Maths News 2011 [F]:Maths newsletter 1 24/3/11 17:33 Page 2

Oxford Mathematical Institute Spring 2011, Number 9 Newsletter

We hope that you enjoy receiving this annual Newsletter. We are interested to receive your Sam Howison comments, and also contributions for future Newsletters. A note of welcome Please write to the editor: Robin Wilson On 1 January Prof. Sam Howison, former Director of the MI Newsletter Oxford Centre for Industrial and Applied Mathematics and Mathematical Institute of the Nomura Centre for Mathematical Finance, took over 24–29 St Giles Oxford OX1 3LB, the reins as Chairman of the Mathematical Institute from or send e-mails to him, c/o Prof. Nick Woodhouse. [email protected] Sam Howison writes: I took over as Chairman on opportunity and put the vision into practice in Design & production by Baseline Arts the first of January, the lowest ebb of the year the often byzantinely complex context of a but also a time of new beginnings. Walked into collegiate university. We’re now a large, science- my office on the first day; phone rang as I took style department with an annual budget greater off my coat: six burst water pipes in the Gibson than the total of EPSRC's funding for research in Building (our beach-head on the Radcliffe mathematics. We owe an enormous debt of Infirmary site). Welcome to your new job, Mr gratitude to Nick and all who sup ported him. Chairman. However, we face some serious challenges. The My main first impression is that I inherit a episode of the leaking pipes is a pointed department at the top of its game. The list of reminder of one of them: our physical honours and awards later in the Newsletter infrastructure is woefully inadequate and we shows that our academics are world-leading, and urgently need our new building . With planning they’re supported by a first-rate administrative permission secured, the detailed discussions are and support staff. According to the Research continuing, but we need to secure further Assessment Exercise of 2008, we’re the leading funding to proceed. In this Newsletter, we are research department in the UK, and have one of reaching out to all our alumni to ask you to the largest and best undergraduate intakes as support us in whatever way you can. More well. information about the building and its p rogress can be found on pages 4 and 5. These things don't just happen; they have to be planned and executed. We’ve been through a The financial situation of universities is very period of tremendous change in the last few uncertain following the Comprehensive Spending years, during which the whole structure of the Review and ahead of the increase in tuition fees. Photo by Ruth Preston by Ruth Photo department was more or less rebuilt from Moreover, we’re gearing up for the Research I am confident that scratch. When Nick Woodhouse took over in Excellence Framework, the successor to the we’ll overcome 2001, we were a small, humanities-style Research Assessment Exercise; in 2013, all department in a fairly centrally controlled research in UK mathematics departments will be these challenges university. Following the North Report, many assessed and the results will determine much of and I look forward central functions, both academic and financial, our funding until around 2020. to playing my part were devolved to newly created Divisions and their departments. At a stroke, departments had I am confident that we’ll overcome these in the years to freedom to steer their own courses. It was a challenges and I look forward to playing my part come. huge achievement on Nick's part to see the in the years to come. I

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Maths and Philosophy A short history of the Maths How to raise and Philosophy Degree one billion Helen Carasso, St Anne’s 1976 pounds... The Oxford degree in Mathematics and for in order to attack the problems Philosophy – originally a three-year BA which arise in present-day philosophy (Hons) degree and now also offering a of mathematics much more technical four-year route to an MMathsPhil – machinery is needed than is generally owes its origins to The Kneale Report possessed by philosophers with a of the mid-1960s that considered the purely arts background, and the establishment of Joint Schools to motivation for the mathematical include Philosophy within the university. problems arises from the investigations of the foundations of mathematics. At about the same time, a group of Oxford academics were meeting It specified that the mathematical regularly to discuss topics in elements of the course should be mathematical logic. One of them, John taught by practising mathematicians, Crossley, recalls the role that these and saw the degree as offering an all- informal meetings played in creating a round education bridging the arts and Mathematics and Philosophy degree: sciences. Michael Dummett put up the idea that, emulating a mixture of the BPhil in Pioneer students sat the first Philosophy and PPE, we should p ropose Mathematics and Philosophy a Joint Honour School in Mathematics Moderations in 1969, while others sat and Philosophy. Our colleagues were the first finals examinations in 1970, positive. Graham Higman, who perforce having switched to the newly-created had learnt logic for his group theory Joint Honours course after taking Maths word problems, supported us. Freddie Mods in 1968. Ayer supported us. There was a price – or rather no price – no new money Since then, some 600 students have was to be required. That was possible, read for the joint degree and, while the and so Mathematics and Philosophy course has always been one of the Professor Alain began. Robin Gandy was recruited and smaller ones on offer in Oxford, its Goriely, Director he cosseted, cajoled and sustained the supporters believe the effort was of OCCAM, came new degree. worthwhile, as John Crossley explains: up with this It was a struggle at times, but the idea innovative way of was, and is, a good one. The advertising Oxford combination of technical skill and deep University’s billion understanding that Mathematics and pounds fund- Philosophy represents will endure. I raising campaign.

