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Number 14 • Spring 2015

We hope that you will enjoy this annual newsletter. We are interested to receive Oxford tops the list your comments, and also contributions for future Our Mathematical Sciences submission to the 2014 Research Excellence Framework (REF), which newsletters. Please contact the covered all research in UK universities, was assessed as outstanding in every respect. We received editor, Robin Wilson, c/o the highest proportion of top grades across the whole UK for research publications and the impact [email protected] of our research outside academia, and the equal highest proportion for our research environment. Design & production by Baseline Arts The results can be (and have been) turned into league tables in many ways, but they all put Oxford Mathematical Sciences at the top.

Every six years UK universities are assessed for the Prof. Peter Howell underpins software used quality of their research, and funding is allocated by major glass manufacturers worldwide, accordingly. In the 2008 Research Assessment enabling precise control in making the glass Exercise we also did very well, and this year’s sheets and fibres that are ubiquitous in a wide outstanding result reflects the continuing range of products. extraordinary quality of our faculty and research fellows, as well as the breadth, depth and impact n Finding moonshine. ‘Impact’ included public of our core and interdisciplinary research, all engagement, as long as it stemmed from underpinned by the University’s investment in the research. One of our case studies traced mathematical sciences in the last decade. this kind of impact from Marcus du Sautoy’s Glass production at Schott AG book Finding Moonshine, which describes the Particularly noteworthy were our impact case way that mathematicians go about solving studies. Here is an outline of five of them: further their research problems. This book has had details can be found on the research page of the excellent reviews, leading to many TV, radio Institute’s website www.maths.ox.ac.uk. and online appearances by its author. n Influencing HIV/AIDS policy in India through n The HYDRA code, pioneered by Prof. Mike Giles, mathematical modelling, where Prof. Philip is Rolls-Royce’s standard computational tool Maini’s research team has played a significant to model and analyse the flow of air in their role in shaping the Indian Government’s engines. It is sophisticated enough to enable response to the growing HIV/AIDS crisis. the company to carry out extensive in silico design optimisation before actual engine n Helping the ‘Greeks’ to run faster, where trials, and has led to considerable savings and Rolls-Royce’s Trent 1000 mathematical techniques developed by improvements in engine efficiency. n engine Prof. Mike Giles have led to substantial reductions in the complexity of the Monte Carlo computer simulations run by large banks, cutting both computing costs and energy consumption. ’Greeks’ is a term used by the industry for measures of risk that are used to minimise possible future losses due to fluctuations in the market. n Mathematics in the design and manufacture of novel glass products. Glass is an unforgiving substance to make: flaws are very evident and hard to rectify, so precise control during manufacture is critical. A model developed by

