The Oxford Mathematics Newsletter • Spring 2019 Mathematics and music Latest research Oxford Maths Festival 400 years of Savilian Professors of Geometry 1 Round up • Oxford Mathematics • Spring 2019 Head of Contents Departmental News Department’s letter Departmental News 3 Obituary: Sir Michael Atiyah 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). Abel Prize, 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 mathematicians 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 Copley Medal, 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 Andrew Wiles 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 number theory to algebraic geometry and Oxford mathematician 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 numbers on our MSc in Mathematical and Theoretical Oxford Mathematics Merchandise Physics, 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 England. 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 Isaac Newton Institute, and Chancellor these opportunities. of the University of Leicester. He was awarded the Fields Medal 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 topology forward to in the coming year. annual newsletter. We are interested which describes ways in which spaces apart as number theory 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 time 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 integrals. 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 mathematical physics. As his ideas on the Oxford Mathematics YouTube Design: William Joseph structure to identities in areas 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 Frances Kirwan FRS, London 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 Edmond Halley’s edition of Apollonius’s Conics Oxford of the Savilian Chairs of Geometry and Astronomy. 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 infinity the Sheldonian Theatre 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, Ptolemy’s Almagest, and the ‘new Arithmetica Infinitorum on infinite series, 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, Robert Boyle, university still mainly concerned with teaching. chaos, number theory and the Riemann zeta function. Savile Collection in the Bodleian Library, and a fine Robert Hooke, Christopher Wren and others, In September he takes up his Oxford appointment, memorial to him, flanked by Euclid and Ptolemy, can Sir Henry Savile John Wallis played an important role in establishing the It was in the 20th century that the Savilian professors James Joseph Sylvester and two months later he will become the next be seen in Merton College Chapel.