LONDON MATHEMATICAL SOCIETY

NEWSLETTER No. 420 December 2012

Society LMS COUNCIL DIARY for Ephrem’s work. Overall, the Meetings 12 October 2012 Society’s finances are in reason- able shape – taking inflation into A personal view and Events account, the Society effectively 2012 The meeting opened with a few broke even – but there is no room moments silence in remembrance for complacency, especially when 18-19 December of Anne Bennett. Anne had considering the current discus- LMS Prospects in provided important support to sions around academic publish- Mathematics Meeting, Council, as well as to the many ing. In addition, as Rob pointed Manchester Committees which came under out, there is the salutary fact that page 19 her wing, and we all benefited the Society’s invested assets now from the extraordinary amount are nominally worth roughly the 2013 of work she did to ensure the same as they were worth a dec- 1 Friday 1 March smooth running of Society busi- ade ago, excluding the current Mary Cartwright ness. As Fiona Nixon so elo- value of De Morgan House. At the Lecture, London quently described in her tribute May Council meeting, Rob had page 6 to Anne (which appeared in the made a compelling argument for previous Newsletter), Anne made exploring the possibility of the Monday 18 March Northern Regional a real difference both to the So- Society investing in property, and Meeting, Newcastle ciety and to the staff at DMH at today’s meeting he presented page 14 with whom she worked. Coun- the worked-up business case. cil will feel her loss very keenly. After a thoroughgoing discus- Tuesday 26 March We agreed that a fitting way to sion, we agreed to the purchase LMS Meeting at BMC, remember Anne would be to es- of residential rental property Sheffield tablish a Women in Mathematics in central London as part of the 18-19 April Prize in her name, with the de- Society’s investment portfolio. Women in tails of the prize to be worked Rob Curtis also reported on the Maths Day out by the Women in Mathemat- results of the Members Survey Cambridge ics Committee. which took place over the sum- 10-14 June The most substantial business mer. Just over 40% of members LMS Invited Lectures, matter of the day was to con- responded to the survey, with Edinburgh sider and approve the Trustees’ 83% voting in favour of expand- page 21 Report and Annual Accounts so ing the criteria for Ordinary that they can be presented at the Membership and 71% voting in Friday 5 July AGM. Rob Curtis, the Treasurer, favour of expanding the criteria LMS Meeting, London who fluently guided us through for Associate Membership. It was NEWSLETTER the papers, congratulated gratifying to see such a conclusive Ephrem Belay for the excellent outcome and one that will con- ONLINE: work he had done in preparing tribute towards expanding the Go to the accounts, noting too that reach of the Society. We agreed newsletter.lms.ac.uk the auditors were full of praise the appropriate amendments to LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 420 December 2012

the criteria for membership, and these will be the item, to commission a sample article. LMS Prizes 2013 LMS INVITED LECTURES reported at the AGM. Finally, as a member of the 2015 Celebra- With the advent of the option of electronic tions Committee, I was very happy to report Call for Nominations SERIES 2014 voting in the forthcoming Society Elections, we that plans for celebrating the 150th anniversa- The London Mathematical Society wel- Proposals for the 2014 lectures are sought from spent some time discussing the election proce- ry of the Society are progressing well. The Cel- comes nominations for the 2013 prizes to any member who, in addition to suggesting a dures. For this item we had the benefit of the ebrations Committee is working closely with recognise and celebrate the achievements topic and lecturer, would be prepared to organ- presence of the Scrutineers, Don Collins and other Committees of the Society and many in and contributions to all aspects of math- ise the meeting at their own institution or a suit- Peter Saunders, which was extremely helpful. ideas are already either under way or under ematics, including applied mathematics, able conference centre. While we felt that a move to electronic only consideration (fireworks have not yet been mathematical physics and mathematical as- The annual Invited Lectures series consists voting was a desirable aim, it was agreed that excluded!). It was pleasing to note that the pects of computer science. In 2013, the LMS of meetings at which a single speaker gives a this should not be rushed and that while it was BMC - which is going to be held in Cambridge Council expects to award: course of about ten expository lectures, examin- hoped that members would take up the option in 2015 - contacted the Committee about the • The De Morgan Medal. the Society’s ing some subject in depth, over a five day period of electronic voting, the option to vote by pa- anniversary even before the Committee had premier award; the only grounds for the (Monday to Friday) during a University vacation. per should be maintained for the time being. had a chance to contact them. award of the Medal are the The meetings are residential and open to all The Society’s website made its customary ap- June Barrow-Green candidate’s contributions to interested. pearance on the agenda. However, this time mathematics. It is intended that the texts of the lectures the main item for discussion was a proposal CONGRATULATONS • The Senior Whitehead Prize for work in, given in the series shall be published. In addi- from an outside organisation. Plus (http:// influence on or service to mathematics, tion to full expenses, the lecturer is offered an plus.maths.org/content), a free online maga- Congratulations to Professor Abolghassem or recognition of lecturing gifts in the honorarium for giving the course. A grant is also zine produced by the Millennium Mathematics Ghaffari (elected an LMS member 22 May 1957) field of mathematics. given to the host department to support attend- Project, directed by Professor John Barrow at who celebrated his 105th birthday earlier this • The Naylor Prize and Lectureship for ance at the lectures. 2 Cambridge, would like to produce content for year. work in, and influence on, and For further details, visit the 3 the website. We all thought it seemed a prom- Also this year Dame Kathleen Ollerenshaw contributions to applied mathematics Society website: www.lms.ac.uk/content/ ising proposal – there is a strong desire among (elected an LMS member 25 January 1945) and and/or the applications of mathematics, invited-lecturer-proposals. Council members for the site to contain more Professor Joseph Lehner (elected an LMS mem- and lecturing gifts. Enquiries about the Invited Lectures should be actual mathematics! – and encouragement was ber on 16 February 1950) both celebrated their • The Berwick Prize in recognition of an directed to the Programme Secretary at the Soci- given to the President, who had introduced 100th. outstanding piece of mathematical re- ety ([email protected]). The deadline for the sub- search actually published by the Society mission of proposals is Friday 7 February 2013. during the eight years ending on 31 Recent previous lecturers have been: LMSLMS Newsletter Newsletter http://newsletter.lms.ac.uk http://newsletter.lms.ac.uk December 2012. 2012 A. Borodin (MIT) EditorialEditorial office: office: [email protected] [email protected];; LondonLondon Mathematical Society,Society, • The Whitehead Prizes for work in and Determinantal Point Processes and DeDe Morgan Morgan House, House, 57–58 57–58 Russell Russell Square, Square, LondonLondon WC1B 4HS 4HS (t: (t: 020 020 7637 7637 3686; 3686; f: 020 f: 020 7323 7323 3655) 3655) influence on mathematics. Representation theory Articles:Articles: please please send send articles articles to to [email protected] [email protected] For further information and 2011 E. Candes (Stanford) EventsEvents calendar: calendar: please please send send updates updates andand correctionscorrections to [email protected]@lms.ac.uk nomination forms, please visit the Compressed Sensing Advertising:Advertising: for for rates rates and and guidelines, guidelines, seesee www.lms.ac.uk/newsletter/ratecard.htmlwww.lms.ac.uk/newsletter/ratecard.html LMS website (www.lms.ac.uk/content/nomi- 2010 M. Bramson (University of Minnesota) nations-lms-prizes) or contact Duncan Tur- Stability of Queuing Networks GeneralGeneral Editor: Editor: Mr Mr A.J.S. A.J.S. Mann Mann ([email protected]) ([email protected]) ReportsReports Editor: Editor: Professor Professor R.A. R.A. Wilson Wilson (r([email protected])[email protected]) ton, Secretary to the Prizes Committee at The LMS Invited Lecturer 2013 will be Fe- ReviewsReviews Editor: Editor: Dr Dr C.M. C.M. Roney-Dougal Roney-Dougal ([email protected])([email protected]) the Society (tel: 020 7927 0801, email: priz- dor Bogolomov (Courant Institute, NYU) who AdministrativeAdministrative Editor: Editor: S.M. S.M. Oakes Oakes ([email protected])([email protected]) [email protected]). will give lectures on Birational Geometry and TypesetTypeset by by the the London London Mathematical Mathematical SocietySociety at De Morgan House;House; printed printed by by Holbrooks Holbrooks Printers Printers Ltd. Ltd. The Prizes Committee is keen to increase Galois Groups. See poster on page 21 of the PublicationPublication dates dates and and deadlines: deadlines: published published monthly, except August.August. Items Items and and advertisements advertisements by by the the the number of nominations it receives and, Newsletter. firstfirst day day of ofthe the monthmonth priorprior toto publication,publication, or the closest precedingpreceding workingworking day.day. 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Contributions to the Newsletter to the concept of ‘academic age’—rather Meeting rooms and catering are available in are made under a non-exclusive licence; please contact the author or photographer for the rights to are made under a non-exclusive licence; please contact the author or photographer for the rights to than date of birth—in order to take ac- De Morgan House. For terms and availabil- reproduce.reproduce. The The LMS LMS cannot cannot accept accept responsibilityresponsibility for the accuracyaccuracy ofof information information in in the the Newsletter Newsletter. . count more fully of broken career patterns. Views expressed do not necessarily represent the views or policy of the London Mathematical Society. ity, please call 020 7927 0800 or email room- Views expressed do not necessarily represent the views or policy of the London Mathematical Society. The closing date for nominations is Friday Charity registration number: 252660. [email protected]. Charity registration number: 252660. 18 January 2013. LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 420 December 2012