ISSUE 14 / 2 Obituaries

Throughout his early career, Bryce model of clarity: as the subject unfolded, maintained regular contact with applied the board was filled with economical analysts in the US, especially in Madison, spare notes in his characteristic hand, Wisconsin, where he spent a number of and the audience invariably left feeling sabbatical years, greatly expanding his that they had witnessed a tour de force of range of contacts. He had many offers applied analysis. to cross the Atlantic and in 1988, facing imminent mandatory retirement in the Many throughout the mathematical UK and feeling that (unlike today) applied community remember Bryce with great analysis was not properly appreciated fondness: for his kindness and support at Oxford, he moved to Pittsburgh. He for students and colleagues, for his remained there until 2007 when he intensely amused laughter, for his rapt returned to the UK, basing himself in concentration on an explanation, and for Oxford’s Centre for Nonlinear PDEs for the his zest for life and for mathematics. remainder of his career. Let the last word be Bryce’s: when asked Bryce was elected FRSE in 1974 and FRS what advice he would give a young in 1992. He received the Whittaker Prize mathematician, he replied simply: ‘Have of the Edinburgh Mathematical Society fun’.* Bryce certainly did that. in 1965, the Keith Medal and Prize of Bryce McLeod the Royal Society of Edinburgh in 1987, * Interview with John Ball, and the Naylor Prize and Lectureship http://www.maths.ox.ac.uk/node/24862 in Applied Mathematics of the London A version of this obituary appeared in the Mathematical Society in 2011. John Bryce LMS Newsletter in November 2014, and is reproduced with permission of the London Considering himself a problem-solving Mathematical Society. n McLeod mathematician rather than a builder of general theories, he liked to focus FRS FRSE, on a specific hard problem and to find DAME KATHLEEN OLLERENSHAW, something new to say about it that was has died at the age of 101. A former rigorous, interesting and useful. He solved undergraduate at Somerville College, 1930–2014 problems with consummate skill across she wrote her Oxford doctoral thesis on Sam Howison an extraordinary range of areas, including ‘Critical lattices’ under the supervision fluid mechanics, general relativity, of T. W. Chaundy before moving to the Following a First Class BA degree in plasma physics, mathematical biology, University of Manchester. She later Mathematics & Natural Philosophy superconductivity, Painlevé equations, became President of the Institute of from the University of Aberdeen in coagulation processes, nonlinear Mathematics and its Applications and 1950, Bryce McLeod was awarded diffusion and pantograph equations. Lord Mayor of Manchester, and was a a scholarship to Oxford University He had long-lasting and productive government advisor on educational where he received another First collaborations with many distinguished matters. In her 90s she wrote a Class BA degree in 1952. His tutor at mathematicians, both applied analysts prizewinning article on pandiagonal Christ Church was T. W. Chaundy, a like himself and modellers whose magic squares. n specialist in differential equations, differential equations had caught his who was influential in shaping Bryce’s interest: he often looked at new problems SANDY GREEN FRS has died at the intellectual path and co-authored the unearthed by colleagues working in a age of 88. A distinguished algebraist first of his 150+ papers. more applications-focused way. His work who worked at Bletchley Park during was characterised by great lucidity of World War II and later taught at the After a year as a Rotary Foundation thought and ingenuity of argument. Universities of Manchester, Sussex Fellow in Vancouver and two years’ and Warwick, he was awarded the National Service, Bryce returned to Oxford Although he worked on many different London Mathematical Society’s Senior to complete a DPhil degree with E. C. problems, some general themes emerged and Titchmarsh in 1958. Following two years – in particular, the importance of for his work in group representation as a mathematics lecturer at Edinburgh similarity solutions as indicators of more theory. He retired to Oxford, where he University, Bryce returned to Oxford general behaviour, and the development participated in the mathematical life in 1960, with a Fellowship at Wadham of powerful techniques for ‘shooting’ and served on a committee reviewing College, and remained there until 1988, methods, especially with several the mathematics curriculum. n becoming a University Lecturer in 1970. parameters. A McLeod lecture was a

