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The Newsletter • Spring 2019

Mathematics and music Latest research Oxford Maths Festival 400 years of Savilian Professors of

1 Round up • Oxford Mathematics • Spring 2019 Head of Contents Departmental News Department’s letter Departmental News 3 Obituary: Sir Mike Giles was granted to Oxford’s Mathematical and the world around us. We are 400 years of Savilian Professors 4 Institute as part of the Queen’s 90th immensely proud to have Andrew as a of Geometry birthday celebrations. It is the first Regius colleague at the Mathematical Institute Professorship awarded to Oxford since in Oxford. Comings and goings 5 1842, and one of only three Regius Chairs in mathematics in the UK (the others being In 2016 Andrew was awarded the On 1 September, Mike Giles, Professor of Scientific Research: Hooke and Titchmarsh Fellows 6 at Warwick and St Andrews). , the highest honour in Computing and Professorial Fellow of St Hugh’s mathematics, for his stunning proof of Mathematics and music 7 Professor Martin Bridson, former Head of Fermat’s Last Theorem, a challenge that College, took over from Martin Bridson as Head of Oxford’s Mathematical Institute, writes: stumped for 350 years. Appointments and achievements 8 The award of the Regius Professorship In recognition of this transformative work, the Mathematical Institute. Mike writes: to Oxford recognised both our pre- he was also awarded the , OMMS – 9 eminence in fundamental research and the Royal Society’s oldest and most In preparing to write these few words, I looked back at the introductory first cohort for the new MSc degree the enormous benefits that flow to society prestigious award. words of my predecessors, Martin Bridson and before him Sam Howison, from mathematics. It is entirely fitting that and one thing they commented on was the way in which the job Oxford Maths Festival 10 the first holder of this Professorship Andrew’s proof has subsequently opened involves responding to the wide variety of issues which arise, sometimes appointed should be Sir Andrew Wiles. Nobody up new fields of inquiry and approaches to A visit to Rio 11 exemplifies the relentless pursuit of mathematics. In his current research he is unpredictably. The sheer diversity of these took me a bit by surprise in Regius Professor of mathematical understanding in the developing new ideas in the context of the my first term, constantly switching between teaching, research funding, Outreach and demystifying Oxford Mathematics at Oxford service of mankind better than him. His Langlands Program, a set of far-reaching undergraduate admissions, committee meetings, outreach activities, dedication to solving problems that have and influential conjectures connecting preparing for new academic appointments, etc. Where are they now? defied mankind for centuries, and the theory to and Oxford Sir Andrew Wiles stunning beauty of his solutions to these the theory of automorphic forms. Andrew Research and social media has been appointed by Her Majesty the problems, provide a beacon to inspire and will remain the Royal Society Research On the teaching side, our new MSc, the Oxford MSc in Mathematical Queen to be Oxford’s first Regius Professor sustain everyone who wrestles with the Professor of Mathematics at Oxford and Sciences (OMMS), is off to a very good start with a first cohort of 36 Public Lectures 12 of Mathematics. The Regius Professorship fundamental challenges of mathematics a Fellow of Merton College. students; this will increase to around 90 by 2023. We are also planning to increase the on our MSc in Mathematical and Theoretical Oxford Mathematics Merchandise , and our joint degree in Mathematics and Computer Science, Alumni Weekend Obituary: and have begun discussions with Economics on a possible new degree in Mathematics and Economics. Sir Michael Atiyah 1929–2019 Brexit is still looming large, and it is still hard to predict what the We were very sorry to hear of the death consequences for us will be. Another significant change for research in January of Michael Atiyah. Michael was funding is the creation of UKRI (UK Research and Innovation), which brings a giant of mathematics. He held many together the seven Research Councils, Innovate UK and Research . positions including Savilian Professor of This is increasingly channelling funding through major initiatives, such as Geometry here in Oxford, President of the the Industrial Strategy Challenge Fund and Prosperity Partnerships, so we Royal Society, Master of Trinity College, Cambridge, the founding Director of the are working to develop ideas for major research projects aligned with Institute, and Chancellor these opportunities. of the University of Leicester. He was awarded the in 1966 and Another big focus right now is on preparations for REF 2021, the next the Abel Prize in 2004. instalment of the Research Excellence Framework which determines the Michael’s work spanned many fields. level of the core funding we receive from Research England. Get in touch Together with Friedrich Hirzebruch he laid the foundations for topological K-theory, Sir Michael Atiyah So, on these and other fronts there’s a great deal of variety to look We hope that you will enjoy this an important tool in algebraic forward to in the coming year. annual newsletter. We are interested which describes ways in which apart as and group Michael began to consider quantum field to receive your comments, and also can be twisted. His Atiyah–Singer index representations. theory more seriously, and ultimately contributions for future newsletters. theorem, proved with Isadore Singer became one of the founders of what is Please contact the editor, Robin Wilson, in 1963, vastly generalised classical His later work was inspired by theoretical loosely called ‘quantum mathematics’. c/o [email protected] results from the 19th century (the physics – and coincided with the arrival Riemann–Roch and Gauss–Bonnet of Roger Penrose in Oxford. The two Michael gave his generously in @OxUniMaths theorems) and the work of his teacher exchanged ideas and realised how modern the promotion of his subject. In May facebook.com/OxfordMathematics William Hodge on harmonic . contributions to algebraic geometry 2018 he gave a Public Lecture here in instagram.com/oxford.mathematics It also provided an entirely new bridge formed the appropriate framework for Oxford, entitled ‘Numbers are Serious www.maths.ox.ac.uk between analysis and topology which Penrose’s approach to the equations but they are also Fun’. It can be watched could act as a mechanism for giving of . As his ideas on the Oxford Mathematics YouTube Design: William Joseph structure to identities in as far developed, at the urging of Ed Witten, Channel.