LMS GRANT SCHEMES site for further details: www.lms.ac.uk/content/ Spitalfields Days Visits to Britain computer-science-small-grants-scheme-7. Grants of up to £500 are available to support an Under this Scheme, applications may also be Next Closing Date for Research LMS Spitalfields Day, which have been run since made by any mathematician in Britain wish- Grant Applications: 31 January 2013 Childcare Supplementary Grants 1987 and are in honour of the Society’s predecessor, ing to host a visit by a young Russian postdoc- Grants of up to £200 are available to parents work- the Spitalfields Mathematical Society (1717-1845). toral mathematician who wishes to spend a Applications are invited for the following grants: ing in mathematics to help with the cost of childcare A Spitalfields Day is a one-day meeting, which is few weeks in Britain giving a series of survey • Conferences and postgraduate research when attending a conference or research meeting. usually associated with a long-term symposium on lectures on the work of their Russian seminar. conferences held in the UK (Schemes 1 and 8) The Society believes that all parents working in a specialist topic at a UK university. Selected partici- The LMS is offering grants to the host insti- • Celebrating new appointments (Scheme 1 mathematics should be able to attend conferences pants, often distinguished experts from overseas, tution to meet the visitor’s actual travel and • Visits to the UK (Scheme 2) and research meetings without being hindered by give survey lectures (or other types of lecture acces- accommodation costs of up to £1,500. Appli- • Joint Research Groups (Scheme 3 – see childcare costs. Institutions are expected to make sible to a general mathematical audience) on top- cations should include the following: below about renewal of Scheme 3 grants) provision for childcare costs and parents are en- ics in the field of the symposium. Further details 1. Name and brief CV of the visitor. • Research in Pairs (Scheme 4) couraged to make enquiries. However, where this can be found on the LMS website: www.lms.ac.uk/ 2. A brief description of the course of • International short visits with the main focus is not available, the Society administers a Childcare content/spitalfields-days#applications. lectures. on Africa (Scheme 5) Supplementary Grants Scheme. Further details can Young British and Russian 3. A letter or email of agreement from the For full details of these grant schemes, and to be found on the LMS website: www.lms.ac.uk/ head of the host department, including Mathematicians Scheme download application forms, visit the LMS web- content/childcare-supplementary-grants. the proposed dates of the visit. site: www.lms.ac.uk/content/research-grants. Visits to Russia Financial and academic reports will be re- • Applications received by 31 January 2013 will Small Grants for Education Applications are invited from young British post- quired after the visit. be considered at a meeting in February. Funding for grants up to £800 is available to stimu- doctoral mathematicians who wish to spend a few Further details of the Scheme can be found • Applications should be submitted well in late interest and enable involvement in math- weeks in Russia giving a series of survey lectures on on the LMS website: www.lms.ac.uk/content/ 4 advance of the date of the event for which ematics from Key Stage 1 (age 5+) to Postgraduate the work of their school. international-grants#YBR. Applications re- 5 funding is requested. level and beyond. Anyone working/based in the The LMS is offering grants of up to £500 to meet ceived by 31 January 2013 will be considered • Normally grants are not made for events which UK is eligible to apply for a grant. If the applicant is the travel costs, while the host should apply to the at a meeting in February. have already happened or where insufficient not a member then the application must be coun- Russian Academy of Sciences for funding towards Enquiries should be made to the Grants Ad- time has been allowed for tersigned by an LMS member or another suitable local expenses for accommodation and subsist- ministrators: Sylvia Daly, Elizabeth Fisher and processing of the application. person such as a Head teacher or senior colleague. ence. Please contact Sylvia Daly ([email protected]) Barbara Graczyk (tel: 020 7291 9971/3, and Queries regarding applications can be addressed The next deadline for applications is 31 January for information before contacting the Russian 0207 927 0808, email: [email protected]). to the Grants Administrators or the Programme 2013. Please see the website for further details: Academy of Sciences for funding. Applications to Secretary (see below) who will be pleased to www.lms.ac.uk/content/small-grants-education. the LMS should include the following: LMS SUBSCRIPTION discuss proposals informally with potential ap- 1. A brief academic case for the visit, Reminder plicants and give advice on the submission of an LMS-EPSRC Short Courses including a description of your current research application. The Society and EPSRC offer funding of up to interests, and an outline of your planned work Members are reminded that their annual sub- Grants Administrators: Sylvia Daly, Elizabeth £12,200 (including honoria for organisers) towards during the visit (no more than one side of A4). scription, including payment for publications, for Fisher, Barbara Graczyk (tel: 020 7291 9971 / 3, and the cost of running a one-week Short Course 2. A brief CV (no more than one side of A4). the period November 2012 – October 2013 was 0207 927 0808, email: [email protected]). which provides high quality training for postgrad- 3. A brief budget. due on 8 November 2012, and should be paid by 8 Programme Secretary: Rob Wilson (r.a.wilson@ uate students in core areas of mathematics. For 4. A letter of invitation from the head of the host December 2012 at the latest. qmul.ac.uk). further information on Short Courses and how department in Russia, which must state explic- In the case of members who already have a di- Other LMS Grants & Funding to submit a proposal, please visit: www.lms.ac.uk/ itly that your accommodation and subsistence rect debit set up, no action need be taken. All content/short-course-organisers. expenses will be met by them. This should in- members should now have received a reminder Computer Science Small Grants (Scheme 7) clude provisional dates for the visit. via email or letter, detailing how to pay their Funding for grants up to £500 is available to sup- Research Workshop Grants Financial and academic reports will be required subscription. If you have not received a remind- port a visit for collaborative research at the inter- The Society offers grants to support for Research after the visit. er please contact the Membership Department face of Mathematics and Computer Science either Workshops held in the UK. Requests for support In exceptional circumstances, applications may (email: [email protected]; tel. 020 7291 by the grant holder to another institution within (for travel and subsistence of participants, and be considered from strong research students who 9973 or 020 7927 0808). the UK or abroad, or by a named mathemati- reasonable associated costs) in the range £1,000- are close to finishing their doctorates. Applica- Subscription forms, direct debit mandate forms cian from within the UK or abroad to the home £10,000 will be considered. For further informa- tions should include a strong case and the student and further information can be downloaded base of the grant holder. The next deadline for tion and application forms, visit: www.lms.ac.uk/ should obtain a letter of recommendation from from the LMS website at www.lms.ac.uk/content/ applications is 31 January 2013 – see the web- content/research-workshops-grants. his/her supervisor. paying-your-subscription. LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 420 December 2012

LONDON MATHEMATICAL SOCIETY MARY CARTWRIGHT LECTURE AND SOCIETY MEETING Friday 1 March 2013 De Morgan House, 57-58 Russell Square, London WC1B (Nearest tube: Russell Square)

Programme:

3.30 Opening of the meeting

Jeff Lagarias (University of Michigan) 6 From ABC to XYZ 7

4.30a Te

5.00 Mary Cartwright Lecture Margaret Wright

(Courant Institute, New York University) Evening Post Courtesy of the South Wales

A Mathematical Journey Mary Cartwright giving a in Non-Derivative Optimization lecture at Swansea University

To register, please contact Elizabeth Fisher/Katy Henderson (womenin- [email protected]) by Friday 22 February. Late registrations for places may be still be accepted, subject to availability.

The reception will be followed by a dinner at the DoubleTree by Hilton Lon- don West End, at a cost of £35 per person, inclusive of wine. If you would like to attend the dinner, please contact Elizabeth Fisher/Katy Henderson ([email protected]) by Friday 22 February.