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History of Mathematics to her perceptions Jacqueline of what teaching and learning at third- year undergraduate level should be. Students were led to handle evidence in Anne Stedall, the context of history of mathematics and how to use sources, both primary and 1950–2014 secondary, effectively. She supervised many third- and fourth-year dissertations. Peter Neumann In a very different area, jointly with Cath Jackie Stedall came to Oxford in Jackie Stedall and Peter Neumann, 2008 Wilkins, she designed and managed the October 2000 as Clifford Norton Student Part B Structured Projects in applied in the History of Science at Queen’s translations, commentary) to the online mathematics. This third-year course has College. In due course she became edition of the manuscripts of Thomas some highly innovative features that Senior Research Fellow in the Oxford Harriot cover a wide range of scholarship. have proved a great success. She won Mathematical Institute and at Queen’s They are cogently argued and written in awards for teaching excellence on two College, posts from which, knowing a lucid and attractive style. She was as separate occasions. that she had incurable cancer, she took comfortable with the fine detail of textual early retirement in December 2013. analysis and reconstruction (Harriot, Jackie was exceptionally well organised. Brouncker, Wallis) as with synoptic She never missed a deadline. University This was her fifth career. Following studies of individual authors (Harriot, lectures and classes, seminar and studies at Cambridge and Canterbury Pell, Wallis) or of large areas such as conference papers, all were prepared she had been a statistician, Overseas algebra or the history of mathematics months ahead, never more than a Programmes Administrator for War itself. She gently challenged traditional few weeks after she had accepted a on Want, a full-time parent, and a orthodoxies. She earned an international commission. Book manuscripts, copy schoolteacher, before she became a reputation – twice, for example, she for journals she edited, all reached the historian of mathematics. Although her received invitations (courteously declined) publisher safely before the contract date. career as a full-time researcher, scholar to lecture at the International Congress of and university teacher spanned less than Mathematicians. She was a great scholar, teacher, editor fourteen years, it was greatly influential. and organiser. More than that: to very Her nine books, more than twenty articles, Her Oxford teaching was equally many of us she was a great colleague and major contributions (transcriptions, successful. She moulded the course on and friend. n

A surprising connection arose the other Head of day. Ulrike Tillmann (Topology), Samson Abramsky (Computer Science) and Heather Harrington (Mathematical Biology) are Department’s organising a course on Computational Algebraic Geometry. Topological ideas find letter applications in data science; this is just one Sam Howison manifestation of the ubiquitous impact woman. The imbalance runs deep: for of ‘Big Data’. By the time you read this, the example, fewer than 1000 girls get A* in We are delighted with the outcome national Alan Turing Institute will have Further Maths A-level, compared with over of the REF (page 1), which testifies to been launched (see page 8), with Oxford as 2400 boys. You can help us by convincing the quality of Mathematical Sciences a founding partner. Mathematics is central all the clever girls you meet that maths is research at Oxford, as well as to a to its work, and data science will be of a wonderful subject for them. To see what great deal of hard work in preparing increasing importance for mathematicians we are doing in this sphere, please visit the submission. It is a fantastic worldwide. the Good Practice pages on our website, springboard for the next few years. I www.maths.ox.ac.uk. do wonder, however, whether these Another vitally important topic for assessments end up dictating our us is the area of ‘Good Practice’. How This is my fifth and last letter as Head of behaviour: certainly there is now a do we create and sustain a working Department; next year you will hear from six-year hiring cycle, and there are environment to match the quality of our my successor, Martin Bridson. It has been less obvious impacts as well. We must mathematics? The ‘gender gap’ is a huge an honour and a privilege to be Head of never forget our main goal, to pursue issue for mathematics, highlighted by the our wonderful department at this exciting mathematics at the highest level with award of a 2014 Fields Medal to Maryam period in its history, and to work with all its infinite variety and connections. Mirzakhani, the first to be awarded to a present and former members alike. n

OXFORD MATHEMATICAL INSTITUTE NEWSLETTER . SPRING 2015 . ISSUE 14 / 3 Feature article

century, culminating in work of Robert Prime-time mathematics Rankin from 1938 showing that, amongst the primes less than X, there are two Ben Green FRS, Waynflete Professor of Pure Mathematics consecutive primes differing by at least log X times f(X), where In the last 18 months there has been a great deal of progress in the study of f(X) = c log log X log log log log X / 2 prime numbers, and four Oxford mathematicians have been involved in various (log log log X) aspects of this work. for some constant c; this function f(X) tends to infinity with X. Over the last 75 years it had become a notorious problem to improve this function f by more than a constant factor. Indeed, the late Hungarian mathematician Paul Erdős offered 10,000 dollars for doing precisely this.