Oxford Mathematics degrees

John Crossley There are now five mathematics- Mathematics: introduced in the More formally, the main paper that related degrees at Oxford. 19th century proposed the new course for approval Mathematics and Philosophy: 1968 by the appropriate University They are available as 3-year Mathematics and Computer committees argued: courses, leading to a BA degree, Science: 1985 There is a natural bridge between the and 4-year courses, leading to an Computer Science: 1994 two disciplines in the philosophy of MMath or MComp degree. Mathematics and Statistics: 2003 mathematics and mathematical logic,

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Applied mathematics The place to be for PDE!

Emma Waters Project Manager at the Mathematical Institute OxPDE Members, January 2011 Partial differential equations (PDE) are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena. The behaviour of every material object, with length scales ranging from sub-atomic to astronomical and time scales ranging from picoseconds to millennia, can be modelled by PDE or by equations with similar features.

With an EPSRC Science & Innovation award of £3.3 million, the Oxford Centre for Nonlinear PDE (OxPDE), launched in 2007, has focused on the fundamental marked the beginning of the fourth year contributing to national PDE events. analysis of nonlinear PDE and numerical of OxPDE. He brings to the Centre OxPDE has formed successful collaborative algorithms for their solution. More expertise in the mathematical analysis of links with other UK PDE centres based in recently, areas of interest have expanded nonlinear hyperbolic PDE, an area of Swansea, Bristol, Warwick, Bath and to include the calculus of variations, research that was not previously Cambridge, with a particularly strong nonlinear hyperbolic systems, inverse represented in the UK. cooperation with the Maxwell Institute in problems, homogenization, infinite- Edinburgh, the other Science and dimensional dynamical systems, geometric With twelve faculty members, six Innovation Centre in the UK. With firm analysis for PDE arising in solid and fluid postdoctoral researchers, and eleven foundations in the field of nonlinear PDE mechanics, materials science, liquid research students, the Centre runs a now in place in the UK, the OxPDE crystals, biology and relativity. The Centre, thriving visitor programme, an active Centre’s focus for the foreseeable future based in the Gibson Building, is a vibrant events programme, a regular Monday is to continue to create critical mass in and stimulating research environment, seminar series and a Thursday lunchtime the UK and to establish and maintain a providing leadership in the field of seminar series, a dedicated technical solid exchange programme with groups nonlinear PDE within the UK. report series, and a highly successful from across the world. undergraduate summer research project The inaugural lecture of Gui-Qiang Chen, scheme. Outreach activities include Sir John Ball, OxPDE’s Director, comments: Professor in the Analysis of Partial hosting national PDE events and visitors’ We are very lucky to have attracted to Differential Equations, held last November, calendars, in addition to supporting and Oxford outstanding researchers in PDE from different parts of the world. OxPDE is now recognized as a significant international centre, and is certainly the strongest research group in PDE that there has been in the UK in my lifetime. We hope to strengthen it still further in the future. I

(Further information on OxPDE can be found on the website: www.maths.ox.ac.uk/oxpde.)

The inaugural lecture of Gui-Qiang Chen,

Photo by Peter Hudston by Peter Photo November 2010

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New building

we were given the green light to proceed to RIBA Above left: Front view stage F, which involved going out to tender, of the new Maths The new building Institute appointing a contractor and proceeding to the Nick Woodhouse Former Chairman of the detailed design stage. This will take us until June, Above: View from Mathematical Institute when a decision will be made on whether to start Woodstock Road construction of the building itself. We must secure Above right: Common The cover page of our first Newsletter in 2003 further funding before then if the project is to Room told of the forthcoming move to the new continue without a break. In the meantime, Far right: Upper building. Although Oxford sets its own pace, demolition is complete and the work on the site Walkways and Atrium the move at last appears real and imminent. infrastructure is well under way. After eight years, we at least have the drains in place. Below: Spacious and Contractors have been appointed, diggers are light Interior Lobby at work, and the timetable to hand over in As Margaret Rayner recounts in her chapter in Below right: Access to 2013 has been set out in detail. The planning Oxford Figures1, nearly 40 years passed between the Mezzanine meetings have progressed from discussing Hardy’s plea to the University administration for broad principles to debates on the positioning adequate facilities for mathematicians and the of lecterns and electrical sockets. opening of the Institute's first purpose-built quarters in the late 1960s. That was a huge step The last few years of planning have been as frustrating as they have been exhilarating. We were assigned a fantastic site between two 18th-centry masterpieces, the original Infirmary building and the Radcliffe Observatory (the Tower of the Winds), but one that has brought with it the obligation to respect both buildings to the exacting standards of English Heritage. Not an easy challenge: it introduced complex geometric constraints, and the need to design a building with no ‘back’.

