Two Veni grants for decisive mathematical research

News - 22 December 2021 - Communication

Young mathematicians Carolina Urzúa Torres and Kristin Kirchner have both received a NWO Veni grant for their promising research. Both of them will develop more efficient computational methods. For Maxwell's equations, which form the mathematical basis for dealing with electromagnetic radiation, and for evaluating large spatiotemporal datasets – that is, data that has been collected over time and space.

Towards a numerical understanding of electromagnetic waves

Although it is quite possible to make an abstract model of electromagnetic waves, it has so far been very difficult, if not impossible, to apply numerical methods to these models. "Think of magnetic Maglev trains, for example", observes Carolina Urzúa Torres, "which fortunately work well in real life. As soon as you try to capture that complex and continuously varying reality in a precise, mathematical simulation you run into numerous problems." At the heart of these problems are the time-dependent Maxwell equations. Because the amplitude of electromagnetic waves changes continuously and unpredictably, a numerical simulation of that reality is often very inaccurate. "There are ways to avoid that, but they are often sloppy shortcuts. I want to work on a solid method."

But the potential impact of Urzúa Torres' research is much larger than just magnetic trains. Numerical simulation of electromagnetic wave propagation is essential in the design of almost all telecommunication systems and modern electronics. With a possible new mathematical framework, more complex problems can be solved, making countless new innovations possible. "From new antennas to new communication systems and new electromagnetic scanners that can do even more precise analysis," adds Urzúa Torres.

A new horizon for spatial statistics

Kristin Kirchner’s research takes place at the intersection of numerical mathematics and statistics. A rare combination that could eventually lead to a breakthrough in the field of spatial statistics. Her Veni project focuses on developing new models and computational methods which can be used for making inference or prediction about spatio-temporal data. Caused by the technological progress in the last decades, in particular with regard to data collection and storage capacities, such datasets have become increasingly common in various scientific fields, such as the environmental sciences or medical imaging. Depending on the application, the spatial location may correspond to the geographical position, as for instance for climate data, but it can also refer to the position in networks or the human body; and the time horizon can vary from seconds to years.

While statisticians have come a long way in developing the field of realistic and practical dependence structures for spatial phenomena in geosciences, ecology, epidemiology and medical imaging, there has been a distinct lack of relevant state-of-the-art numerical expertise, leading to a conflict between model complexity and computational feasibility. It is this conflict that Kristin Kirchner is addressing in her research. "As you can imagine, there are countless variables when forecasting weather, for example. However, since computing power is limited and the models are ultimately too complex, many of these variables cannot be included in forecasting", explains Kristin Kirchner. She therefore aims at developing computational methods resulting in more reliable and effective predictions.

“The wide applicability of my computational methods is one of the reasons why I regard it as crucial to share my results with everyone. My ultimate goal is therefore to make my methods available in the package R-INLA for the statistical software environment R, which is used by practitioners in science and industry."

Veni Vidi Vici

Veni grants, together with Vidi and Vici, are part of the NWO Talent Programme, which is aimed at excellent researchers who have recently obtained their doctorates. Within the Talent Programme, researchers are free to submit their own subject for funding. In this way NWO encourages curiosity-driven and innovative research. NWO selects researchers on the basis of the quality of the researcher, the innovative character of the research, the expected scientific impact of the research proposal and possibilities for knowledge utilisation.

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