Remarkably, in August 2014 the problem was solved twice, independently, at almost precisely the same time – by James Maynard, and by myself in collaboration with Kevin Ford, Sergei Konyagin and Terry Tao. Maynard uses methods related to his work on small gaps, but the connection between the two problems is by no means obvious Four Oxford number-theorists: Xiannan Li, Ben Green, James Maynard and Roger Heath-Brown, 2014 – and is in fact very surprising. My coauthors and I rely in part on work done In May 2013, previously unheralded 600. Unlike Zhang’s argument, Maynard’s by Tao and myself over the last ten years mathematician Yitang Zhang of the argument has the virtue that one could on arithmetic progressions of primes, University of New Hampshire caused teach it in its entirety in a one-term such as 5, 11, 17, 23, 29; again the nature a sensation by proving that there are graduate course. Moreover, Maynard of the link between this and large gaps infinitely many pairs of consecutive (and independently Terry Tao) have between primes is far from self-evident. prime numbers differing by at most obtained a result significantly stronger 70 million. While this may sound like than Zhang’s – that one can find infinitely One of the attractions of working in an enormous number – indeed it is many triples of consecutive primes, prime number theory is the profusion of conjectured that infinitely many pairs all contained in an interval of length easily-stated unsolved problems. Quite of consecutive primes differ by 2 (the bounded by some constant C – and a famous one is the question of showing twin prime conjecture) – no-one had similarly for quadruples, quintuples, and that there are infinitely many squares previously been able to establish any so on. Using Maynard and Tao’s ideas, a which, when increased by 1, are prime: finite bound at all. further Polymath project has succeeded for example, 62 + 1 = 37 is prime. This in reducing Zhang’s 70 million to 246, the problem remains beyond reach, but Zhang’s work set off a feverish effort to best bound currently known. this year Roger Heath-Brown (Professor reduce the number 70 million as far as of Pure Mathematics at Oxford) and his possible. An online collaborative project Consecutive primes lying close together postdoc Xiannan Li proved a highly non- called Polymath explored a variety of constitute an unusual situation. The trivial result on a similar kind of problem. different avenues, some of them very number of primes less than X is around They showed that there are infinitely technical and computational, and X / log X (this is the prime number theorem) many squares to which one may add the succeeded in reducing the gap from 70 and so the average gap between a prime fourth power of a prime in such a way million to 4680. of size around X and the next prime is log that the resulting number is still prime X, which tends to infinity as X does (and, in (for example, 52 + 24 = 41 and 42 + 34 = 97). Meanwhile, recently graduated Oxford particular, is eventually much larger than DPhil student James Maynard, in 70 million). So, what about the question James Maynard has recently been Montreal for a year as a postdoc, opposite to that studied by Zhang, of awarded a Clay Research Fellowship for was pursuing his own approach to finding consecutive primes much further three years. With him back in Oxford as the problem. This paid spectacular apart than the average? a Fellow by Examination at Magdalen dividends when, in November 2013, he College, Oxford’s research in prime announced a relatively short argument This question was studied in several number theory has never been in such reducing the gap still further to around papers in the early part of the 20th good shape. n

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Chebfun and dolfin-adjoint Nick Trefethen FRS, Professor of Numerical Analysis

Most problems of continuous mathematics cannot be solved analytically – just look at almost any partial differential equation, nonlinear system of equations, or optimisation problem. Numerical analysts develop algorithms to solve them numerically, and for generations Oxford’s Numerical Analysis Group has been the UK leader in this area.

