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Jim Murray is one of the leading mathematical biologists of our times and the Inaugural Hooke Lecturer here in Oxford. In this wide-ranging interview with Philip Maini, Professor of Mathematical Biology in Oxford, Jim talks about his career, the range of his work, his successes and failures and his hopes and expectations for a subject that is the pointing the way for the future of applied mathematics.

This interview is the second in a series of interviews with distinguished Oxford Mathematicians, intended to shine a light on the work they do and the beauty and power of their subject. The first interview with Bryce McLeod is also available.

Arguably mathematicians are the scientific all-rounders, applying their skills to a range of subjects from chemistry and medicine to engineering and economics. In some cases these skills extend even further. Professor Alain Goriely, Statutory Professor of Mathematical Modelling in Oxford, has just won second prize in the Weird and Wonderful section of the 2014 National Science Photography Competition, organised by the Engineering and Physical Sciences Research Council (EPSRC) for his photograph of a gömböc. A  gömböc is a convex three-dimensional homogeneous body which, when resting on a flat surface, has just one stable and one unstable point of equilibrium. Its existence was conjectured by Russian mathematician Vladimir Arnold in 1995 and proven in 2006 by Hungarian scientists Gábor Domokos and Péter Várkonyi.

A limited edition Gömböc, labelled #2013, the year of the opening of the Andrew Wiles Building in Oxford, was purchased with generous support from Otto Albrecht and Tim and Leona Wong and can be found on display in the building. The Gömböc in Alain's photograph, a gift from Otto Albrecht, is made of plexiglass which generates intricate and intriguing light patterns. The mathematics of the Gömböc can be seen in the background.

Advances in quantum cryptography mean that we can protect our secrets even when our communications are being spied on or we are using devices built by our enemies, according to an Oxford University researcher.

Revelations of the extent of government surveillance have thrown a spotlight on the insecurity of our digital communications. Even today's encrypted data is vulnerable to technological progress. Writing in this week's Nature, Professor Artur Ekert of Oxford University and the National University of Singapore, and co-author Renato Renner of ETH Zurich, explore what physics tells us about keeping our secrets secret.In the history of secret communication, the efforts of code-makers have been matched time and again by the ingenuity of code-breakers. It is already believed that one of today's most widely used encryption systems, RSA, will become insecure once a quantum computer is built. But that story need not go on forever.

'Recent developments in quantum cryptography show that privacy is possible under stunningly weak assumptions about the freedom of action we have and the trustworthiness of the devices we use,' says Professor Ekert of Oxford University's Mathematical Institute, who is also Director of the Centre for Quantum Technologies at the National University of Singapore.

Over 20 years ago, Professor Ekert and others independently proposed a way to use the quantum properties of particles of light to share a secret key for secure communication. The key is a random sequence of 1s and 0s, derived by making random choices about how to measure the particles (and some other steps), that is used to encrypt the message. In the Nature Perspective, Ekert and Renner describe how quantum cryptography has since progressed to commercial prospect and into new theoretical territory.

Even though privacy is about randomness and trust, the most surprising recent finding is that we can communicate secretly even if we have very little trust in our cryptographic devices – imagine that you buy them from your enemy – and in our own abilities to make free choices – imagine that your enemy is also manipulating you. Given access to certain types of correlations (form the quantum world or elsewhere), and having a little bit of free will, we can protect ourselves. We can even protect ourselves against adversaries with superior technology that is unknown to us.

'As long as some of our choices are not completely predictable and therefore beyond the powers that be, we can keep our secrets secret,' says Renner, Professor of Theoretical Physics at ETH Zurich, Switzerland. This arises from a mathematical discovery by Renner and his collaborator about 'randomness amplification': they found that a quantum trick can turn some types of slightly-random numbers into completely random numbers. Applied in cryptography, such methods can reinstate our abilities to make perfectly random choices and guarantee security even if we are partially manipulated.

