Cox’s thesis on numerical mathematics was awarded the Stieltjes prize on a ceremony last Friday. The yearly prize, worth 2,500 euro, honours the best thesis in mathematics from a Dutch university.
The selection committee had received sixty-seven theses, which they narrowed down to a shortlist of seven. From these, the jury decided to award the Stieltjes Prize to Sonja Cox’s thesis on numerical mathematics. Cox defended her thesis at the TU delft on March 12, 2012.
Jury chairman Prof. Michel Dekking (EEMCS, TU Delft) praised the quality of Cox’s work (‘a considerable improvement over the earlier literature’) and referred to two large articles in prestigious journals that Cox published together with her PhD supervisor Prof. Jan van Neerven (EEMCS).
“It has been a colossal job”, Van Neerven agrees. “Eighty pages in Numerische Mathematik has cost her two years of work and endless reviews to get an absolutely flawless piece of work. If you flip through her thesis, of which the article makes part, you’ll see pages full of the most delicate approximations. I think the jury has considered the article in her deliberations.”
Cox, from Canadian and German descent and raised in the Netherlands, has worked on differential equations that underlie physical formulas describing heat transport, fluid flows and diffusion phenomena. The problem with these is that they describe an ideal world, in which fluctuations and approximations play no role – as they do in our real world. In practice an engineer has to feed his formula noisy data and hope for reliable outcomes.
Cox has been able to prove that despite the noise, numerical approximations of the differential equations will converge to a solution within a set error limit. And she has also shown that the speed of convergence is close to the theoretical limit.
Cox now works as a postdoc at the ETH in Zurich in search of faster convergence of partial differential equations.
During her PhD research, she has developed a method that not only gives an answer with error limits at one given time, but guarantees that the outcome is within the uniform error limit at any given time of the trajectory. That work is so new that the editors of the scientific journal Numerische Mathematik dedicated 80 pages for it. Another part of Cox’s research was published in the equally prestigious SIAM Journal of Numerical Analysis.
Her works could, and probably will be relevant for practical numerical calculations of flow, heat and stress. However, the theory has to be translated into computer algorithms first. “And we’re not very skilled in the numerical handwork”, Van Neerven says apologetically.
Sonja Cox, ‘Stochastic Differential Equations in Banach Spaces: Decoupling, Delay Equations and Approximations in Space and Time’, PhD supervisor Jan van Neerven (EEMCS), 12 Maart 2012.