This is a field with users! Our end-product is If Chebfun started numerical software relied on by scientists with a white- Nick Trefethen meets Leonhard Euler and engineers around the world. How haired professor, does anybody compute the eigenvalues dolfin-adjoint Applications of dolfin-adjoint are taking of a matrix? Almost certainly by calling comes from a Farrell places. As he remarked: a computer code with a name like eig blue-eyed boy. One day you can be working on which is descended from Fortran programs Patrick Farrell problems in generating electricity from written in the 1970s. grew up in tidal turbines, the next you’re solving western Ireland problems in cardiac electrophysiology 2014 was a year of two memorable and completed Patrick Farrell, EPSRC for diagnosing damage to the heart, software achievements for the NA Group. his PhD degree at Early Career Research the third in elastic imaging of cancerous One was the release of a completely Imperial College Fellow tissue. While I was a postdoc I went to sea rewritten Version 5 of Chebfun, a MATLAB before joining for a month with the oceanographers, package whose vision is ‘numerical the Mathematical Institute two years sailing across the Atlantic, gathering computation with functions’. Scientists ago. In 2014 he began to get world-wide data that lets us deduce the transport of may traditionally be interested in recognition for the Python software heat in the ocean. Become an applied working with continuous functions, but project he created called dolfin-adjoint mathematician, and see the world! numerical algorithms force them to deal (www.dolfin-adjoint.org). with approximating discrete vectors. The software scene these days is very The Chebfun project takes the view that Like Chebfun, dolfin-adjoint is all different from in the 1970s. It’s all about scientists shouldn’t have to pay attention about computing at a higher level online collaboration, files stores in the to these matters in the 21st century. In of abstraction than was usual in the cloud, issue trackers readable by the MATLAB or Python, you might type sum(v) last century: the key word is adjoint. world, Skype video-calls to South Africa to add up the entries of a vector v or In the 20th century, advances and and Delaware and Norway. And what max(v) to find the maximum. In Chebfun, algorithms and hardware enabled us we do with our mathematics keeps on such commands are overloaded to give to solve all kinds of ‘forward problems’ getting more remarkable. n analogous results for continuous objects. on computers, such as determining Thus sum(f) gives the definite integral of a the flow around an aeroplane or the function f, and max(f) gives its maximum. force distribution in a solid structure. In MATLAB, you solve a system of equations Ultimately, however, we would like to Ax = b by typing x=A\b; in Chebfun solve inverse problems: what structure you solve an integral or differential gives us the behaviour we want? The equation Lu = f by typing u=L\f. All this is mathematics of such problems is made possible by algorithms based on fascinating. Whenever you have one approximation of functions by Chebyshev operator that carries information polynomials. I started the project in 2003, forward, there is a dual adjoint operator and now we have a team of ten. that carries information backward. Optimisation becomes feasible if you Chebfun has thousands of users around can realise the adjoint computationally. the world, and its impact seems to Dolfin-adjoint is based on a method that be doubling roughly every two years: Farrell devised to do this automatically in the number of Google scholar hits for the context of the FEniCS finite-element 2005–2006, . . . , 2013–2014 were 5, 14, 58, software. Given a FEniCS high-level 104 and 186. Look at our online examples specification of a problem, dolfin-adjoint at www.chebfun.org to see how much fun elegantly constructs the dual at the same Approximation to an optimal heat-conductor hands-on mathematics can be these days! high level. computed with dolfin-adjoint