Round up • Oxford Mathematics • Spring 2019 3 400 years of Comings and goings

Savilian Professors John Ball Sir John Ball FRS has retired as Oxford’s Sedleian Professor of Natural Philosophy and Director of the Oxford Centre for Nonlinear Partial Differential Equations. He was a Fellow of The Queen’s College. of Geometry For his distinguished contributions to the world of mathematics, John was elected a Fellow of the Royal Society in 1989, and received its prestigious The current Savilian Professor of Sylvester Medal in 2009. He was President of the Geometry is FRS, Mathematical Society from 1996 to 1998, who was appointed to the Chair in and President of the International Mathematical Union 2017. A former DPhil student of from 2003 to 2006. An interview with him can be Michael Atiyah, she specialises in Robin Wilson viewed on the Oxford Mathematics YouTube Channel. algebraic and symplectic geometry, and writes: The Savilian Chairs 2019 marks the 400th anniversary of the founding in of Geometry have always ’s edition of Apollonius’s Conics Oxford of the Savilian Chairs of Geometry and . played an important role in the mathematical life of Oxford. But who was Savile, and which distinguished figures have I feel delighted and honoured A contemporary caricature of Henry Smith been Professors of Geometry? to be part of this tradition.

Sedleian Professor of Natural Philosophy Sir Henry Savile was Warden of Merton College as Savilian professor, Wallis made many important and introduced the word ‘matrix’ to mathematics. Jonathan Keating FRS, Henry Overton Wills Professor from 1585 until his death in 1622. An internationally contributions to mathematics. His 1655 book on An enthusiastic poet, his inaugural Savilian lecture in of Mathematics at the University of Bristol, has been renowned scholar and enlightened teacher of conic sections introduced the symbols for the included a sonnet dedicated appointed to the Sedleian Chair of Natural Philosophy mathematics and astronomy, he regularly lectured on and ‘greater than or equal to’, while his 1656 book, ‘To a Missing Member Of a Family Group of Terms in in succession to Sir John Ball. He has wide-ranging Euclid’s Elements, ’s , and the ‘new Arithmetica Infinitorum on infinite , greatly an Algebraical Formula’. Sylvester attempted, largely interests, but is best known for his researches into astronomy’ of Copernicus. These lectures and his influenced the young Isaac Newton in Cambridge a few without success, to establish a research tradition in a random matrix theory and its applications to quantum many other writings are preserved in the extensive years later. With his Oxford colleagues, , university still mainly concerned with teaching. chaos, number theory and the Riemann zeta function. Savile Collection in the , and a fine , and others, In September he takes up his Oxford appointment, memorial to him, flanked by Euclid and Ptolemy, can Sir Henry Savile played an important role in establishing the It was in the 20th century that the Savilian professors and two months later he will become the next be seen in . Royal Society of London in the . became increasingly involved with research activities. President of the London Mathematical Society. G. H. Hardy, in particular, spent eleven of his most In 1619 Savile founded the Chairs of Geometry and Wallis was succeeded in 1704 by Edmond Halley, who productive years in Oxford, writing over 100 papers The Sedleian Chair is one of Oxford’s oldest Astronomy that bear his name and which were to have held the Savilian Chair of Geometry for 38 years. His on a range of mathematical topics and running regular professorships, having been founded in 1621. Recent