There are limited funds available to contribute in part to the expenses of members of the Society or research students to attend the meeting. Please contact Elizabeth Fisher/Katy Henderson ([email protected]) for further information. LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 420 December 2012

ANDREI GONCHAR RUSSELL SMITH JORAM LINDENSTRAUSS together. When this barrier was finally broken, we jointly investigated the still puzzling prob- Andrei Gonchar died on 10 October 2012, at Dr Russell Alexander Smith, who was elected a Professor Joram Lindenstrauss, who was elect- lems of Fréchet differentiability. It became a the age of 81. He was born in Leningrad (now member of the London Mathematical Society ed a member of the London Mathematical very enjoyable long term ‘on and off project’ St Petersburg), graduated from school in Yere- on 18 November 1965, died on 19 August 2012, Society on 17 October 1974, died on 29 April (as Joram called it), developed during his visits van (Armenia), and enrolled in Moscow State aged 86. 2012, aged 75. to London, Warwick and Prague (where Jaro- University in 1949. From 1954 to 1957 he was Lorna Smith writes: Russell was born in Ka- David Preiss writes: Joram Lindenstrauss was slav Tišer joined our work), but mainly during a postgraduate student at the same university, toomba in New South Wales, Australia. He professor of the Hebrew University of Jerusa- my two longer and many shorter visits to Je- with Sergei Mergelyan as his advisor, and he studied for a BSc at New England University Col- lem, member of the Israeli Academy of Scienc- rusalem. In spite of that, we would probably taught there from 1957 to 1991. Since 1964 lege Armidale and Sydney University where he es, foreign member of the Austrian Academy never be finished were it not for the support he was also a research fellow and a head of was awarded a University Medal in Mathemat- of Sciences, recipient of the Israel Prize in of Joram's family and especially of his wife, department at the Steklov Mathematical In- ics. In 1948 he was awarded the Barker Travel- Mathematics, Banach's medal winner, teacher Naomi. We finally managed to put all the bits stitute. He was a member of the Soviet (now ling Scholarship and came to St John’s College, and adviser of numerous outstanding math- and pieces together in Autumn 2011 when Jo- Russian) Academy of Sciences since 1987 (a Cambridge where he took the Cambridge ematicians and founder of a powerful school ram was already seriously ill, and he still saw corresponding member since 1974) and held Mathematical Tripos and then continued to a of modern functional analysis. He was born in the appearance of our research monograph high administrative posts at the Academy for PhD supervised by Dame Mary Cartwright. Af- Tel Aviv in 1936 and educated at the Hebrew Fréchet Differentiability of Lipschitz Functions some period of time. From 1992 to 1993 he ter the PhD Russell returned to Australia, to a University of Jerusalem, where he was deeply and Porous Sets in Banach Spaces in February was the Organizing Director of the Russian lectureship at Sydney University, but he then influenced by his teacher Aryeh Dvoretzky. He 2012. In spite of his deteriorating health, after Foundation for Basic Research, a newly formed came back to the UK in 1954, to a lectureship held longer term visiting positions at the Yale finishing this work we still discussed directions government agency supporting fundamental at Durham University. Russell stayed at Durham University, University of Washington, Univer- in which further research may go. research. University throughout the rest of his career, sity of California, University of Texas and Texas 8 Gonchar’s interests in mathematics were fo- progressing first to Senior Lecturer and then to A&M University and a number of other shorter MICHAEL EASTHAM 9 cused on rational approximation of functions. Reader in 1968, a role he held until his retire- term positions. Via his deep results, books, lec- He was one of the central figures in the devel- ment in 1990. In 1985 he was awarded an ScD tures, survey papers and collaborations (for Professor Michael Stephen Patrick Eastham, opment of the modern theory of Hermite-Padé by the University of Cambridge. the luckiest of us) he enormously influenced FRSE, who was elected a member of the Lon- approximations and orthogonal polynomials Russell's research interests concentrated the development of modern mathematics. don Mathematical Society on 19 December with varying weight. He brought forward a around the theory of Ordinary Differential It is impossible to describe Joram's main 1963, died on 27 October 2012, aged 74. radically new method of solution of classical Equations. He published papers in number discoveries in a brief note. Without any at- Malcolm Brown and Desmond Evans write: problems in rational approximation, which is theory relating to sums of squares and worked tempt for serious investigation, I quickly asked Michael Eastham will be remembered as a based on vector equilibrium problems of po- on the functional equations of L-series related several colleagues what they think should be leading mathematical analyst who contributed tential theory in the presence of an exterior to quadratic forms and the distribution of ra- mentioned. The most popular answers were extensively to the theory of ordinary differen- field. Now this method is widely used in theo- tional points on hypersurfaces, as well as im- Johnson-Lindenstrauss Lemma, Lindenstrauss- tial equations. retical and practical investigations. With its proving an error term in a result of Ramanujan Tzafriri characterization of the Hilbert space Michael was born in London on 2 December help Gonchar solved Varga’s famous ‘1/9’ prob- concerning squares of the sum of the divisors as the unique Banach space all of whose 1937. After attending Manchester Grammar lem. He reported on this result at the Interna- of integers. The breadth of his interests also closed subspaces are complemented, Linden- School, he entered Merton College, Oxford in tional Congress of Mathematicians in Berkeley enabled him to contribute to a range of in- strauss-Pelczynski version of Grothendieck's 1956 and graduated in 1959 with double first in 1986 and it received ample recognition. terdisciplinary areas, including collaborating ‘Fundamental Theorem’ and its applications, class honours in Mathematics. He then was a He paid much attention to publishing activi- with mathematical physicists working on string Lindenstrauss-Rosenthal local reflexivity,.... research student of the eminent analyst Profes- ties of the Academy. For 25 years he was the theory. His book Classical Banach Spaces written joint- sor E.C. Titchmarsh and obtained his DPhil in editor-in-chief of Matematicheskii Sbornik, the Russell was a dedicated teacher who gave ly with Lior Tzafriri, became the basic reading 1962; during 1959-61, he was a Domus Senior oldest Russian mathematical journal. Thanks very clear and well-presented lectures. Both for everyone interested in the theory of Ba- Scholar at Merton College. He was admitted in part to Gonchar’s warm relations with Sir students and colleagues benefitted from his nach spaces, and the more recent Geometric to the Degree of Doctor of Science of Oxford Michael Atiyah, a partnership in journal pub- helpfulness and the encouragement that he Nonlinear Functional Analysis written jointly University in 1974. After lectureships in Read- lishing between the Russian Academy of Sci- gave. He always had time to listen, and gave with Yoav Benyamini, is becoming similarly ing (1962-65) and Southampton (1965-69), he ences, the London Mathematical Society and well thought-out and sympathetic advice. influential. spent the years 1969-88 in the University of Lon- Turpion Ltd has been actively developing since Russell was devoted to his wife Katherine, Like so many others, I was deeply influenced don, at Chelsea and then King's Colleges, be- the mid-1990s. who died sadly in 2001. He is survived by by Joram's work. A referee called me ‘a mathe- ing promoted to Professor in 1980. He received Nikolai Kruzhilin and Sergei Suetin four children, five grandchildren and eight matician of Lindenstrauss's school’ long before the Keith Prize and Gold Medal of the Royal Steklov Mathematical Institute, Moscow great-grandchildren. political situation allowed us to meet and work Society of Edinburgh in 1978 and was elected LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 420 December 2012