OXFORD MATHEMATICAL INSTITUTE NEWSLETTER . SPRING 2015 . ISSUE 14 / 5 People

Appointments... Karin Erdmann was Terry Lyons FRS has continued as President of University Lecturer in Pure the London Mathematical Society. We are delighted to welcome the following Mathematics, with particular James Maynard has won the 2014 SASTRA new Faculty members of the Mathematical interests in representation Institute. Ramanujan Prize, awarded annually to a theory and homological mathematician below the age of 32, for his University Dan Ciubotaru ( algebra, and Tutorial Fellow contributions to number theory (see page 4). of Utah, USA): Associate at Somerville College. Professor of Pure John Norbury and his Richard Haydon was Professor of Mathematics and Tutorial co-author Ian Roulstone Mathematics, with interests in functional Fellow at Somerville have won the Louis J. analysis and topology, and Tutorial Fellow at College. Research interests: Batten Author’s Award INVISIBLE Brasenose College. IN THE STORM by the Council of the THE ROLE OF MATHEMATICS Representation theory of IN UNDERSTANDING WEATHER reductive groups, unitary representations, David Stirzaker was Research Fellow in American Meteorological Hecke algebras, reflection groups. Mathematics, with particular interests in Society for their recent probability and its ramifications, and Tutorial book Invisible in the IAN ROULSTONE & JOHN NORBURY (Oxford / Radek Erban Fellow of St John’s College. Storm on the role of Royal Society University mathematics in understanding weather. Research Fellow): Professor Achievements... of Mathematics and Ebrahim Patel has won the IMA’s Early Career Tutorial Fellow at Merton This has been another excellent year for Mathematician Catherine Richards Prize 2014 College. Research interests: awards and achievements. for his article ‘Pendulum pattern perception’. Mathematical biology, At the 2014 International Congress of Kishan Patel was awarded the 2014 Kansjoerg multiscale modelling, partial differential Mathematicians in Seoul, Korea, Ben Green Wacker Prize of the European Consortium for equations, stochastic simulation algorithms, FRS and Jonathan Pila gave invited plenary Mathematics in Industry for a Master’s thesis on molecular dynamics, gene regulatory lectures, while Konstantin Ardakov, David Industrial mathematics. networks, chemotaxis, collective animal , FRS and Conlon Terry Lyons Tom Sanders Jonathan Pila has won a Carol Karp Prize, behaviour. gave invited section lectures. Dame Frances awarded every five years by the Association Vicky Neale (Cambridge): Kirwan FRS was a member of the ICM Fields for Symbolic Logic for an outstanding book or Whitehead Lecturer at the Medal Committee. paper on the subject. Mathematical Institute was awarded Ruth Baker Mason Porter has won the 2014 Erdős–Rényi and Balliol College. a London Mathematical Prize, awarded annually to a young scientist for Public understanding Society research achievements in network science. and communication of for her outstanding mathematics (see page 7). contributions to Angkana Ruland has won the University of Bonn’s Hausdorff prize for a thesis on partial Robert Style (Yale, USA): mathematical biology. differential equations. Departmental Lecturer in Martin Bridson, Whitehead Professor of , a DPhil student, won a SIAM Mathematical Modelling. Mathematics, has been elected a Fellow of Iain Smears Research interests: Soft the American Mathematical Society for his Student Paper prize for an article published in matter, elasticity, fluid contributions to geometric group theory. the SIAM Journal on Numerical Analysis. dynamics, capillarity, Miguel Walsh has won the 2014 Ramanujan geophysics, and general Marcus du Sautoy OBE, Simonyi Professor Prize for his outstanding contributions to problems involving modelling of physical and for the Public Understanding of Science, has ergodic theory and number theory. industrial processes. been awarded the Sir George Thomson Gold Medal by the Institute of Measurement and Kit Yates has won a Silver Award in the Andrew Thompson Control; awarded quinquennially it recognised mathematics category of the SET for Britain (Duke University, USA): ‘his considerable efforts to promote a positive Awards for his work on the swarming of locusts. Departmental Lecturer public perception of mathematics’ and cited in in Computational particular his BBC television programmes on OTHER AWARDS: Mathematics. Research Precision: The Measure of All Things. He was also Mathematical Institute teaching awards were interests: analysis of awarded the Christopher Zeeman Medal for the given to Karin Erdmann, Peter Howell, high-dimensional data, Promotion of Mathematics to the Public by the Colin Macdonald, Michael Monoyios, Oliver with particular interests in compressed Institute of Mathematics and its Applications Riordan, Jackie Stedall, David Stirzaker and sensing, optimisation and image processing and the London Mathematical Society. Paul Tod. applications. Ben Green FRS, Waynflete Professor of Pure Fernando Alday received OUSU’s ‘Most Retirements and Mathematics, has been awarded the Royal Acclaimed Lecturer’ award in the Mathematical, departures... Society’s biennial Sylvester Medal (named Physical & Life Sciences Division. after Oxford’s former Savilian Professor J. Academics have never taken retirement very J. Sylvester FRS) for his work on primes in The Building was one of eleven seriously, regarding it more as an asymptotic arithmetic progression and other recent results buildings to win a South Regional Award by the state, but while the formal stage exists we in number theory (see page 4). Royal Institute of British Architects (RIBA). mark it. This year we saw the retirement FRS, Savilian Professor of The Mathematical Institute has received of three long-standing members of the Geometry, has been awarded an Honorary a University Green Impact Award for department: Doctorate of Science by the University of achievements in a number of environmental Warwick. areas. n