a profound influence on the teaching and development house in New College Lane records his residence there, advanced classes in . He also argued holders have been George Temple (1953–68), of these then-neglected subjects. For the Geometry in a building used for Savilian professors for 200 years. the need for a mathematical institute. Although Albert Green (1968–79) and Thomas Brooke Benjamin position he first sent for Edmund Gunter, inventor of Although mainly remembered for predicting the return he was not a geometer, Hardy always insisted on (1979–96). Like them, Jon Keating will be a Fellow of several navigational and astronomical instruments, of the that bears his name, Halley established giving a series of lectures on geometrical topics. His The Queen’s College. who came ‘and brought with him his sector and his mathematical credentials with a fine edition of successor, E. C. Titchmarsh, declined to be involved in quadrant, and fell to resolving of triangles and doeing Apollonius’s Conics, published in 1710. geometrical pursuits, and since then the designation a great many fine things’. Said the grave knight, ‘Doe ‘Savilian Professor of Geometry’ has been taken to John Wallis’s portrait you call this reading of geometrie? This is showing of in Oxford’s Examination For the next 100 years, the Savilian Professors of include any of pure mathematics. Meanwhile, the G. H. Hardy tricks, man!’ and so dismisst him with scorne and sent Schools Geometry were mainly astronomers who made research tradition has been continued by all the later for Briggs, from Cambridge.’ few contributions to mathematics – for example, Savilian professors: Michael Atiyah, , John Smith, who held the position for 30 years, Richard Taylor, and Frances Kirwan. Henry Briggs, the first Savilian Professor, worked on spent most of his time in Cheltenham and wrote on eclipses and on navigation, and had recently become ‘The Use and Abuse of the Cheltenham Waters’. Nick Woodhouse involved with the newly invented logarithms of Professor Nicholas Woodhouse has retired as John Napier. The inventor of ‘logs to base 10’, Briggs The next mathematician of note was Henry Smith, Events President of the Clay Mathematics Institute, a spent his early Oxford years producing a table of who made major contributions to the theory of The 400th anniversary of the Savilian Chair of Geometry will be position that he has held since 2012. A Fellow of 30,000 such logarithms, calculated by hand to no numbers, introduced the ‘Smith form of a matrix’, and celebrated in the autumn with an exhibition at the Bodleian Library and a Wadham College, he led Oxford’s Mathematics fewer than 14 decimal places. He died in 1631, and is published a ‘Cantor set’ eight years before Cantor did. special one-day meeting in Oxford of the British Society for the History Department from 2001–10. His research interests buried in Merton College Chapel. Edmond Halley of Mathematics. Further information about the Savilian professors are in geometric quantisation theory and twistor Henry Smith’s successor was the brilliant but eccentric can be found in the book Oxford Figures (ed. J. Fauvel, R. Flood and R. theory, and he has written a number of books on Following the English Civil War of the 1640s the James Joseph Sylvester, who was appointed in 1883 Wilson), , 2013. the subject. He is succeeded as President of the Clay post was awarded to John Wallis, who had been a at the age of 69. Sylvester made major contributions Mathematics Institute by Professor Martin Bridson, codebreaker for the Parliamentarians. In his 54 years to invariant theory and combinatorial mathematics, Waynflete Professor of Pure Mathematics.