to a Fellowship of the Royal Society of Edin- MATHEMATICS IN THE However, the UK has played an important of today’s techniques. UK mathematics un- burgh in 1982. From 1988 until 1991 he was role in most of these changes – a far great- derpins computer simulations all over the Professor of Mathematics in Bahrain and NEW ELIZABETHAN AGE er role than its relative size would suggest. world! was Honorary Research Professor at Cardiff (60 Years of British Mathematics) Thus, for the period 1998–2008, Scotland and The speed and memory size of comput- University School of Computer Science and In- England were respectively second and fourth ers grew rapidly and it became much easier formatics from 1995. This article arose from a discussion meeting in the world for citations per paper published to collect data. But while data can now be Michael was a widely acknowledged author- organised by the Parliamentary and Scientific in the mathematical sciences1. Although we gathered on a massive scale, it is much harder ity on the spectral theory of differential equa- Committee entitled British Scientific Achieve- concentrate on research in the rest of this to work out what to do with it. Many of the tions, and was particularly well-known for ment over the Last 60 Years, which took place article, it is worth remembering that most fundamental ideas behind the mathematical his analytical skills. He made many significant in July 2012. A number of distinguished speak- researchers are also teachers, and we rely on treatment of data sets, statistics, were formu- contributions to such topics as the asymptotics ers were invited to present at the meeting: them to pass on the intellectual thrill of the lated in the 1920s at Rothamsted by Fisher. of solutions of linear differential systems, the Professor Brian Cox, Professor Dame Nancy discipline and to create the skilled workforce This tradition of excellence in statistics within deficiency index problem, periodic problems, Rothwell, President, Society of Biology and needed in the banking, computing, engi- the UK has continued during the new Eliza- spectral concentration and resonances. He Professor Lesley Yellowlees President, Royal neering and pharmaceutical industries. bethan age, making it possible to analyse the was the author of 124 research publications Society of Chemistry. The audience included The rise of computers and the ubiquity of effect of new drugs, or the meaning of the and five books. several mathematicians and the Council for smart technology form one of the greatest human genome, much more efficiently, and Michael is survived by his widow, Heather, the Mathematical Sciences (CMS) was asked changes to our lives since 1952. The early pro- also to analyse models of systems with uncer- two sons and four granddaughters. He was a by the Secretary of the Parliamentary and Sci- totypes of this technology were developed tainty (financial markets, spread of epidem- dear friend and will be greatly missed by all entific committee to contribute this article to by Alan Turing and others at Bletchley Park ics, life expectancy of smokers ….). Perhaps who knew him. the meeting report, which was first published (to decode the German ENIGMA machine) the most influential statistical contribution in the autumn issue of Science in Parliament and then at the National Physical Labora- of the jubilee years has been Sir David Cox’s 10 ISAAC NEWTON INSTITUTE magazine. tory (NPL) and the University of Manchester. 1972 paper3 allowing mathematical models 11 Turing committed suicide in 1954, so he only to be built on actuarial life tables, so permit- Call for Proposals In June 1993 Andrew Wiles gave a series of just makes it into the new Elizabethan age, ting causal inferences based on sparse data. The Institute invites proposals for research seminars at the newly-created Isaac Newton but his achievements in computing, logic and This work has been fundamental to countless programmes in all areas of the mathematical Institute for Mathematical Sciences in Cam- mathematical biology have had an immense medical and actuarial studies. In a related lat- sciences and their applications. The Scientific bridge. In the final minutes of the last semi- influence. As computers began to be used to er development, the former Director General, Steering Committee usually meets twice each nar he claimed to have solved a 350 year old solve complex engineering problems in in- Knowledge and Innovation, at BIS, Sir Adrian year to consider proposals for programmes mathematical problem: Fermat’s Last Theo- dustries such as aeronautics, the UK contribu- Smith, showed how useful information could (of 4-week, 4-month or 6-month duration) to rem. This became headline news across the tion was key to creating a new mathematical be obtained from probabilistic models 4. This run two or three years later. Proposals to be world because of the romance in the story discipline, numerical analysis, which emerged technique, called Markov Chain Monte-Carlo considered at these meetings should be sub- (lone British mathematician solves ancient to ensure that these large computations – inference (or MCMC for short), is now ubiqui- mitted by 31 January or 31 July respectively. mystery), and also because the problem itself computations that can now be done on a tous throughout the sciences. Details on submitting proposals are available is relatively easy to state. The interest gen- laptop! – were reliable. Here we mention The internet and world wide web brought on the website (www.newton.ac.uk/callprop. erated by this achievement is rare for math- two examples. James Wilkinson worked with computers into our daily lives, with new pos- html). ematics, though many other developments in Turing on the early computers at the NPL in sibilities and problems. The method used to Anyone interested in making a proposal is mathematical science over the last 60 years Middlesex, where he discovered ways of ana- process secure financial transactions on-line encouraged to contact the Director, John To- are on a par with it. This is partly because lysing floating point arithmetic that enable is based on number theory, specifically the land, by telephone or email, for advice and mathematics is often seen as too abstruse or the accuracy of computer calculations to be difficulty of finding the prime factors of large informal feedback (tel: 01223 335980, email: specialised for ‘ordinary people’; and partly understood. His methods remain as valid as numbers. The RSA algorithm at the heart of [email protected]). because major advances in applied math- ever for today's largest supercomputers2 and this method was first developed by Clifford The Isaac Newton Institute is a national ematics and statistics are often sub-plots of he went on to develop other now standard Cocks, a number theorist working at GCHQ. research institute based in Cambridge, UK. bigger stories in biology, physics, economics tools in algebraic manipulation. In many in- Unfortunately no one at GCHQ appreciated It attracts scientists from all over the world or engineering. dustrial and scientific problems some quan- its potential (it was filed as ‘secret’) and the to research programmes in all areas of the In this article we want to redress this in- tity needs to be optimised. In the 1970s such algorithm is now known by the initials of the mathematical sciences. At any time there are visibility and stress the key international role concerns prompted the UK mathematicians US-Israeli team that patented the method in two visitor programmes at the Institute, each played by British mathematics. Mathematics Roger Fletcher and Mike Powell to develop 1978! with about twenty participants. For more in- has changed enormously over the new Eliza- methods for solving optimisation problems Not all new mathematics is immediately formation see www.newton.ac.uk bethan age, and this has been a global effort. numerically that are still the basis for many applicable, and a fundamental development LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 420 December 2012

of the new Elizabethan age has been the re- applications to the life sciences, mathemati- needed to facilitate this. Modern statistical Penny Davies, Patrick Dorey, Jerome Gaunt- naissance of geometry. Geometry and phys- cians now work in teams with other scientists methods allow information to be extracted lett, Nick Higham, Oliver Jensen, Stephen ics have been intertwined through most of as equal partners. Mathematical modelling is from data in previously unimagined ways. Senn, Richard Thomas and Mike Titterington their history, but drifted apart in the 60 years also used to inform policy decisions: strategies The deep interconnections between dif- for helpful guidance, some of which we ig- leading up to 1980. However, starting from for the foot and mouth outbreak of 2001, the ferent areas of mathematics, and between nored due to lack of space. discussions between Sir Michael Atiyah and distribution of vaccines, and the safety of air mathematics and the sciences, that have Ken Brown, University of Glasgow the American physicist Ed Witten, the picture flights through volcanic ash clouds in 2010, emerged are similarly mysterious and could Paul Glendinning, University of Manchester has changed greatly over the last 35 years, were all assessed using mathematics. not have been foreseen in 1952.This does not and now the connecting road is a motorway. So what lessons can we learn from the suc- mean that all future developments are un- References and notes Atiyah is one of the six UK Fields medallists cess of UK mathematical science in the jubilee predictable – it is clear that the mathematisa- 1. Figures from Thomson Resuters at (the mathematical equivalent of the Nobel years? Here are some observations from the tion of the biological sciences will continue www.timeshighereducation.co.uk/story.asp?sectio Prize) – only France and the US have more – chalk-face. apace and holds some exciting prospects, ncode=26&storycode=406463 Denmark were first, and has been a central figure in world math- • Structures must be flexible enough to al- and understanding climate change provides the USA third. ematics during the new Elizabethan age. The low many flowers to bloom: nobody can a challenge – but it does make it likely that 2. J. H. Wilkinson, Rounding Errors in Algebraic Pro- maths-physics motorway is not just one-way: predict what the next breakthrough will the next real innovations will, by definition, cesses. Englewood Cliffs, New Jersey: Prentice Hall, in the striking example of mirror symmetry be, far less from where it will appear. be surprises. 1963 from string theory, Philip Candelas, now at • The time between formulation of a semi- The UK has been at the forefront of change 3. D.R. Cox, Regression models and life tables, J Roy- Oxford, and his collaborators were able to nal mathematical idea and its application over the past 60 years, and we need to ensure al Statistical Society B 34 (1972), 187-220. use the amazing intuition of the physicists to may be brief (as in Cox’s 1972 work on it remains at the cutting edge of progress for 4. A.E. Gelfand and A.F.M. Smith, Sampling-based predict the solution of a century-old problem regression analysis) or very long (as in the next 60 years. Not just for the intellectual approaches to calculating marginal densities, J. in classical geometry (“counting the number Turing’s 1936 discussion5 of thinking ma- excitement of discovery, but also for its soci- American Statistical Association 85 (1990), 398-409. 12 of rational curves in the quintic”). chines, now at the heart of Artificial Intel- etal impact. How will the next 60 years go? 5. A. Turing, On computable numbers, with an ap- 13 Mathematical physics itself (quantum theo- ligence). It is misguided to aim to reward All we can say is: watch this space! plication to the Entscheidungsproblem, Proc. Lon- ries and relativity) has also changed dramati- only a fast pay-off. Worse, even with the Acknowledgements: We are grateful to don Math. Soc. 42 (1936), 230-265. cally. Stephen Hawking and Roger Penrose, best intentions this policy tends to lead to both working in mathematics departments, incremental research rather than real inno- described the mathematical structure of vation, which is inherently unpredictable. black holes, stars so massive that even light • The openness and non-hierarchical struc- cannot escape their gravitational pull. Hawk- ture of British culture allows new ideas to ing went on to show that there is a sense in gain a foothold, new talent to find a ready which black holes actually do emit radiation! audience. The existence of the Higgs particle that may • Diversity (of scale of organisation, of mode have been observed recently and which is of research – solo/team, interdisciplinary/ responsible for mass in quantum theory was narrow, applications-focused/blue skies) is predicted by Peter Higgs at the University of key. Edinburgh, with others including Tom Kib- All the above features of UK mathematical ble at Imperial College, using mathematical science have been massively aided by the dual arguments. support system for funding research, allow- With advances in both methods and com- ing new ideas to start with small first steps, puting power, the scope of what mathemati- new talent to develop from a wide base (it is cians can model has expanded. This has led to worth remarking that the Cambridge math- changes in the way that weather forecasting ematician and Fields Medallist Sir Tim Gowers is reported (using ideas from chaos theory) has never held a research council grant). and the increasing use of mathematics in The key message from the last 60 years is modelling financial markets. The sophistica- that most progress has been through glorious tion of computer models is such that a model surprises. No one except a few crazy science of the human heart at Oxford can be used fiction writers could have predicted the way to make predictions about heart treatments computers would come to pervade our lives, without using a living subject. Often, in such nor the way that new mathematics would be A computer generated prediction by the Met Ofice of the position of a volcanic ash cloud (Crown Copyright) LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 420 December 2012

LONDON MATHEMATICAL SOCIETY NORTHERN REGIONAL MEETING

Monday 18 March 2013

Herschel Building, Newcastle University

Programme:

2.00 pm Opening of the meeting

Volodymyr Mazorchuk (Uppsala)

3.15 pm Ivan Smith (Cambridge) 14 15 4.30 pm Tea/Coffee

5.15 pm Bernhard Keller (Paris 7)

6.30 pm Reception and Buffet at The Penthouse

These lectures are aimed at a general mathematical audience. All interested, whether LMS members or not, are most welcome to attend this event.