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give students a chance to experience Institute life as an Oxford Maths undergraduate. Public lectures outreach During these weeks it was a pleasure to and interviews have mathematics alumni joining us for Rebecca formal dinners and question-and-answer Dyrol Lumbard Cotton-Barratt sessions with the students. Linking graduates and possible graduates breaks Telling the world about the pleasures Saturday morning may not seem the down barriers, allowing students to see (and very rare pains) of mathematics has most natural time to do mathematics. what they can do with their degrees, and been a highlight of our recent activities. Nevertheless, the enthusiastic descriptions is only possible thanks to alumni who are from Year 9 Oxfordshire school students willing to give their time and energy to talk A series of public lectures has taken of our Royal Institution Mathematics to these brilliant young people. place in the Andrew Wiles Building, and Masterclasses suggests that early starts are several are available online. Lectures no barrier for budding mathematicians. Marcus du Sautoy’s ‘Marvellous have ranged from Jim Murray on how The five masterclasses covered such Mathemagicians’ (see Newsletter 10) mathematical biology can explain the topics as measuring symmetry, Efron’s continue to visit schools around the lack of three-headed monsters and dice, the king chicken theorem, and country and further afield. During the prevent marriage breakdown, via a talk binary encoding, giving the students an past year they have visited dozens of on mathematical stamps and Alain opportunity to explore maths beyond the schools, inspiring students of a wide Goriely talking about how mathematical school curriculum. As summed up by one variety of ages and ability to engage with modelling can move participant at the end of the course: There and enjoy maths. They now do an annual between the climate is so much you don’t even know that you tour in March to visit the Dulwich Colleges and the brain and many don’t know – it is endless. in China, Singapore and South Korea, and points in between, to continue to support the local Oxfordshire Cédric Villani on the Infinity was also the theme of several Science Festival. Their mathematical ‘Birth of an Idea’ that led group presentations by participants on walking tours in Oxford and London are to his award of a Fields the University of Oxford’s UNIQ Summer still available (see www.mathsinthecity. Medal in 2014. Schools. Aimed at students from areas com), and are ideal for those curious and schools with low progression to about the mathematics around us – in A highlight of the year higher education, these week-long courses buildings, patterns and people. n was our Inaugural Christmas Lecture by Andrew Wiles, whose several UK Maths Trust events. Indeed, The Story of Equations Public part of my role is to develop a programme attracted over 700 engagement with of residential maths summer schools for requests for places. teenagers (the sort of students who might The Public Lecture mathematics one day become Oxford maths students), series is targeted at anyone with an Vicky Neale building on the Institute’s successful interest in the subject, from sixth-formers UKMT summer camps and our links with to the wider general public. Please keep I am very fortunate to be the first holder PROMYS, the American programme for an eye on our website, www.maths.ox.ac. of the Whitehead Lecturership at the budding mathematicians which is now uk, for details. The website also includes Mathematical Institute, which combines expanding into Europe. We’re looking for interviews with a number of prominent undergraduate teaching at Balliol with ways to expand the department’s activities Oxford mathematicians, including Jim public communication of mathematics. in this area – for example, by seeking Murray, Bryce McLeod, funding for undergraduates to work on and . n Since arriving in Oxford I’ve been their own summer research projects, while ‘spreading the word’ by appearing in BBC also inspiring the younger students at the Radio 4 programmes on the beauty of summer schools. mathematics, one of which also featured Oxford mathematicians Ben Green and On a less serious note, I was delighted Peter Neumann. I also appeared on Start to be involved with the Institute’s first the week and Melvyn Bragg’s In our time ‘Mathematical Bake-Off’, in which staff discussing ‘Euler’s number, e’. and students showed huge creativity and baking flair, and we even had a For much of my time I give talks to the mathematical craft afternoon towards public and to school students around the end of Michaelmas term. There’s no Mathematics is a piece of cake: the country, and I have contributed to boundary that maths cannot cross! n the Mathematical Bake-Off.