4 Round up • Oxford Mathematics • Spring 2019 Round up • Oxford Mathematics • Spring 2019 5 Research: Mathematics and music

Hooke and Titchmarsh fellows James Sparks

In order to realise its ambition of bringing the world’s Radu Cimpeanu In November a capacity audience enjoyed an (Hooke Fellow) most talented mathematicians at all career stages to What happens when aircraft fly Oxford Mathematics Public Lecture on the links Oxford, the Mathematical Institute has invested in through clouds? between mathematics and music, followed by a some high-profile research fellowships – the Hooke stunning performance of J. S. Bach’s Goldberg Variations Fellowships (named after Robert Hooke) in applied by the Sinfonia. The talk was presented mathematics, and the Titchmarsh Fellowships (named by James Sparks, Fellow of Oriel College and the after E. C. Titchmarsh) in pure mathematics, Here, two Mathematical Institute’s Director of Graduate Studies. of our current fellows outline their current interests; James writes: fuller details can be found on the Institute’s website.

David Hume Right: An aircraft Mathematicians have always been drawn to Right: James Sparks’s I also talked about the important role played by (Titchmarsh Fellow) flying through a high mathematical structures that are simple, natural, and Oxford Mathematics creativity in mathematics, something that isn’t A continuum of expanders liquid water content elegant to define, but which turn out to have a hidden Public Lecture always appreciated by non-mathematicians. The environment (painting On a cloudy or rainy day, aeroplanes have to fly depth and complexity. Such structures are often way that mathematicians create, especially in the A network (or graph) is a collection of by Anca Pora). through very humid conditions. Tiny drops of water regarded as beautiful, and uncovering them has kept Below: James Sparks early stages of an idea, is often very non-linear and vertices (points) and edges (lines connecting two hit the surface of the aircraft and start accumulating, countless mathematicians occupied for decades. talks on mathematics intuitive, with more linear and methodical reasoning vertices). They are used to encode everything from Right: The geometry forming thin liquid films and rivulets. Once a certain and music at the usually coming in later. In music I think that composers transport infrastructure to social media interactions, of a water droplet with altitude is reached, temperatures fall sharply and these Last autumn I had the enormous privilege of working Queen Elizabeth Hall often work in much the same way, and that they and from the behaviour of subatomic particles to diameter D hitting patches of water may quickly freeze and become a with the City of London Sinfonia on a Bach and the in London. do so for similar reasons: in both mathematics and the structure of a group of symmetries. A common a solid surface with real danger. In fact, after human error and mechanical Cosmos concert series. We toured the UK across seven music one is simultaneously trying to create and theme throughout these applications, and therefore velocity U∞ at an failure, icing is one of the main hazards. venues, with three different programmes featuring discover interesting and beautiful structures within a of interest to civil engineers, advertisers, , angle θ.] music by, or inspired by, Johann Sebastian Bach. As a constrained and abstract system. Symmetry also plays and mathematicians (amongst others), is that it U∞ mathematician and former Cambridge organ scholar, a key role in both, not just aesthetically, but also as a is important to know how well connected a given I’ve always been fascinated by the connections tool for building and discovering structure, and as an water droplet D blow-o network is. 10 µm < D < 500 µm between mathematics and music, and Bach’s music organisational principle. stick in particular. Each programme featured a talk about Given a network, its cut size is the smallest number air angle of inscidence θ solid surface these various connections, interspersed with musical I think that Bach’s music shares many aesthetic qualities of vertices that we need to remove so as to excerpts and performances of complete works. with beautiful mathematics. Bach would often start disconnect the network; for example, trees are poorly Attempting to understand the detailed effects in this The tour started in our very own Mathematical with a simple but elegant musical idea, and from connected (with cut size 1), while complete graphs are scenario leads to what applied mathematicians call a Institute with Bach’s Goldberg Variations, arranged it systematically build a large and complex musical highly connected (see pictures to the right). multi-scale problem. Here, one needs to model and for string orchestra by Dmitry Sitkovetsky. Before a work. He did this by using strict musical forms, such account for the complex high-speed air flow around complete performance of this monumental work, I as canons and fugues. In these compositions Bach In my current work I explore how cut sizes behave the aircraft, while trying to investigate the detailed began by talking about the aesthetic and artistic side took his elegant starting pattern of notes, and applied for certain networks (specifically, Cayley graphs surrounding physical processes such as of mathematics, and conversely the abstract and various ‘musical maps’ to it – that is, maps that take of finitely generated groups) that are ‘negatively violent drop impact, with features changing at the mathematical side of music. My introductory words the original pattern of notes to another pattern, curved at large scale’: this area is of particular sub-micron scale inside the capture region on the can be found on the Oxford Mathematics changing it in some way, but also preserving its form. interest in group theory, and plays a key role in recent aircraft surface. If we add further physical effects such YouTube Channel. The rich and intricate textures of Bach’s music result proofs of important conjectures in low-dimensional Above: A tree and a as temperature, a rich and difficult landscape emerges, from applying these maps repeatedly, in a carefully topology. For such a negatively curved group, the complete graph. which can be dealt with only through a combination constructed manner. I talked about this using several of cut size seems to be related to the dimension of an of mathematical tools. the Goldberg Variations as illustrations, accompanied associated fractal ‘at infinity’. With John Mackay and Below: The associated by excerpts played by the City of London Sinfonia. Romain Tessera, we have established this link for fractal at infinity of a Advances made through matched asymptotic an interesting collection of such networks, and are typical ‘negatively curved’ and complex analytical arguments, as well as the Writing music like this involves a great deal of analytical working on developing the mathematical machinery group is topologically a development of state-of-the-art computational skill, and is very similar to solving a mathematical that is needed to generalise our results. ‘Menger sponge’. tools capable of addressing the significant topological problem. It is very much a process that is part creation, changes in the flow, help us to unravel the individual part discovery: having fixed a musical idea, the laws of droplet deformation, break-up, and subsequent harmony control how it can fit together using these fragmentation, thereby transferring this insight different types of repetition. The skill of the composer into quantifiable features for experimentalists and is not only to discover the hidden music within a theme, engineers. The developed drop impact models but also to create the right theme in the first place. address key questions at a fundamental level, with Mathematics works in much the same way! Bach’s the conclusions of the study extending towards the genius meant that he was able to use this approach to improvement of anti-icing techniques at a time of create beautiful music that also has a more abstract expansion and diversification of the relevant sectors mathematical beauty. For me, it is that combination in the industry. that makes his music so special.