To register, please visit www.mas.ncl.ac.uk/triangulations/index.php?p=6. Registration closes on 31 January 2013.

The Society Meeting forms part of the workshop on Triangulations and Mutations from 18-22 March. For further details visit: www.mas.ncl.ac.uk/ triangulations/index.php?p=6.

There are funds available to contribute in part to the expenses of members of the Society or research students to attend the meeting and workshop. Requests for support, including an estimate of expenses, may be addressed to the organisers ([email protected]). LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 420 December 2012

MATHEMATICS POLICY ROUND-UP • Brian Cox – physicist and broadcaster status as a world leader in research and • Lord Martin Rees – former President, higher education’. The full statement is November 2012 Royal Society and Astronomer Royal available at www.britac.ac.uk/news/news. HIGHER EDUCATION SCHOOLS AND COLLEGES • Andre Geim – Nobel laureate (Physics cfm/newsid/813. 2010) Postgraduate Education Cambridge to support teaching of new • Lesley Yellowlees – President, Royal Soci- Equal opportunities for boys and girls? The Higher Education Commission has pub- mathematics A-levels ety of Chemistry The new IOP report, It’s Different for Girls, lished its report on Postgraduate Education. A new maths education programme is be- • Lord William Waldegrave – former Chief shows that many schools fail to ensure equal The Council for the Mathematical Sciences ing launched by the University of Cam- Secretary to the Treasury and Science opportunity for boys and girls in A-level (CMS) responded in April 2012 to a call for bridge which aims to provide innovative, Minister physics. The report is available at http://tiny- evidence to inform this report. The final re- rich and stimulating materials to help • Ben Goldacre – doctor and author of Bad url.com/c8kow3z. port calls for 'the postgraduate sector to be support and inspire teachers and students Science, and Bad Pharma brought in from the cold and fully embraced of advanced post–16 mathematics. The A report on how the proposals could be The National Numeracy Challenge as part of an integrated education system. It £2.5m programme is funded by the De- implemented is available at www.nesta.org. National Numeracy has launched a Chal- identifies policy shifts which will be needed partment for Education, initially for three uk/library/documents/4GROWTH.pdf. lenge that aims to reduce the number of to ensure that Britain remains a competitive years. adults with low levels of numeracy by over place to do research and do business. It also It will be led by Professor Martin Hy- ‘Serious deficit’ in UK quantitative skills one million in the five years from 2013–2018. explores access to postgraduate education, land, Head of the Department of Pure A position statement – Society Counts – The first phase of the Challenge will bea “the next frontier of widening participa- Mathematics and Mathematical Statistics, published by the British Academy says that three-year collaborative project to improve tion”, and makes recommendations on how and Lynne McClure, Director of NRICH, ‘the UK has a serious deficit in quantitative work/life skills for 500,000 adults of working postgraduate provision should be funded part of the University’s Millennium Math- skills in the social sciences and humanities. age in the UK by 2015. More information is 16 in the future'. The full report is available at ematics Project. More information will be This deficit threatens the overall competi- available at http://tinyurl.com/c269dcn. 17 http://tinyurl.com/ctcdrc4. available in due course. tiveness of the UK’s economy, the effective- Dr John Johnston ness of public policy-making, and the UK’s Mathematics Promotion Unit Segregation of HE sector New plans to boost computer science A report - The Future of English Higher teaching Education: Two Scenarios on the ‘As part of the government's mission to Changing Landscape designed specifically ensure Britain competes and thrives in the to look at where the coalition reforms to global race, Education Secretary Michael higher education would lead the sector Gove has set out plans to boost the teach- over the next decade has been published. ing of Computer Science by training up The report concluded that 'research will be the first generation of outstanding new focused in just 25 universities by 2025 as teachers’. More information is available the UK sector becomes more stratified'. The at http://tinyurl.com/99vuz5f. full report is available at http://tinyurl.com/ c3ezlre. OTHER

The cost of the Government's reforms of Reinvest the 4G windfall in science and the financing of higher education technology A recent Higher Education Policy Institute The Campaign for Science and Engineer- (HEPI) report argues that the ‘government ing (CaSE) and the National Endowment has seriously underestimated the cost to for Science, Technology and the Arts (Nes- the public purse of its HE policies’. The re- ta) have launched a new campaign called port concludes that ‘the government's as- 4Growth. The campaign calls on the gov- sessment of the cost of its HE policies still ernment to invest the proceeds from the depends on highly uncertain and optimistic forthcoming 4G spectrum auction. Lead- assumptions and remains too low’. More in- ing figures from science and technology formation is available at http://tinyurl.com/ have signed an online petition supporting dybecz8. the campaign. These include: LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 420 December 2012

BRITISH MATHEMATICAL COLLOQUIUM 2013 LMS PROSPECTS The 65th British Mathematical Colloquium will take place at the University of Sheffield from 25 to 28 March 2013. IN MATHEMATICS MEETING

Plenary speakers: • John Baez (Riverside) • Mikhail Kapranov (Yale) • Ragni Piene (Oslo) • Laurent Saloffe-Coste (Cornell) • Guy Henniart (Paris) • Thomas Schick (Göttingen)

Professor Baez's lecture will be a public lecture on the subject of mathematics and the environment and will be a Mathematics of Planet Earth 2013 event.

18 Morning speakers will include: 19 • Konstantin Ardakov • Tim Dokchitser • Lasse Rempe-Gillen • June Barrow-Green • Tony Dooley • Gesine Reinert • Tom Bridgeland • Tom Leinster • Stuart White • Gavin Brown • Zinaida Lykova

Afternoon workshops: • Noncommutative Algebra and Representation • Category Theory Theory • History of Mathematics • Number Theory • K-Theory and Analysis • Probability • Mathematical Higher Education • Topology

There will be opportunities for contributed talks either by individuals or, in workshop format, by groups with a common interest. Proposals for contributed talks or workshops are particu- larly welcome from postgraduate students.

Anyone interested should contact Eugenia Cheng ([email protected]) or David Jordan ([email protected]). For further information visit the website at www.sheffield.ac.uk/maths/bmc2013.

The colloquium is supported by an LMS Conference grant. LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 420 December 2012

LMS INVITED LECTURERS 2013

Professor Fedor Bogolomov (Courant Institute, NYU)

Birational Geometry and Galois Groups 10-14 June 2013 University of Edinburgh

The lectures will discuss the relation between the structure of the Galois group of algebraic closure of a field of rational functions and the structure of the field itself. More precisely, they will cover how to extract effectively birational invariants (i.e. geometric invariants of projective models of the field from the Galois group).

There will also be supplementary lectures by:

G. Brown (Loughborough) Fano 4-fold hypersurfaces I. Cheltsov (Edinburgh) Finite subgroups of Cremona group T. Logvinenko (Warwick) Derived categories and birationality 20 21 University and local Guesthouse accommodation will be available.

Limited financial support is available with preference given to UK research students. Please contact the organisers for further details ([email protected], [email protected]). Deadline for funding: 1 May 2013.