'As well as there being exciting scientific developments in the past few years, the topic of cryptography has very much come out of the shadows. It's not just spooks talking about this stuff now,' says Ekert.

The authors conclude: 'The days we stop worrying about untrustworthy or incompetent providers of cryptographic services may not be that far away'.

The Perspective article, entitled ‘The ultimate physical limits of privacy', is published in this week's Nature

Congratulations to Dr Christian Yates, Research Fellow at the University of Oxford, who has won the Silver Award in the mathematics category of the SET for Britain awards for his work on locust swarming. Find out more about the devastating consequences of locust swarming, how, counterintuitively, randommness helps swarms of locusts stay together and how understanding cannibalism in locusts might be the key to dispersing the swarms.

Oxford Mathematicians Lloyd Chapman, a DPhil student, and Konstantinos Koumatos, a Postdoctoral Researcher, will be presenting posters to MPs and a panel of expert judges, as part of SET for Britain on Monday 17 March. Lloyd will demonstrate his work on mathematical modelling of cell growth in tissue engineering devices while Kostas' research relates to the mathematics of phase transitions in crystalline solids and, in particular, proposes a deep mathematical explanation for a peculiar nucleation mechanism observed in a shape-memory alloy.

On presenting his research in Parliament, Lloyd said, “I think it's very important for mathematicians and scientists to communicate their work with a wider audience, and it's fantastic to be given the opportunity to do this in such a special setting".

Lloyd and Kostas's work, together with that of colleagues Giovanni Alberti and Christian Yates, demonstrates both the range of mathematics in Oxford but also the reach that the subject has across all scientific disciplines.

The SET for Britain is generously sponsored by the Clay Mathematics Institute.

Giovanni S Alberti, 26, a DPhil student here at the University of Oxford, hailing from Imperia in Italy, is joining colleague Christian Yates at the Houses of Parliament to present his mathematical research to a range of politicians and a panel of expert judges, as part of SET for Britain on Monday 17 March.

Giovanni’s poster on research about the mathematical aspects of some newly emerging hybrid medical imaging modalities will be judged against dozens of other mathematicians’ research in the only national competition of its kind.

On presenting his research in Parliament, he said, “combining the beauty of Mathematics with the importance of medicine is a fantastic job, and I am delighted to have the opportunity to share my research with those in government”.

Dr Christian Yates, Research Fellow at the University of Oxford, will be presenting a poster about the mathematics of locust swarming to MPs and expert judges on Monday 17 March, as part of SET for Britain. Christian’s work will be judged against dozens of other mathematicians’ research in the only national competition of its kind.

Christian, who also works on discovering the causes of African trypanosomiasis (sleeping sickness) and cell migration during embryo formation, amongst other topics in Mathematical Biology, was shortlisted from hundreds of applicants to appear in Parliament. 

On presenting his research in Parliament, he said, “As a researcher I aim to communicate my work to as wide an audience as possible. I also think it’s important to be able to explain and justify the work I do. Presenting my work in Parliament will provide me the opportunity to do both.”

Andrew Miller MP, Chairman of the Parliamentary and Scientific Committee, said, “This annual competition is an important date in the parliamentary calendar because it gives MPs an opportunity to speak to a wide range of the country’s best young researchers. 

“These early career engineers, mathematicians and scientists are the architects of our future and SET for Britain is politicians’ best opportunity to meet them and understand their work.”

Christian’s research has been entered into the Mathematics session of the competition, which will end in a gold, silver and bronze prize-giving ceremony. Judged by leading academics, the gold medallist receives £3,000, while silver and bronze receive £2,000 and £1,000 respectively.

Professor Bryce McLeod was one of Oxford's most well-known mathematicians, and an international authority on linear and nonlinear differential equations. In this interview with John Ball, he reflects on his career.

This interview is the first in a series of interviews with distinguished Oxford Mathematicians, intended to shine a light on the work they do and the beauty and power of their subject.