The sense that the project is now moving rapidly is not false: there has indeed been decisive progress over the past year. In the summer, we finally obtained planning consent for Rafael Viñoly’s beautiful and imaginative design. Despite the growing gloom about university finance in general, and HEFCE capital funding in particular,

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New building

forward, but, with the passage of another 40 but it has not been easy to build on that at a time The new Viñoly years, the St Giles' building has proved inadequate of financial crisis and with the final shape of the building will to cope with the growth of mathematics in Oxford building still unclear. The decisions of the last year and with the changing styles of teaching and have allowed us to move forward on that front as bring us all research. The Institute is now spread over three well, and the development campaign now has new together on one sites: the St Giles' building, Dartington House in momentum, with the project accorded high priority site and provide Little Clarendon St, and the Gibson Building, a in the Campaign for Oxford. 1950s ward block grimly awaiting demolition on for the whole the North-West corner of the old hospital site. The coming months will be critical. The Oxford There is not enough space. First- and second-year University has asked us to raise £36M, half the mathematics lectures are held in the Museum, physical dispersal cost of the project, from our friends and inhibits research collaboration, and there is supporters. We have secured £10M towards this community. nowhere to create a sense of community for the target, but there is still a long way to go.

undergraduate mathematicians. Before construction can begin, we must 1. John Fauvel, Raymond demonstrate the support of our alumni through Flood and Robin Wilson, The new Viñoly building will b ring us all together donations and pledges. This edition of the Oxford Figures: 800 Years of the Mathematical on one site and provide for the whole Oxford Newsletter provides you with the opportunity to Sciences, Clarendon Press, mathematics community. There will be room to offer your support. I Oxford, 2000. create a proper working environment for research students, faculty, visitors, and the growing cohort of post-docs. Undergraduates will have somewhere to grab a cup of coffee between lectures, write up their notes, and chat to their lecturers and contemporaries.

Above all, the brief has focused strongly on the promotion of interaction: there is to be a single entrance lobby to maximize those crucial chance encounters that seed breakthroughs, and a large common-room looking out on the Tower of the Winds for teatime discussions. The layout, with offices opening off atria, will make it impossible even for our most elusive colleagues to creep into their offices unobserved.

The fundraising campaign was boosted by the extremely generous initial gift from the Clay family, Maths News 2011 [F]:Maths newsletter 1 24/3/11 17:34 Page 7

People

Appointments...

