications in Mathematical Physics. His papers have had a large influence on the highly active field of low regularity general relativity and a number of researchers are following up on the ideas laid out in his thesis.
