THE MAN WHO KNEW INFINITY - London Mathematical Society · 2018-01-16 · THE MAN WHO KNEW INFINITY...

NEWSLETTER No. 457 April 2016

SOCIETY MEETINGS AND EVENTS• 15April:WomeninMathsDay,Cambridgepage 26

• 20April:HirstLecture&SocietyMeeting,StAndrewspage 5

• 22April:WomeninMathsDay,Edinburghpage 26

• 23June:NorthernRegionalMeetingpage 36

• 8July:GraduateStudentMeeting,London

• 8July:HardyLecture&SocietyMeeting,Londonpage 11

• 21July:SocietyMeetingatthe7ECM,Berlinpage 37

• 15September:MidlandsRegionalMeeting

• 11November:GraduateStudentMeeting,London

• 11November:AnnualGeneralMeeting,London

• 20December:SW&SouthWalesRegional

Meeting,Bath

NEWSLETTERONLINE:newsletter.lms.ac.uk @LondMathSoc

THE MAN WHO KNEW INFINITYFilm Review

Oneofthemostinteresting“reallife”storiesaboutmathematicsistheHardy-Ramanujanrelationship.Thiswaswelldescribed in the book The Man Who Knew Infinity by Robert Kanigel andthis has now been transformed intothefilmunder review. It stars JeremyIrons (Hardy), Dev Patel (Ramanujan)andTobyJones(Littlewood).The film starts with a speech madetowardstheendofHardy’slifewherehedescribedRamanujan"asthemostromantic figure in the recent historyof mathematics" and the whole filmcanbeseenasaromance,ifnotalovestorydescribingtheirrelationship.Aswithanyclose relationship there are conflicts. Severalscenesareabout theneed forproof.Thefilmdescribes Ramanujan as finding his formulaethrough intuition and Hardy tries to tell himthat he could not publish his results withoutproof,whichisoneofthemajorthemesofthefilmandsymbolicoftheculturalclashbetweenthetwo.HesendsRamanujantosomelecturesgiven by people with far less talent, whichcauses conflict but finally, he doesmanage toprovehisresultsandthis ledtopublicationbytheLondonMathematicalSociety,probablythefirsttimethenameofourSocietyhasappearedinafilm!Atatimewheninterestinmathematicsishigh,but the school-learned fear of it remains for

many,itiswelcometohaveafilmthatdepictsthe loveofmathematics inaveryhumanway.Ramanujan is portrayed as being motivatedby aesthetics, by form, and by a thirst forknowledge.Additionally,thethemesofculture,class and race serve to humanise thematerialandthesometimesoff-putting imageofmath-ematicianscomesoutwell.Hardy, inparticular,while beingdepicted as awkward and lackingin social skills, is treated with real warmthby the end, and some scenes areput aside tobrieflymentionhisanti-warpolitics,aswellasthoseofRussell,butnot inanyheavyhandedway. However, the idea that the motivationfor learningmathematics isaveryhumanone,and that mathematicians can come from allbackgrounds isonethat I thinkwillbehugely

LMS NEWSLETTER http://newsletter.lms.ac.uk

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AwardsAbelPrize2016.........................................CecilKingTravelScholarship.....................ClayResearchFellows2016......................

Calendar of Events

LMS ItemsCouncilDiary..............................................FundingforUndergraduateMathematical Society Meetings...........LMSGrant Schemes..................................Hardy Lecture Tour..................................LMSLibraryatUCL...................................

LMS MeetingsDavid Crighton Lecture............................Hardy Lecture & Society Meeting.........Hirst Lecture..............................................LMSGreshamCollegeLecture.................LMSResearchSchool,QUB.......................NorthernRegionalMeeting&Workshop............................................SocietyMeeting at 7ECMBerlin.............Women in Maths Day..............................

MeetingsBayesianMethodsforNetworks..............BSDEs......................................................CombinatoricsatOxford..........................ComputationalandAnalyticProblemsinSpectralTheory..................Data Linkage and Anonymisation..........ECSTATIC 2016...........................................GraphLimitsandStatistics.......................Groups St Andrews 2017.........................Modelling, Analysis and Simulation.......

