Stieltjes prize 2018-2019
The jury for the Stieltjes Prize decided to award the prize for the best mathematical dissertation published in the academic year 2018-2019 to Ivan Yaroslavtsev (TU Delft). Ivan Yaroslavtsev will present his work during the first day of the NMC.
Ivan Yaroslavtsev received his PhD degree cum laude, at the Technical University Delft, with supervisors Jan van Neerven and Mark Veraar, for his thesis “Martingales and Stochastic Calculus in Banach Spaces”. The subject of his thesis research lies between the areas of probability theory and (functional and harmonic) analysis.
Martingales are stochastic processes where at each given time the future expectation of the random variable equals the at that time existing and known value of that random variable. Martingales have been applied widely, from physics to financial mathematics. The infinite-dimensional generalisation to Banach spaces, however, runs into difficulties, which Yaroslavtsev by an ingenious approach has managed to overcome.
The Banach spaces to which the theory applies have the so-called UMD property, which has been characterised in terms of Hilbert transforms, a.o. by Bourgain. The proper context here turns out to require a weak topology. Yaroslavtsev proves a decomposition theorem of the type proven by Meyer and Yoeurp in the classical case, he derives Burkholder-Davis-Gundy inequalities, and he provides the foundations for a theory of stochastic integration in this generality. By doing this he solves a number of long-standing problems in stochastic analysis.
Yaroslavtsev has showed himself to be a very productive mathematician. At the time of his thesis defense, he had authored 16 papers, his thesis of about 300 pages is based on only part of those. Despite the rather technical topic, the thesis is written in a clear and accessible manner.He has shown mathematical depth as well as independence He has solved problems which his supervisors had struggled with for a number of years, and according to one expert he has realised the extension of the theory to Banach spaces in this generality ” almost single-handedly”, and he has displayed substantial mathematical creativity. Experts use terms like “breakthrough”, “rare achievement” and “outstanding quality”, and the expectation is that the results will have a considerable impact on the field.
About the Stieltjes prize
Since 1996, the Stieltjes prize is awarded for the best Dutch dissertation that has been defended at a Dutch university. All Dutch dissertations automatically participate in this competition.
The Stieltjes prize is named after Thomas Joannes Stieltjes (1856-1895) and is awarded by the Platform Wiskunde Nederland (PWN). The prize is 2,500 euros, made available by the Compositio Mathematica Foundation.
The jury consisted of Erik van der Ban (UU), Odo Diekmann (UU), Aernout van Enter (RUG, chair), Richard Gill (UL), Frans Oort (UU), Marc Uetz (UT) and Kees Vuik (TUD), with assistance from Marieke Kranenburg (UvA, secretary). A total of 88 dissertations were assessed this time. External advice was obtained at various stages of the assessment.