OXFORD MATHEMATICAL INSTITUTE NEWSLETTER . SPRING 2015 . ISSUE 14 / 7 Epsilons and deltas

asymmetry and entropy. The sculpture other researchers as he sought a way was created in cast aluminium by artist into a problem or sought new productive Mat Chivers, using a combination of areas for research. They also contain many hand-made and contemporary digital unpublished results and observations envisioning and fabrication processes. that are still relevant to the active areas of current research that he pioneered.

Under the aegis of the Clay Mathematics Institute, Glenys Luke and Graeme Segal have led a project to make the notes Alumni events available online. This work in progress can be seen on the CMI website: the Last year’s Mathematical Institute Garden scans are complete and accessible, and Party was held in the Andrew Wiles Glenys is working on the index which had building during the University’s Alumni reached 1992 at the time of writing. weekend. The speaker was Sir Roger Penrose FRS. Alan Turing Institute This year’s lecture will be given by Prof. Oxford University is one of five Ben Green FRS and will take place on universities involved with the creation 19 September. You can book on Mathematical and the activities of the new www.maths.ox.ac.uk/about-us/alumni/ Alan Turing . The new Institute focuses alumni-garden-party. posters Institute on the analysis and application of big data and algorithm research, and will be In addition to the annual Garden Party Posters featuring mathematicians are based in London. we held a successful alumni evening last displayed in the basement of the Andrew November at Staple Inn Hall in London. Wiles building. A new series of historical We plan to hold more such evenings as posters features G. H. Hardy’s Oxford Years, The Penrose paving we invite alumni to share their thoughts and it is intended to follow these with posters on John Wallis, Charles Dodgson and ideas about Oxford Mathematics. The paving in front of the Andrew Wiles (Lewis Carroll) and other Oxford-based building is constructed from just two mathematicians. The posters can be different diamond-shaped granite tiles, Celebrating Sir viewed on the Institute’s website at each adorned identically with stainless www.maths.ox.ac.uk/about-us/history. Michael Atiyah steel circular arcs. There are many ways of covering the infinite plane with A one-day Quillen notebooks these tiles, matching the arcs as we go. conference was Every such pattern is non-repetitive and held last year to Daniel Quillen contains infinitely many exact copies of celebrate the 85th (1940–2011) moved the pattern in the picture. The non- birthday of Sir from MIT to Oxford repeating arrangement was discovered Michael Atiyah, OM, in 1984 to succeed by Roger Penrose in 1974. This version, FRS, FRSE, Fields with its circular adornments, was Medal winner and as the Waynflete designed by him in 2012. n former Oxford Professor. His Savilian Professor of Geometry. Guest standing as one speakers included Oxford mathematicians of the leading Nigel Hitchin and Graeme Segal. The mathematicians of his time had already meeting also marked the publication by been recognised by the award of a Fields Oxford University Press of the seventh Medal in 1978 for his foundational work volume of his Collected Works. on K-theory. Mathematical During his long career, Quillen kept a detailed record of his mathematical sculpture research. The 30,000 pages of notes left on his death give a fascinating insight The entrance lobby of the Institute into the working of a great mathematical now displays Axiom, which combines mind. They show how he tackled the mathematical ideas of symmetry, problems, often reworking the ideas of

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