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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