6 Round up • Oxford Mathematics • Spring 2019 Round up • Oxford Mathematics • Spring 2019 7 Appointments… OMMS – first cohort for We welcome the following new Faculty members. the new MSc degree

Dr Kathryn Gillow OMMS Course Director

At the time of last year’s Round up, our new master’s Mathematics at the University of Warwick. I was born and raised in , but my father is from the UK and Anna Ananova André Henriques Jason Lotay programme, OMMS (the Oxford Masters in my mother is from Serbia, so I have three nationalities. (Imperial, London) (Oxford) (UCL, London) Mathematical Sciences), was still somewhat abstract. Departmental Lecturer Departmental Lecturer Professor of Pure Mathematics My experience in Oxford so far has been fantastic. Research interests: pathwise integration, Research interests: Mathematical physics, and Fellow of Balliol College This changed in October when we welcomed our first Studying mathematics is my primary reason for being at functional Ito , rough path studying conformal field theory with tools Research interests: differential geometry, cohort of 36 students onto the course. They came from Oxford, but I have enjoyed the social aspect of college theory, pathwise optimal control and from operator . particularly Riemannian manifolds with special life here. I also enjoy sports and spend much time model-free finance. holonomy, and related geometric flows. 17 countries with degrees from 32 institutions, bringing running and cycling round Oxford. a new diversity to the current fourth-year population One notable aspect of OMMS is how it has brought which they joined. This new MSc course will help us to together people with very diverse personal and attract outstanding mathematicians from around the academic backgrounds. I feel that this has enriched my …and Achievements learning experience here, while enabling me to make a world to Oxford at an early stage of their careers. diverse group of friends. This has been another excellent year for awards and achievements, with a diverse range of prizes and recipients. OMMS is a joint venture with our colleagues in the My interests lie in mathematical biology, especially Department of Statistics, and our students can study in the areas that relate to human biological sciences. courses chosen from the fourth-year programmes in Being able to choose from the Mathematics, Statistics Sir John Ball FRS has received the Heather Harrington has Gergely Röst has been given an both departments, as well as some computer science and Computer Science departments has allowed me 2018 Leonardo da Vinci Award from the been awarded a Whitehead inaugural András Gács Award at the modules. Some of our first cohort have chosen to to tailor my studies to my interests and goals. After European Academy of Sciences. Prize by the London Eötvös Loránd University in Budapest specialise in particular areas of interest, while others this Master’s course, I wish to pursue a PhD degree. Mathematical Society for motivating students to embrace the opportunity that OMMS provides to My hope is to be able to conduct research in the field Helen Byrne has been for her researches into pursue mathematics. experience a truly eclectic mix of courses. A key of mathematical biology, in order to make meaningful awarded the 2018 mathematical biology. feature of the OMMS course is the dissertation, and Xavier Gonzalez contributions to the global community. Leah Edelstein-Kesket Andreas Sojmark has been awarded these projects are now under way on a varied range Prize by the Society of Kristian Karadjiev has been awarded the the Bar-Ilan Young Researcher Prize in of topics. We look forward to seeing the finished Jason Wong writes: Mathematical Biology. Graham Hoare Prize by the Institute of Financial Mathematics. dissertations after Easter. I did a BSc degree in Mathematics at the University of Mathematics and its Applications for an Warwick, before moving to St Hugh’s for OMMS. I was Xenia de la Ossa has article on ‘Connecting the dots with Nick Trefethen FRS Here are some comments from three of the first born and raised in Hong Kong, but have lived in the UK for been awarded the Dean’s Pick’s theorem’. has been awarded OMMS students: the last seven years. I am proud to call both places home. Distinguished Visiting Honorary Degrees by the Professorship by the Jochen Kursawe has Universities of Fribourg Xavier Gonzalez writes: My interests loosely lie in the field of statistical learning. Fields Institute in Toronto, been awarded the 2018 (Switzerland) and I have recently graduated summa cum laude in I am particularly interested in efficient for Canada, to work on the Reinhart Heinrich Prize Stellenbosch Mathematics from . As an estimating parameters and making predictions from homological of by the European Society (). undergraduate I studied modular forms under the complex data sets. The design and study of such mirror symmetry. for Mathematical and direction of Professor Ken Ono, one of my role Chloe Colson algorithms involve as well as high- Theoretical Biology. Francis Woodhouse models. Having won a Rhodes scholarship, which dimensional probability and statistics. I was thereby Mike Giles and Alain Goriely have been has been given the funds international students for postgraduate study at drawn to the OMMS programme by the sheer breadth appointed Fellows of the Society for Ursula Martin CBE and Vicky Neale have H. D. Landahl Mathematical Oxford, I am now an OMMS student at Balliol. I knew and depth of its courses. I don’t think there are many Industrial and (SIAM). won Suffrage Science Awards celebrating Biophysics Award by that I wanted to continue my study of mathematics courses where you can learn about both statistical women in science. the Society for while also exploring applied mathematics, statistics, machine learning and computational ! Ian Griffiths has won a Vice-Chancellor’s Mathematical Biology. computer science, and physics, and OMMS was Innovation Award for his work on the the perfect fit. I have also joined the Oxford Maths The academic work in Oxford is intense, but people here mitigation of arsenic poisoning. Ambassadors, and get involved with outreach events. are more approachable than I imagined. I am the OMMS student representative and also sing in the Chapel Choir I enjoy the Mathematical Institute, where there is at St Hugh’s. always something exciting going on. I love the wide range of options and diversity of thought in OMMS, Jason Wong I hope next to work as a research scientist before New undergraduates: This year saw the New graduates: We also welcomed and will reflect on my OMMS experiences as I decide possibly pursuing doctoral studies. OMMS has exposed Student arrival of 180 men and 93 women from 43 new DPhil students – 13 from the UK, how to spend my second Rhodes year in Oxford. me to much contemporary mathematics developed to Intake 33 nationalities, ranging from Afghanistan 15 from the EU, and the remainder from address modern challenges, such as small but high- to Syria, Kazakhstan to Greece, and Argentina, , , India, Israel, Chloe Colson writes: dimensional data sets. This gives me a sense of the 2018 Malaysia to Pakistan. 70% of the UK entry Kenya, Mexico, Norway, South Africa I’m an OMMS student at St Catherine’s College. Before fluidity of mathematics and of its relevance in was from state schools. and the USA. coming to Oxford, I completed a Bachelor’s degree in today’s world.