For further details on the 2013 Invited Lectures please visit: www.maths.ed.ac.uk/cheltsov/fedya/

VISIT OF SIMOS MEINTANIS • Newcastle University, 22 February Fourier-type inference for GARCH models Professor Simos Meintanis (National and Kap- with heavy-tailed innovations odistrian University of Athens, Greece) will be (contact Daniel Henderson: SPRINGER BOOK ARCHIVES If you were the author of a Springer or visiting the Department of Mathematical Sci- [email protected]) Birkhauser book published earlier than 2005, ences at Durham University within the period • Durham University, 25 February The Springer Book Archives (SBA) project and have not already been contacted by February to mid-March 2013. Professor Mein- The probability weighted empirical is an effort to breathe new life into older Springer in this connection by email, please tanis' recent research has focussed on the use characteristic function and goodness-of-fit books published between 1842 and 2005 by visit the page www.springer.com/SBAauthor of the empirical characteristic function (ECF) testing (contact details below) making them available electronically and, if and let us know about it. If you know some- in order to tackle challenging inferential • University of Kent (Canterbury), appropriate, in print. Many of these titles are one who is potentially concerned, for in- problems in Statistics. Research during this 28 February currently out-of-print. SBA books will thus stance a retired colleague or even the family visit will particularly focus on goodness-of-fit Goodness-of-fit procedures for spherically be preserved for future generations of scien- of a deceased colleague, please alert them testing for unsupervised learning techniques symmetric distributions tists and need never go 'out-of-print' again. to this and ask them to contact us via www. and on predictive inference using the ECF. (contact Efang Kong: [email protected]) Authors will have free access to their elec- springer.com/SBAauthor. During his visit to the UK, Professor Mein- For further details contact Frank Coolen tronic version. They will receive royalties on tanis will present three lectures (please check ([email protected]). This visit is both print and electronic sales. This article is included at the request of Springer. with the contact persons for further details): supported in part by an LMS Scheme 2 grant. LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 420 December 2012

ANALYSIS DAY VISIT OF CRAIG EVANS • Holger Kanz (Warwick) VISIT OF RAFAEL BENGURIA • Jürgen Kurths (Potsdam) Postponed Analysis Day will be held on 7 January 2013 • Mark Pollicott (Warwick) Professor Rafael Benguria (Pontificia Uni- at the University of Bristol. The day will begin This visit, announced in the November issue of the • Catherine Rouvas-Nicolis (Bruxelles) versidad Católica de Chile) will be visit- with coffee at 11 am with the first talk at 11.30 LMS Newsletter (page 14) has been postponed. • Antonio Speranza (Camerino) ing London, Bristol and Reading from 19 am. The last talk will end at 5.15 pm, followed For further information please contact the organ- • Sandro Vaienti (Marseille) January to 2 February 2013. He will give by dinner. The speakers are: iser Geoffrey Burton ([email protected]). Some funds for PhD-students are available. the following talks: • David Preiss FRS (Warwick) Do we really For further information contact Tobias Kuna • London Analysis Seminar, Imperial know what Lebesgue null sets are? ([email protected]) or visit the website at College, 24 January • Dorin Bucur (Université de Savoie) Isoperi- STATISTICAL MECHANICS www.personal.reading.ac.uk/~sms07kt/NeSEE. Estimate for the indirect coulomb metric inequalities and free discontinuity AND EXTREME EVENTS The meeting is supported by an LMS Conference energy for two and three dimensional problems grant and co-financed by the ERC-grant NA- atoms • Peter Topping (Warwick) Ricci flow on non- IN EARTH SCIENCE MASTE - Thermodynamics of the Climate System. • Bristol, 28 January compact surfaces A conference on Non-equilibrium Statistical Exact asymptotic behavior of the • Bernard Helffer (Orsay) On nodal domains Mechanics and the Theory of Extreme Events in LEGACY OF GOODSTEIN Pekar–Tomasevich functional and spectral minimal partitions: a survey Earth Science will take place at the University of • Reading, 29 January His Centennial and the Wittgenstein For more information email Michi- Reading from 8 to 11 January 2013, part of the in- Rigorous results for the minimal speed el van den Berg (m.vandenberg@bris- ternational initiative of the year of Mathematics Connection of Kolmogorov–Petrovskii–Piscounov tol.ac.uk) or Isaac Chenchiah (Isaac. for Planet Earth 2013. The conference will bring There will be a one day meeting at the Univer- monotonic fronts with a cutoff [email protected]) or visit the website at together mathematicians working in Non-equi- sity of Leicester on Friday 14 December 2012 to For further information contact Profes- http://goo.gl/l9H3j. librium statistical mechanics, Random dynami- commemorate the centenary of the birth of Reu- sor Leonid Parnovski, University College 22 cal systems, Extreme events together with Earth ben Louis Goodstein. The meeting will focus on London ([email protected]). The visit 23 WINTER COMBINATORICS Science. Goodstein's mathematical research, particularly is supported by an LMS Scheme 2 grant. MEETING Earth Sciences of fluid phenomena sparked an in logic and related areas, and the influence that ever increasing interest scientifically and in the this has had on subsequent research in mathe- BSHM NEUMANN The 14th Annual Winter Combinatorics Meet- general public with subjects as climate change, matics (and related fields). The talks will be given ing will take place at The Open University, Mil- weather prediction and in particular prediction by: BOOK PRIZE ton Keynes, on Wednesday 30 January 2013. It of extreme and hence dangerous damaging and • Mathieu Marion (Université du Québec � The British Society for the History of Math- is intended that the talks will be of interest to expensive weather events. With rare exceptions Montréal) ematics (BSHM) is pleased to announce all those working in combinatorics or related the qualitative theory of dynamical systems and • Mitsuhiro Okada (Keio University, Tokyo) the biennial Neumann Prize for 2013. The fields. The speakers are: statistical mechanics and the theory of extreme • Jan von Plato (University of Helsinki) prize is awarded for a book in English (in- • Mireille Bousquet-Mélou (Université Bor- events developed without any contact with earth • Mike Price (University of Leicester) cluding books in translation) dealing with deaux 1) sciences and their paradigms and had, again with • Mary Walmsley (University of Leicester) the history of mathematics, aimed at a • David Conlon (University of Oxford) few exceptions, no influence on Earth Scientists. • Harvey Rose (University of Bristol) broad audience and published in 2011 or • David Evans (University of East Anglia) The aim of the conference is to bring Earth Sci- • Stan Wainer (University of Leeds) later. The prize is named in honour of • Iain Moffat (Royal Holloway, University of ences in contact with mathematicians working in Further details can be found on the web page Peter M. Neumann, OBE, a former BSHM London) the aforementioned areas. The list of speakers http://www2.le.ac.uk/departments/mathematics/ President and longstanding contributor to • Steven Noble (Brunel University) includes: legacy-of-goodstein the Society. The value of the prize is £600. For full details, including the schedule, titles • Christian Beck (QMUL) Everyone is free to attend although we do Nominations for the prize are invited and abstracts when they become available, see • Freddy Bouchet (Lyon) require people to register; please go to the web from individuals and publishers. Nomina- http://wcm.open.ac.uk. Anyone interested is • Ira Didenkulova (Tallinn) page to do this. Whilst people can register on tions should be sent to the chair of the welcome to attend. Some funds for travel ex- • Ana Cristina Moreira Freitas (Porto) the day, it would be very helpful if people could judging panel, Norman Biggs (n.l.biggs@ penses are available for research students who • Jorge Miguel Milhazes de Freitas (Porto register in advance wherever possible. lse.ac.uk). Publishers should send three wish to attend the meeting: requests should • Davide Gabrielli (Roma) The meeting is supported by an LMS Confer- copies of their nominated book(s) to Pro- be made to Robert Brignall (r.brignall@open. • Christian Maes (Leuven) ence grant. Included in this support is travel fessor Norman Biggs, Chair: BSHM Neu- ac.uk). • Michael Ghil (Paris) funding for PhD students to attend the meeting. mann Prize, Department of Mathematics, The organizers are grateful for support of • Rosemary Harris (QMUL) If you are a PhD student and would like to ap- London School of Economics, Houghton this event from the London Mathematical So- • Mark Holland (Exeter) ply for such funding, enter the details when you Street, London WC2A 2AE, United ciety and the British Combinatorial Committee. • Giovanni Jona-Lasinio (Roma) register. Kingdom. LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 420 December 2012

SHEFFIELD • Jean Bertoin (ETH, Zürich) at 3.45 pm The 2012 Applied Probability Trust Lecture PROBABILITY DAY Almost giant clusters for percolation on Sheffield Probability Day will take place in large trees with logarithmic heights Lecture Theatre 7, Hicks Building, University Tea and coffee will be available at 3.15 pm of Sheffield on Wednesday 30 January 2013. in Room I15, Hicks Building. All are welcome. The speakers are: For further information contact Chris Drew • James Norris (Cambridge) at 2.15 pm (tel: 0114 222 3763, email: spd@sheffield. A consistency estimate for Kac's model of ac.uk). The meeting is sponsored by the Ap- elastic collisions in a dilute gas plied Probability Trust.

SUMMER SCHOOL AND WORKSHOP 15 – 19 July 2013 in association with the Newton Institute programme Polynomial Optimisation 24 (15 July - 9 August 2013) 25

Organisers: (Chair) Adam Letchford (Lancaster University), Joerg Fliege (Southampton University) Jean-Bernard Lasserre (CNRS Toulouse) and Markus Schweighofer (Konstanz University).

Optimisation problems that involve polynomials are currently receiving a great deal of attention, due to their generality, their challenging nature and their wide range of practical applications. These two events provide an opportunity for researchers to learn more about this new, exciting and growing field.

The Summer School will begin in the morning of Monday 15 July and finish at lunchtime on Wednesday 17 July. It will consist of a series of tutorials from the following five in- ternationally respected invited speakers:

• Emmanuel Candès (Stanford University) • Michal Kocvara (University of Birmingham) • Jesús De Loera (University of California, Davis) • Tim Netzer (Leipzig University) • Bernd Sturmfels (University of California, Berkeley)

The workshop will begin at lunchtime on Wednesday 17 July and finish in the afternoon on Friday 19 July. It will consist of a series of contributed talks, and a poster session for PhD students and post-docs.