Luis-Fernando Alday Dominic Vella Radek Erban, OCCAM (Institute for Advanced (Cambridge) to a Research Fellow, has Study, Princeton) University Lecturership been awarded a Philip to a Lecturership in in Applied Leverhulme prize for Mathematical Physics Mathematics and a his work in applied and a Fellowship at Fellowship at Lincoln mathematics. Hertford College. Research interests: College. Research interests: fluid and Roger Heath-Brown FRS, Marc string theory, super-symmetric gauge solid mechanics, particularly the effects Lackenby, Philip Maini, Oliver theories,conformal field theories and of surface tension. Riordan, Gregory Seregin and Xunyu string/gauge theory dualities. Zhou were all invited speakers at the Thomas Bridgeland ...and farewells 2010 International Congress of (University of Sheffield) Mathematicians in Hyderabad, India. We’re sorry to say to a Senior Research goodbye to John Colin Macdonald, OCCAM University Fellowship at All Souls. Norbury (Lincoln), Lecturer, has won the 2010 SIAM Research interests: faculty member of Richard DiPrima Prize. homological techniques OCIAM, in algebraic geometry and relations with Bill Morton, Former Professor of string theory and mirror symmetry. Numerical Analysis, has been awarded John Ockendon FRS the De Morgan Medal, the London Christopher Douglas (St Catherine’s), first Mathematical Society’s highest award (University of Director of the Oxford (given every three years). California, Berkeley) Centre for to a University Collaborative Applied Graeme Segal FRS, Lecturership and a Mathematics (OCCAM), Emeritus Fellow of All Fellowship at Keble Souls College, has College. Research interests: algebraic and Michael been awarded the and geometric topology, 3- and 4- Vaughan-Lee, Fellow Royal Society’s dimensional topological quantum field in Mathematics at Sylvester Medal. I theory, elliptic cohomology. Christ Church. (J. J. Sylvester was appointed Oxford’s Savilian Professor of Geometry in 1883.) Kevin McGerty (Imperial College, Sir Martin Taylor FRS, Vice-President London) to a Royal of the Royal Society, has taken up Society University Achievements residence as Warden of Merton College. Research Fellowship and a Fellowship at It has been another bumper year for Nick Trefethen FRS, Christ Church, and a University awards and appointments: Professor of Numerical Lecturership in Pure Mathematics Analysis, has taken up thereafter. Research interests: David Acheson, Emeritus Fellow of the position of interactions between representation Jesus College, has been appointed President of SIAM, the theory and algebraic geometry, in President of the Mathematical International Society particular quantum groups, D-modules Association for 2010–11. for Industrial and Applied Mathematics. He was also awarded the 2010 IMA and non-commutative resolutions Philip Candelas, Gold Medal by the Institute of Rouse Ball Professor Alexis Vasseur Mathematics and its Applications. (University of Texas at of Mathematics, has Austin) to a been elected a Fellow Robin Wilson, Lecturer at Pembroke Professorship of of the Royal Society. College, has been appointed Vice- Mathematics and a President of the British Society for the Fellowship at Lincoln Marcus du Sautoy, Charles Simonyi History of Mathematics, and an College. Research interests: partial Professor for the Public Understanding Honorary Fellow of Gresham College, I differential equations, and especially of Science, has received an honorary London. their applications to fluid mechanics. D.Sc. degree from the University of Bath.

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People

Obituary: Dr Patrick Martineau

We are sorry to representations of the Suzuki groups, college. The wider university also report the death the splitting of group representations, benefitted, especially during his tenure on 6 September and how groups of automorphisms of the secretaryship and then the 2010 of Dr Patrick affect the structure of a group. chairmanship of the Estates Bursars Martineau, Committee. Although inclined to play Patrick’s writing was clear and austere, Emeritus Fellow of his cards close to his chest, fledgling at the right level of abstraction. (One Wadham College. A group theorist, bursars were assisted by frank (but reviewer notes that “the ideas used are Patrick will be remembered by former unattributable) advice. so clear and simple that this paper undergraduates for his algebra could be read with benefit before the Patrick’s last few years were dominated lectures. many other papers on the subject”.) In by the illness that had led to his Brian Stewart writes: Patrick’s his lecturing and teaching Patrick retirement in 2004. But occasionally the mathematical talent was nurtured at adopted the same clear style. But he old Patrick sparked into life: during a home (his father was a wrangler as well brought also a real concern that all his chance meeting last year on my way to as a bishop) and at school (Liverpool students should make the transition to lecture I was given a two-minute Institute). Elected a Scholar at Wadham real mathematics, while tolerating no tutorial on how to treat the adjoint “so College in 1962, he remained as nonsense when he suspected that that those in the Last Chance Saloon Mathematics Fellow from 1968 until someone was in danger of squandering will understand you, Brian”. retirement. their talents. Patrick is survived by his wife Sylvia, and After finals Patrick joined Higman’s Wadham chose Patrick as the their twin children Karen and David. I research group, writing a thesis under University’s Junior Proctor for 1975–76. the supervision of Martin Powell, giving His colleagues then elected him Estates [A version of this obituary appeared in the “odd characterisations” of the Janko Bursar in 1977; from then on he London Mathematical Society Newsletter, group and of the Suzuki groups. This devoted his time and energy to issue 398 (December 2010), and is developed later into studies of the strengthening the finances of the reproduced with permission.]