8 Round up • Oxford Mathematics • Spring 2019 Round up • Oxford Mathematics • Spring 2019 9 A visit to Rio Outreach and Oxford Maths Festival James Maynard demystifying Oxford

Six Oxford mathematicians – Mike Giles, Richard One of the challenges that Oxford Mareli Grady Haydon, Peter Keevash, Jochen Koenigsmann, faces is to make itself approachable, Schools Liaison Officer (Statistics) Miguel Walsh and myself – were invited speakers at not only to aspiring students but to a and Outreach Events Coordinator (Maths) wider world that can see us as remote, the International Congress of Mathematicians (ICM) or worse. In response we are showing in Rio de Janeiro last August. exactly what we do in an unedited form.

The ICM is the world’s largest mathematics so he has been the only mathematician to For Oxford Mathematics this has conference and has met every four years since have received two Fields Medals! comprised live streaming a first-year 1897 (except for a couple of small breaks lecture on dynamics, filming a tutorial, during the wars). It aims to have lectures It is a great honour for a mathematician and making public some examples covering the most important developments to be invited to speak at an ICM. The of the problem sheets that students across the entirety of mathematics over number of Oxford mathematicians that work on. Again, social media have the previous four-year period. were invited to speak, and the breadth of proved a vital tool for showing us in subjects represented – from stochastic this workaday mode. Coupled with our The conference was eventful – and not modelling to decidability and combinatorial extensive school visits and dedicated just in a mathematical way! Unlike typical matchings – demonstrate the continuing events for schools, it all adds up to more specialised maths conferences, strength of mathematics in Oxford. an that might not seem so the ICM is a great place to hear an incomprehensible or remote. We plan overview of the key developments in to do much more. areas of mathematics outside of one’s particular expertise. One highlight is the awarding of the Fields Medals (last year given to , , and ) and the accompanying talks on the work behind the medals. Unfortunately, Birkar’s medal was stolen just after being awarded, but a replacement was readily available,

Where are they now? Research and social Where do our former tutors go when they retire? Here we catch up media with two of them: Mary Lunn of St Hugh’s College and Ian Grant of Pembroke College. Mathematical research reflects issues that society faces today – understanding the materials around us, understanding our bodies, and even our online behaviour – Bubbles, origami, dodgy dice and On the second day, visitors to the Mathematical but it is also about pushing the boundary Institute took part in hands-on activities, went to Mary Lunn Ian Grant of mathematics for its own sake. self-supporting bridges – over two workshops on topics as diverse as cryptography, days last April the Oxford Maths symmetry, catenary arches and problem-solving, Following my retirement in 2007, like My wife Beryl and I retired in 1998, Sometimes this research has real-world and attended lectures on sport, risk, , and the many academics I have kept my hand moving to a retirement complex in applications. The topology of data, as Festival, free and hosted by Oxford mathematics of Lewis Carroll. They also tried their in a little. Work with Glasgow and Cambridge in 2012. I have continued well as its volume, is a case in point. Mathematics, showcased the hand at making something beautiful and mathematical Newcastle Universities involved diversity active building on the embryo project However, our research is also carried in the craft session and challenged each other to of bacteria in water treatment plants. proposed first by David Mayers out for the pleasure of the intellectual creative, fun and surprising sides mathematical board games. We had a grant which ran an experiment and myself at a Workshop in Orsay challenge. As a consequence you might of mathematics. in the laboratory, and which used DNA in 1970. The General-purpose think that the pure side of our research The festival was wholly staffed by volunteer staff and techniques to consider abundance of Relativistic Atomic Structure Program attracts less attention, especially on Adults and children alike were entertained, students, some of whom had never engaged in this ammonia oxidising bacteria which are (GRASP) is now used worldwide and social media – but far from it! Our ‘pure’ challenged and enthused by a variety of activities type of event before. All reported enjoying the essential to keep these plants running. is a major tool of the Computational mathematics case studies are among in central Oxford and in the Mathematical Institute. experience of sharing their enthusiasm for mathematics Atomic Structure consortium the most popular items on our social Our visitors learned about polyhedra and Sierpinski with others. In the Oxford Statistics Department I have (CompAS), based on Malmö and Lund media pages. We can confidently triangles using the medium of balloons, tried to find had two MSc students each year, with the in . report that there is a huge appetite for the shortest route between cities, had fun with The Mathematical Institute hopes to make the main intention of enabling them to analyse mathematical knowledge. bubbles, and played with tangrams. They also learned Oxford Maths Festival an annual event, and is currently data and produce comprehensible reports I am now a permanent visitor to the about Bayesian methods and the application of seeking the sponsorship to allow this to happen. If you on their analysis. These projects form a Atomic Astrophysics group here in Follow us on statistics to proteins, watched the double would like to support the event, please visit part of their assessment. Cambridge, and spend much of my twitter.com/OxUniMaths in its mad spin, and assembled Penrose tiles. They https://mathsfest.web.ox.ac.uk and contact us. time there and on a major update of facebook.com/OxfordMathematics were delighted by a game of chocolate trickery, tied We are sorry to announce that my 2007 monograph which underpins themselves up in knots, and tried to work out The next Oxford Maths Festival will take place here in Daniel Lunn FRSS, Mary’s husband, died the CompAS project. After twenty instagram.com/oxford.mathematics puzzles. the Andrew Wiles Building on 11–12 May 2019. in February. He was a well-loved Fellow years of retirement I feel privileged to to keep up to date with our latest We’d love to see you. and Tutor at Worcester College. be able to continue in active research. research activities.

