Dr Francesco Fournier-Facio is a Herchel Smith Fellow at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. He works in the field of group theory, which is the algebraic language that mathematicians use to talk about symmetry. Symmetry is everywhere in mathematics, and accordingly groups appear as a natural tool to approach all kinds of problems. Group theory is also widely used in physics, chemistry, and computer science. The general principle is that understanding the symmetries of an object of interest can cut down the amount of information needed to understand the object completely. This can make the difference between a problem that simply cannot be solved, and one that is easy to approach.
Despite their initial algebraic appearance, groups have a fundamentally geometric nature. The flavour of Francesco’s research, commonly called geometric group theory, focuses on this. This features a mixture of algebra, geometry, but also topology and dynamics. The main object of Francesco’s research is called bounded cohomology, and it is a tool that allows to encode all the possible ways in which a group can be realized as the symmetries of certain geometric objects.
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Dementia is a topic of considerable public interest. How empirical evidence has contributed to this societal awareness and indeed fear will be covered in this talk. It will span research from the 1980s when not much was understood about dementia up to contemporary perspectives. The focus will be on the epidemiological and public health evidence base, and how this relates to the results published from clinical and lab based research. The findings from UK and other high income countries of reduced age specific prevalence (%) will be explored, and the implications of results from brain based studies that dementia is not inevitable in the presence of ‘alzheimer’ type changes. The role of inequalities, risk varying across countries and time and our knowledge about protective factors have strengthened during recent years, and the balance of high risk with whole population approaches to reducing risk for society will be considered.
One of the many outstanding achievements of G I Taylor was the discovery of relatively simple statistical laws that apply to highly complex turbulent flows. The emergence of simple laws from complexity is well known in other branches of physics, for example the emergence of the laws of heat conduction from molecular dynamics. Complexity can also arise at large scales, and the structural vibration of an aircraft or a car can be a surprisingly difficult phenomenon to analyse, partly because millions of degrees of freedom may be involved, and partly because the vibration can be extremely sensitive to small changes or imperfections in the system. In this talk it is shown that the prediction of vibration levels can be much simplified by the derivation and exploitation of emergent laws, analogous to some extent to the heat conduction equations, but with an added statistical aspect, as in turbulent flow. The emergent laws are discussed and their application to the design of aerospace, marine, and automotive structures is described. As an aside it will be shown that the same emergent theory can be applied to a range of problems involving electromagnetic fields.
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