MISCELLANEA th Some Finals questions from 1828 Invariant Society 75 anniversary 1. What decimal of a week is 1 hour 7 minutes and 14 seconds? The Invariant Society, the University’s Hilary Term 1936. Seventy-five years 2. Find tan ( /4 – /2) in terms of undergraduate mathematical society, on, the 75th anniversary was celebrated θ tan . was founded by three Balliol men – with a number of memorable events, θ

J. H. C. (Henry) Whitehead (Balliol’s including lectures by Leonhard Euler 3. The altitude of the sun was observed mathematics tutor and a distinguished (paying a fleeting visit from the 18th to be half of his declination at six topologist who became Oxford’s century) and Sir Roger Penrose. I o’clock. Prove that twice the sine of Waynflete Professor of Pure the latitude of the place = the secant of the sun’s latitude. Mathematics in 1947), Graham Higman (a second-year undergraduate who Some Finals questions from 1849 succeeded Whitehead in the Waynflete 1. Extract the square root of .313487, Chair in 1960), and Jack de W et (a the cube root of 8242408 and the fourth root of Rhodes Scholar from South Africa who 4 3 1 2 1 1 x – 2x + /2 x – /2 x + /16 was later one of Oxford’s most admired explaining the processes; and show lecturers and greatly loved tutors). that if the square root of a whole number has any decimal figures they neither terminate nor recur. The opening lecture, on ‘Round Leonhard Euler with Rosie Cretney, Invariant Society President numbers’ was given by G.H. Hardy in 2. Under what conditions will the diametral planes of surfaces of the second order intersect in a point?

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Epsilons and deltas

of 13, spent seven weeks last summer in the Big Brother house with fourteen other people, making it to the final show of Series 11 and coming fifth. He recalls: “As the mathematician in the house I’d try to analyse the game in order to give my mind something to Photo by Rob Judges do. In the house everyone gets two votes to nominate someone and the Mathematics and nominated housemates are those with the most votes, so if you find yourself music debate Mathematical nominated, how many housemates can Every year the Vice-Chancellor’s Circle you guarantee voted for you? – this meets for dinner and a debate. This Institute garden wasn't too bad to work out without a year’s topic was: Is music the act of pen and paper. I’d definitely recommend sounding mathematics? parties auditioning for it, as you'll find out how you fare in an environment of extreme Last year’s Mathematical Institute Proposing the motion were Marcus du pressure and paranoia, but it's also a Garden Party was held at St Anne’s, Sautoy, Simonyi Professor for the Public great excuse to let your hair down and and was preceded by lectures on Maths Understanding of Science, and Eric have a really good time.” in and out of the zoo by Prof. Chris Clarke, Heather Professor of Music. Budd and The mathematics of visual Opposing it were Edward Higginbottom, hallucinations by Prof. Paul Bressloff. Director of Music and Choral Professor of Rubik’s cube Music at New College, and Robin Wilson, This year’s event will take place on Emeritus Professor of Pure Mathematics Saturday 16th July, with a lecture at 4 master solves ten at the Open University (now teaching at pm in the Martin Wood Lecture Theatre, Pembroke College). The motion was Clarendon Laboratory, followed by the cubes while defeated by a substantial majority. Garden Party at St blindfolded Anne’s. The lecture will be given by Sudoku puzzle corner Prof. Caroline Series on Indra’s pearls, Fill in the empty cells in the puzzle and there will also below, so that each of the nine letters be an update on the below the puzzle appears just once in new building. each row, column and 3 × 3 b ox, and a mathematical word will appear in one of the rows or columns: the hidden word may appear forwards or backwards, St Anne’s student down or up. on Big Brother (C4) OA N L T

Daniel Sheppard, a fourth-year O mathematics student at Trinity College, O E L finished third in the multiple blindfolded B A challenge at the European Rubik’s Cube O L U Championship in Budapest. N C For this event, he memorized 11 cubes E U N before being blindfolded and solving 10 T of them correctly within one hour. He C T N B Andrew with Titan can solve a normal 3 × 3 × 3 cub e in about 15 seconds and his fastest time A B C E L N O T U Andrew Edmonds, a second-year for one cube is 9.66 seconds. He is mathematics student at St Anne’s who ranked seventh in the world for the 5 × Solution to last year’s puzzle: took his A level maths exams at the age 5 × 5 blindfold event. CONVEXITY (column 5 upwards)

8 / OXFORD MATHEMATICAL INSTITUTE NEWSLETTER . SPRING 2011 . ISSUE 9 Support Mathema cs at Oxford A gi to the Mathema cal Ins tute will help to create a new home for mathema cs at Oxford. Help us to realise this exci ng future for mathema cal excellence by fi lling out the gi form overleaf.

All gi s of £100 or more will be recognised in a Book of Benefactors to be housed £250 in the new Mathema cal funds a large whiteboard Ins tute building for ad hoc problem solving of equa ons

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