10 Round up • Oxford Mathematics • Spring 2019 Round up • Oxford Mathematics • Spring 2019 11 Public Lectures

Oxford Mathematics Oxford Mathematics Public Lectures Oxford Mathematics Public Lectures Oxford Mathematics Public Lectures are Public Lectures Titchmarsh Lecture together with the Simonyi Science Show a mixed bag, by which we mean that they 30.10.18 17.05.18 mix universal themes with tough maths, Michael Atiyah 29.05.19 Numbers are Serious attracting the curious, the academic but they are also Fun The Creativity Code: and (via our large cohort of schools) the How AI is learning to write, Roger Penrose aspiring. They also attract a large online To a I am paint and think a mathematician; 0 audience, the wider public that Oxford to a mathematician, needs to attract (and perhaps convince).

0 0 On average, 30,000 viewers watch some a physicist 3.142

0

0 2.718

√-1 1.618 part of each live broadcast, and this year √-1 √-1 √-1 1.618 1.618 1.618 √-1 1 0 0 1 2.718 √-1 1

0 3.142 0 3.142 0 1.618 0 2.718 2.718 1.618 Will a computer ever compose a symphony, write a prize- Marcus du Sautoy is Simonyi Professor for the Public , who famously0 jumped out of his bath shouting 5–6pm Thursday 17 May 2018

3.142 √-1 1 e √-1 winning novel, or paint a masterpiece? And if so, would we Understanding of Science in Oxford. “Eureka”, also ‘invented’ the√-1 number π. Euler invented and Lecture Theatre 1, Mathematical Institute, Oxford we have also hosted lectures in London had fun with his formula e2πi=1. The world is1 full of important 0 be able to tell the difference? 1.618 0 0 √-1 3.142 numbers waiting to be invented. Why √not-1 have a go? Register at [email protected]√-1 6–7pm Wednesday 29 May 2019 0 0 2.718 3.142 1.618 0 In The Creativity Code, Marcus du Sautoy examines the Mathematical Institute, Oxford In this year’s Oxford Mathematics London Public Lecture in 7–8pm Tuesday 30 October 2018 2.718 nature of creativity, as well as providing an essential guide Michael Atiyah3.142 is one of the world’s leading mathematicians3.142 www.maths.ox.ac.uk/events/public-lectures-events partnership with the Science Roger Penrose reflects Science Museum, London SW7 2DD 0 and a pivotal figure in twentieth and twenty-first century Watch live: https://livestream.com/oxuni/atiyah into how algorithms work, and the mathematical rules Register at [email protected] √-1 1.618 and Solihull as well as in Oxford. on his career. The lecture will be followed by a Q&A with underpinning them. He asks how much of our emotional mathematics.3.142 His lecture will be followed by an interview 2.718 0 mathematician and broadcaster Hannah Fry. Please email [email protected] to register. 0 √-1 with Sir John Ball, Sedleian Professor3.142 of Natural Philosophy response to art is a product of our brains reacting to pattern Watch live √-1 0 and structure. And might machines one day jolt us in to facebook.com/OxfordMathematics here in Oxford, where Michael will talk about his lecture, 1.618 √-1 Watch live √-1 2.718 his work and his life as a mathematician. being more imaginative ourselves? livestream.com/oxuni/du-Sautoy2 facebook.com/OxfordMathematics or view on Livestream: 0 2.718 1 √-1 √-1 0 1.618 1.618 1.618 √-1 √-1 livestream.com/oxuni/Penrose-Fry 2.718 0 √-1 √-1 0