Further information and application forms are available from the website at www.newton.ac.uk/programmes/POP/popw01.html Closing date of the receipt of applications is 28 February 2013. LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 420 December 2012

26 27 LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 420 December 2012

RECORDS OF PROCEEDINGS AT LMS MEETINGS SOUTH WEST & SOUTH WALES REGIONAL MEETING held on 1 October 2012 at Bristol University as part of the Regional Workshop on Quan- tum Probablistic Symmetries. Over 50 members and visitors were present for all or part of the meeting. The meeting began at 2.00 pm with the LMS Treasurer, Professor Robert Curtis, in the Chair. No members were elected to membership. Three members signed the book and were admitted to the Society. Professor Trevor Wooley introduced a lecture given by Professor John Cremona on Unusual modular curves and elusive isogenies. After tea, Professor Wooley introduced a lecture given by Professor Tony Scholl on Special values of L-functions. Professor Wooley then introduced the final lecture given by Professor Karl Rubin entitled Ranks of elliptic curves. 28 The Treasurer, Professor Curtis, expressed the thanks of the Society to the local 29 organisers for putting on such an interesting meeting. Afterwards, a reception was held in the School of Mathematics, followed by dinner hosted at The Lido Restaurant.

POPULAR LECTURES 2012 suringly familiar territory of finding solutions for quadratic equations. He pointed out that Report for these and for other types of equation, we To mark the centenary year of Alan Turing’s can describe a standard method for finding a birth, the 2012 LMS Popular lectures were de- solution and that they can therefore be solved voted to aspects of Turing’s work. mechanically, by a person or a computer sim- On 29 September 2012, an excited audience ply following an algorithm, rather than by any of mathematicians, school students and inter- mathematical understanding or intuition. ested members of the public gathered in the Hilbert’s dream was that it might be possible beautiful concert hall of the new Sir Paul and to solve any mathematical problem mechani- Lady Ruddock Performing Arts Centre, at King cally. More specifically, he asked whether any Edward’s School, Birmingham to listen to two algorithm existed for determining whether distinguished mathematicians speak about as- any arbitrary diophantine equation has a solu- pects of Turing’s work. tion. (A Diophantine equation is an equation where only integer solutions are allowed.) Can anything be salvaged from the wreckage Known as the Entscheidungsproblem (from of Hilbert’s Dream? the German for decision), this can be visual- Sir Timothy Gowers, FRS, Royal Society Re- ised as being a “black box” for which the in- search Professor in the Department of Pure put is an equation and the output is a proof Mathematics and Mathematical Statistics at the or disproof. University of Cambridge, started from the reas- Gödel’s incompleteness theorems prove that LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 420 December 2012

dental observations. Problems can sometimes on a ‘cautious oracle’ which has, in addition into micro-tubules in the nerve synapses has be solved by making use of vague similarities. to the options to reply ‘True’ or ‘False’, can produced some interesting results. He concluded that recent advances in com- reply that it does not know or might simply In his informative and inspiring lecture, Pro- puting suggest that one day a computer might ‘continue pondering indefinitely without ever fessor Penrose used diagrams and cartoons to pass the amended Turing Test. However, no providing an answer at all’. Gödel’s theorem tackle several very complex and controversial computer yet exists that can adequately un- states that computational rules such as math- subjects in such a way as to convince the au- derstand and use natural language, learn from ematical induction are not sufficient for estab- dience, at least briefly, that they could under- experience and recognise and solve interesting lishing the perceivable truths of arithmetic. stand them. problems. This was illustrated by using the example of Many thanks are due to the two distin- Professional mathematicians are not likely Hercules and the Hydra quoted by Kirby and guished speakers, to the LMS for organising to become redundant in the near future! Paris. the lectures and to King Edward’s School for Before the second lecture there was a break Arguments against the possibility of using a hosting the event. in which excellent refreshments were served machine to model the human mind are that: Sheila Mawby Timothy Gowers and the audience had the opportunity to see a 1. Humans are fallible and make errors. Editorial note: The lectures were also given in Lon- little more of the Arts Centre. 2. Algorithms for human understanding are don on 26 June 2012. The lectures were recorded there are some statements for which no proof so vastly complicated that Gödel state- and are available from the LMS: a useful purchase or disproof exists. In the 1930s, Alan Turing On Attempting to Model the Mathemati- ments are completely beyond reach for school and university mathematics departments seeking resources that will stimulate their students and Alonzo Church independently decided cal Mind: A Tribute to A. M. Turing on his 3. We do not know the algorithmic process, (information is available at www.lms.ac.uk/content/ that some functions are “non-computable”. Centenary so cannot construct Gödel statements. popular-lectures-dvds). Professor Gowers discussed modifications Sir Roger Penrose, FRS, Emeritus Rouse Ball Human intelligence depends on awareness to the requirements of the hypothetical black Professor of Mathematics at the Mathematical and understanding. If awareness and under- reviews 30 box by changing the question to whether Institute, University of Oxford presented his standing can be shown to be beyond com- 31 there was a proof within a specified length. lecture as a tribute to Alan Turing, whom he putation, then intelligence is not a matter Game Theory and the Humanities: Bridg- This can be achieved but only by “brute force” had admired ever since he had first heard of of computation. Conscious brain action must ing Two Worlds by Steven J. Brams, 2012 solutions which are of no practical interest. him. depend on a physical process that is beyond (pb reprint), MIT Press, 336 pp, £12.95, ISBN: He suggested that the expectation that a com- Although Alan Turing is now best known as computation. Quantum mechanics may help 978-0-262-51825-3. puter should solve all problems was unfair and the mathematician who cracked the Enigma to explain brain processes. Recent research This is a fascinating book on the application that it might be amended to require ‘reason- code, this lecture referred to less well known of game theory to philosophy, politics, law, lit- able proofs of interesting problems’ that a hu- aspects of his work, based on papers published erature and even the Bible. The author, Steven man could solve. in the late 1930s on computable numbers and Brams, shows that real insight can be obtained To date no computer has passed the ‘Turing systems of logic. A Universal Turing Machine into optimal strategies for dealing with some Test’ to solve a mathematical problem in the is a theoretical concept of a finite state object famous dilemmas way that a human would. The human method with an infinite tape. A Universal Turing Ma- Game theory originated with John Von Neu- involves inspiration and intuition based on ex- chine can perform ANY computation. mann’s famous 1928 paper, elaborated into a perience and value judgements. Humans often Professor Penrose suggested that, when classic 1944 book by Von Neumann and Oskar reason visually whereas computers can only these papers were published, Turing was un- Morgenstern, Theory of Games and Economic reason symbolically. happy about trying to model the mathemati- Behavior. Von Neumann and Morgenstern An example of a problem which is best cal mind with a Universal Turing Machine, as showed that there are 78 structurally distinct solved visually concerned the removal of diag- the mind goes beyond the capabilities of a 2x2 ordinal games: games in which two play- onally opposite squares from a grid of squares Turing machine. (By the 1950s he seemed to ers are each given the option of two strate- and then covering the remaining area with be more optimistic that a computer might one gies, giving four states which can be ranked dominoes. Although humans learn standard day be developed that would be powerful from best to worst. methods, for example for long multiplication, enough to model the human brain.) There is much in this book to interest and at- they can often solve mental arithmetic prob- In order to evade the limitations of Gödel’s tract. Brams is a professor of politics and does lems by seeing shortcuts or ‘tricks’. incompleteness theorem Turing suggested a not fall into the trap of attempting to reduce Professional mathematicians would some- system based on ordinal logic and oracles. The complex dilemmas to oversimplified, mean- times like to be portrayed as having had “flash- oracle should be able to say whether or not a ingless games. Instead, he maintains the essen- es of genius” but, in fact, these are based on given statement was true. tial complexity of each situation and examines a great deal of unrevealed thought and acci- Professor Penrose suggested a model based Roger Penrose the possible moves in a commonsense manner, LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 420 December 2012

