Dr Georg Maierhofer is a Henslow Fellow at Clare Hall and works in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. His research interests lie in Computational Mathematics for Partial Differential Equations (PDEs). PDEs are a central foundation of modern scientific modelling and help describe phenomena as varied as atmospheric processes and the generation and propagation of noise in the form of sound waves. Computational Mathematics is used to simulate nature by solving these PDEs approximately and without such numerical techniques many of humanity’s greatest technological and scientific advances would be impossible – from supercomputers processing terabytes of data on a daily basis for weather forecasting to sophisticated numerical models predicting the movement of atoms in particle accelerators.
Dr Maierhofer’s main research concerns the study of so-called structure-preserving numerical methods for PDEs – algorithms which can replicate the ‘physical behaviour’ of solutions to PDEs, by preserving associated conservation laws such as the preservation of energy. A particular focus lies on the understanding of properties of symplectic methods when applied to infinite-dimensional Hamiltonian systems – differential equations that can be written in a unified formalism that encompasses a powerful mathematical description of many physical systems and their conservation laws. The rigorous understanding of advantages and limitations of such structure-preserving methods could lead to improved simulation tools for example improving the accuracy of weather forecasts.
This research is complemented by a broader interest in the applications of computational mathematics, such as the simulation of extreme ocean waves, and the use of machine learning for the enhancement of classical methods from numerical analysis, for instance in meshing problems and the acceleration of classical solvers for time evolution PDEs.
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Kipling’s “Iron‒Cold Iron‒is master of them all” captures the familiar importance of metals as structural materials. Yet common metals are not necessarily hard; they can become so when deformed. This phenomenon, strain hardening, was first explained by G. I. Taylor in 1934. Ninety years on from this pioneering work on dislocation theory, we explore the deformation of metals when dislocations do not exist, that is when the metals are non-crystalline. These amorphous metals have record-breaking combinations of properties. They behave very differently from the metals that Taylor studied, but we do find phenomena for which his work (in a dramatically different context) is directly relevant.
During the Covid-19 pandemic, U.K. policy-makers claimed to be "following the science". Many commentators objected that the government did not live up to this aim. Others worried that policy-makers ought not blindly "follow" science, because this involves an abdication of responsibility. In this talk, I consider a third, even more fundamental concern: that there is no such thing as "the" science. Drawing on the case of adolescent vaccination against Covid-19, I argue that the best that any scientific advisory group can do is to offer a partial perspective on reality. In turn, this has important implications for how we think about science and politics.
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