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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The fundamental laws of physics look different when reflected in a mirror. This is the statement that the laws of physics have a handedness, what physicists call chirality. This is one of the most important facts that we know about the universe, a fact that, remarkably, goes a long way to fixing the mathematical structure of the laws of nature. I will explain how we know about this handedness, why it’s so important, and why there are still several chiral mysteries that remain unsolved.
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.
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