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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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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