revealing a richness of insight. There is plenty Taking Sudoku Seriously: The Math Behind mathematical concepts, such as equivalence here to convince the sceptic that game theory the World's Most Popular Pencil Puzzle by Ja- classes, modular arithmetic, matrices, graph is not just applied common sense, in particular son Rosenhouse and Laura Taalman, Oxford colouring, polynomials, modular arithmetic, the associated theory of moves (TOM), which University Press, 2012, 226 pp, £13.99, ISBN: and groups of symmetries, explaining these allows players to change their strategies dur- 978-0-19-975656-8. with great clarity and persuading the reader ing a game on the basis of ‘backward induc- If you enjoy solving sudoku-like puzzles this of their relevance. tion’ (learning from initial outcomes). is the book for you, for among its pages you Particularly ambitious (and successful) is Brams begins by surveying literary situations, will find almost 100 puzzles that are sudoku- their chapter on counting, where their aim is from works such as Othello, Tosca and Sir Ga- related – from traditional 9 × 9 puzzles to to enumerate the number of different sudoku wain and the Green Knight. Curiously, he skips variations with such exotic names as Jigsaw Pi patterns. They begin with a careful analysis of lightly over detective fiction and classic games Sudoku, Worms, Just-What-I-Needed Sudoku, the simpler problem of finding the total num- of move and counter move such as Holmes ver- Argyle, Roku-Doku and Rainbow Wrap. Many ber of 4 × 4 sudoku patterns (called shidoku), sus Moriarty. He concludes that the aspects of of the sudoku patterns in this attractively pre- and discover that of the 288 possible patterns, literature where game theory is relevant are sented book appear in full colour. only three are ‘fundamentally different’. They those where a carefully constructed plot is up- But the book is far more than an encyclo- then begin their attack on the 9 × 9 problem, permost, but that in much of literature human paedia of sudoku variations. After teaching where the notion of ‘fundamentally different’ emotion and irrationality dominate proceed- the uninitiated how to solve such puzzles sys- is more tricky to explain, by finding the num- ings, as in life. tematically, the authors clarify the underlying ber of ways of filling in the first three rows, The first intensive analysis is of Biblical di- ideas and strategies in order to inspire and and then estimating the number of ways of lemmas; specifically, Abraham's decision to motivate their readers to appreciate what is completing the remaining six rows. Although obey God and sacrifice Isaac. Should Abraham meant by mathematical problem-solving. Us- the problem is too difficult to solve in full, 32 have defied God? Game theory suggests that ing a range of sudoku-based puzzles as a ve- they manage to convey a good understanding 33 this might have been productive. Brams later hicle, together with such familiar recreations of its complexity, and their estimate of 6.6571 deals with Moses persuasion of God not to generally supports Churchill's maxim, ‘In vic- as the four-colour problem, the 36 officers’ × 1021 is astonishingly close to the correct an- punish the Israelities for the golden calf. By tory, magnanimity’. problem, and the bridges of Königsberg, they swer of 6,670,903,752,021,072,936,960. making God a player in these games, Brams Finally, Brams looks at two-player games manage to introduce a whole range of related The book is already slightly out-of-date. A sheds a new light on God's motives, allowing with incomplete information, and where each central open question, as to whether there ex- him to be scheming, manipulative, sometimes player is trying to learn more about the other. ist any uniquely completable sudoku patterns vengeful, but always a good player. Two classic cases are the Cuban missile crisis, with only 16 given cells (there are many thou- The biblical examples are followed by more where Kennedy and Khrushchev managed to sands with 17), was answered in the negative complex dilemmas: the insoluble problem of resolve the game satisfactorily (fortunately early in 2012. achieving a fair division among competing for the human race), while in the Iran hostage The historical remarks that feature through- goods, and how to resolve conflict by demo- crisis Carter did not, because of his mispercep- out the book are interesting and mainly ac- cratic means, including varied forms of voting. tion of Khomeini's motives. He finishes with curate, with the exception of the Königsberg Next up is the Law. We consider the game Catch-22, and its many related parallels in the bridges problem, where the incorrect spell- played between Nixon and the US Supreme real world (e.g. the torture of witches to elicit ing ‘Königsburg’ appears throughout and Court, in the enforced disclosure of the White confessions), and shows that 12 of Von Neu- where the authors fall into the common trap House tapes followed by Nixon's resignation; mann's games are varieties of Catch-22. of claiming that Leonhard Euler solved it by then the conduct of the Supreme Court in the Brams ends by stating ‘Game theory and drawing a four-vertex graph representing the 1930s, when Roosevelt depended, not always TOM will not, and should not, replace other layout of the city; he didn’t – the graph didn’t successfully, on its delicate balance of votes to modes of enquiry in the humanities’ but that appear until some 150 years later. approve his New Deal. they are ‘especially useful, and sometimes Apart from such infrequent lapses, this Brams then turns to situations that involve even indispensable, in elucidating the strate- book is well written and provides an object frustration and anger, his literary examples be- gic role that conflict and cooperation play in lesson in how to present mathematical prob- ing Macbeth's dilemma as to whether to kill human affairs’. lem-solving to interested students. It can be Duncan, and the strategy of withholding sex in Peter Wadhams warmly recommended. Lysistrata. He looks at the aftermaths of wars DAMTP, Cambridge Robin Wilson

including the Franco-Prussian war and the A version of this review was first published in Plus magazine Pembroke College, Oxford American Civil War to show that game theory (http://plus.maths.org). Author of How to Solve Sudoku LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 420 December 2012

CALENDAR OF EVENTS 14 David Crighton Lectures, Royal Society, London (420) This calendar lists Society meetings and oth- 18 LMS Northern Regional Meeting, er mathematical events. Further informa- Newcastle (420) tion may be obtained from the appropriate 18-22 Analytical and Computational Paths LMS Newsletter whose number is given in from Molecular Foundations to Continuum brackets. A fuller list is given on the Socie- Descriptions Workshop, INI Cambridge (419) ty’s website (www.lms.ac.uk/content/calen- 18-23 Workshop on Triangulations and dar). Please send updates and corrections to Mutations, Newcastle (420) [email protected]. 19 Modelling the World, Gresham College London DECEMBER 2012 25-27 Quantitative Modelling in the 3-7 Quantized Flux in Tightly Knotted and Management of Health and Social Care 7th Linked Systems INI Workshop, Cambridge IMA Conference, Central London (416) (416) 25-28 BMC, Sheffield (420) 11 From One to Many Geometries, Gresham 26 LMS Meeting at BMC, Sheffield College London 14 The Legacy of Goodstein, Leicester (420) April 2013 The London Mathematical Society was established during the energetic and con- 15-17 Thomas Harriot Seminar, St Chad’s 2-5 Higher Structure 2013: Operads and fident heyday of Victorian Britain. With over eighty photographs of previous College, Durham (412) Deformation Theory INI Conference, 17-19 Aspects of Topology in Geometry and Cambridge (418) presidents and De Morgan Medal winners, The Book of Presidents 1865-1965 Physics, Oxford (419) 8-9 Mathematics in Finance IMA Confer- 34 looks at the first 100 years of the Society’s existence. As the book traces the 17-20 Mathematics in Signal Processing IMA ence, Heriot-Watt University (416) 35 Society’s evolution through its Presidents and De Morgan Medallists, we learn Conference, Austin Court, Birmingham (416) 9-11 Large Deviations and Asymptotic Meth- which branches of mathematics were in vogue at any particular time, and come 18-19 LMS Prospects in Mathematics ods in Finance, Imperial College London 18-19 Women in Maths Day, Cambridge- to appreciate the Society’s rich history. Meeting, Manchester (420) January 2013 June 2013 10-14 LMS Invited Lecturers, Fedor 7 Analysis Day, Bristol (420) “This lovely little book is one of the best the London Mathematical Society has Bogolomov, Edingburgh (420) 7-11 Nonlinear Analysis UK-Japan Winter published… This is a book that can – and should – both be read from cover to 11-14 MAFELAP 2013, Brunel School, London (419) cover and dipped into… Dipping into it randomly one sees some of the quirks 20-21 High-Dimensional Inference with 7-11 Symmetry, Bifurcation and Order Pa- Applications, Kent and oddities that make an important institution human” Peter M Neumann, rameters INI Workshop, Cambridge (418) 30-5 Jul British Combinatorial Conference, Queen’s College Oxford. 8-11 Statistical Mechanics and Extreme Royal Holloway College, University of London Events in Earth Science Conference, The Book of Presidents 1865-1965 is available from the London Mathematical Reading (420) july 2013 16-18 British Postgraduate Model Theory Society. 1-2 Bifurcation Theory, Numerical Linear Conference, Manchester (419) Algebra and Applications, Bath • LMS Members price is 22 The Queen of Mathematics, Gresham 1-4 Dense Granular Flows 2nd IMA £15.Full price is £19 College London Conference, INI, Cambridge (416) • To order a copy; please 30 Sheffield Probability Day, Sheffield (420) 3-13 Polylogarithms as a Bridge between 30 Winter Combinatorics Meeting, Open download an order Number Theory and Particle Physics University (420) 5 LMS Meeting, London form from the LMS LMS-EPSRC Durham Symposium website: www.lms. FEBRUARY 2013 8-12 Modern Nonlinear PDE Methods in ac.uk/content/history 19 Are Averages Typical? Gresham Fluid Dynamics, LMS-EPSRC Short Course, College, London Reading (420) MARCH 2013 15-19 Polynomial Optimisation Summer School and Workshop, INI, Cambridge (420) 1 LMS Mary Cartwright Lecture, London 15-25 Graph Theory and Interactions LMS NEWSLETTER LMS MEETINGhttp://newsletter.lms.ac.uk

LMS South West and South Wales Regional Meeting and L-functions of Curves Workshop held at the University of Bristol from 1 to 3 October 2012

36

Qing Lio (Bordeaux) Abelian surfaces with Tate-Shafarevich Congruence of models of elliptic curves group of order 5 times a square