1.618 -1 2.718 2.718 √ 0 3.142 0 0 2.718 √-1 2.718 0 Oxford Mathematics Public Lectures are generously 2.718 Oxford Mathematics Public Lectures are generously 2.718 3.142 1 √-1 √-1 Oxford Mathematics Public Lectures are generously 2.718 1 supported by XTX Markets. supported by XTX Markets. 2.718 √-1 0 2.718 3.142 0 3.142 3.142 √-1 supported by XTX Markets. √-1 1 √-1 0 0 3.142 √-1 0 2.718 2.718 1.618 2.718 This year’s highlights have included 0 2.718 √-1 0 2.718 1 0 0 0 JOSEPH WILLIAM DESIGN: JOSEPH WILLIAM DESIGN: DESIGN: WILLIAM JOSEPH WILLIAM DESIGN: 1.618 3.142 0 √-1 3.142 √-1 0 1.618 1 0 0 1 1 2.718 3.142 0 1 Sir Roger Penrose presenting his latest cosmological research and confessing to Oxford Mathematics Oxford Mathematics Oxford Mathematics Public Lectures Christmas Public Lecture Public Lectures not being proficient at multiplication, 05.09.18 12.12.18 Persi Diaconis telling us that there is Persi Diaconis nothing random about tossing a coin, and Chance and Evidence 30.04.19 Hannah Fry Julia Wolf Hannah Fry discussing the good, the bad The Power of Randomness and the downright ugly of algorithms. 5 9 18 10 Hello World Most of the lectures are available on our 13 25 36 Hannah Fry takes us on a tour of the good, the bad and Oxford Mathematics YouTube Channel. 29 the downright ugly of the algorithms that surround us. Are they really an improvement on the humans they 24 are replacing? Hannah Fry is a lecturer in the Mathematics of Cities at the Centre for Advanced Spatial Analysis at UCL. She is also a well-respected broadcaster and the author of several books including the recently published ‘Hello World: How to be Human in the Age of the Machine.’ Far from taking us down the road of unpredictability and chaos, randomness has the power to help us solve a fascinating range of problems. Join Julia Wolf on a mathematical journey from penalty shoot-outs to 5–6pm Tuesday 30 April 2019 internet security and patterns in the primes. Mathematical Institute, Oxford In this lecture Persi Diaconis will take a look at some of our Persi Diaconis is the co-author of ‘Ten Great Ideas about Julia Wolf is University Lecturer in the Department Register at [email protected] most primitive images of chance – flipping a coin, rolling Chance’ (2017) and is the Mary V. Sunseri Professor of of Pure Mathematics and Mathematical Statistics at a roulette wheel and shuffling cards – and via a little bit of Statistics and Mathematics at . the . Watch live mathematics (and a smidgen of physics) show that sometimes 5–6pm Wednesday 12 December 2018 facebook.com/OxfordMathematics things are not very random at all. Indeed chance is sometimes 5–6pm Wednesday 5 September 2018 Mathematical Institute, Oxford livestream.com/oxuni/wolf confused with frequency and this confusion carries over to a Mathematical Institute, Oxford confusion between chance and evidence. All of which explains Please email [email protected] to register. our wild misuse of probability and statistical models. Please email [email protected] to register. Watch live Watch live facebook.com/OxfordMathematics or view on Livestream: facebook.com/OxfordMathematics or view on Livestream: livestream.com/oxuni/ChristmasLecture2018 livestream.com/oxuni/PersiDiaconis

Oxford Mathematics Public Lectures are generously Oxford Mathematics Public Lectures are generously Oxford Mathematics Public Lectures are generously supported by XTX Markets. supported by XTX Markets. supported by XTX Markets. DESIGN: WILLIAM JOSEPH WILLIAM DESIGN: DESIGN: WILLIAM JOSEPH WILLIAM DESIGN: DESIGN: WILLIAM JOSEPH WILLIAM DESIGN:

Alumni Weekend and Garden Party There is no Oxford Mathematics Garden Party this year as we are concentrating on widening our range of Public Lectures, both in Oxford and across the UK. We shall be in London and Newcastle in the Autumn, and we will be hosting alumni receptions after some of our lectures.

However, we would encourage you to join the many alumni who will attend the University Alumni Weekend on 20–22 September 2019. This will take place in the Mathematical Institute. www.alumni.ox.ac.uk/alumni_home Musette bags Yes, that is what they are officially called and they are currently our Number One bestseller. You can buy all our merchandise from the University Shop (oushop.com).

12 Round up • Oxford Mathematics • Spring 2019