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343130

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ModernTopicsinNonlinearPDEandGeometric Analysis.................................PostgraduateGroupTheoryConference........................................Quantum Physics and Logic....................Random Interacting Systems...................RepresentationTheoryofAlgebraicGroups....................................................ScottishPartialDifferentialEquationsColloquium............................

NewsChalkdust..................................................European News.........................................Mathematics Policy Round-up.................MathematicalSciencesResearchDisplayed inParliament.........................Heilbronn Institute...................................Voice of the Future..................................

ReportsFromSymbolicDynamicstoApproximationMethods........................Integrable Systems in Newcastle............Mirzakhani Society....................................WhybeNoncommutative?.......................

ReviewsExperimental Mathematics......................TheGeometryof theOctonions.............TheManWhoKnewInfinity.....................

VisitsHou,Yong..................................................Kuna,Tobias...............................................Lin, Jyun-Ao...............................................Lomp, Christian.........................................Scott, Dana................................................

No. 457 April 2016Contents

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Editorial officeLondonMathematicalSociety,DeMorganHouse,57–58RussellSquare,LondonWC1B4HS(t:02076373686;f:02073233655)

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General EditorMrA.J.S.Mann([email protected])

Reports EditorProfessorI.A.Stewart([email protected])

Reviews EditorProfessorD.Singerman([email protected])

Administrative EditorS.M.Oakes([email protected])

TypesetbytheLMSatDeMorganHouse;printedbyHolbrooksPrintersLtd.

Publishedmonthly,exceptAugust.Itemsandadver-tisementsbythefirstdayofthemonthpriortopubli-cation,ortheclosestprecedingworkingday.Noticesandadvertisementsarenotacceptedforeventsthatoccurinthefirstweekofthepublicationmonth.

News items and notices in theNewsletter may befreely used elsewhere unless otherwise stated, al-though attribution is requested when reproducingwhole articles. Contributions to theNewsletter aremadeunderanon-exclusive licence;please contacttheauthororphotographerfortherightstorepro-duce. The LMS cannot accept responsibility for theaccuracy of information in the Newsletter. ViewsexpresseddonotnecessarilyrepresenttheviewsorpolicyoftheLondonMathematicalSociety.

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Editorial teamhttp://newsletter.lms.ac.uk

Publication dates and deadlines

resonantforaudiences,as ithasbeenwiththeinterestinTuringinrecentyears.Oneproblemabout anyfilmaboutmath-ematics is how much of our subject toinclude. Anydetailwouldput thegeneralaudience off. Here they get it about right,andsomepraisemustsurelygotoKenOno,whowas themathematical advisor for thefilm. Of course, there are many formulaeshownbutthesecanbeseenasmathemati-calwallpaper.Theydodescribethepartitionfunctionp(n)andactuallyshowthatp(4)=5butthisshouldbeaccessibletoeveryone.One point of comparison would be thefilmGood Will Hunting,whichalsodepicteda–thistimefictional–mathematicalgenius,andwas received fairlypositively. I think itfairtosaythatwhilethatfilmhadalotofcharm,thisfimoutshinesGood Will Huntinginalmosteveryway. The culturalgap is somuch more acute and the historical foun-dationmakesallelementsofthefilmmoregrounded; from the characters, to thewayit presents mathematics to the backdropof the First World War. Most of all it ismore uplifting, embracing thepositivity ofromance, albeit aplatonic romance rootedinaloveofmathematics.The filming is quite beautiful, both inIndiaandinCambridge.Theywereallowedto actually film in Trinity College! Manywell-knownmathematicians are characters.Besides Hardy and Ramanujan we meet

Littlewood, Russell and Major MacMahon.A nice scene is a discussion betweenMacMahon and Ramanujan concerningthe partition function. At first,MacMahondoubts whether Ramanujan’s formula forp(n) could be correct. MacMahon hadcomputed p(200) by hand and then foundthattheanalyticformulaturnedouttogivean extremely accurate answer. MacMahonchangedhismind!EarlierinthefilmRamanujanfailedtobeelectedafellowofTrinityandracismplayeda part here. Towards the end of the film,HardyproposedthatRamanujanbecomeanFRSand inamoving speech,hepersuadedthe other fellows to elect him. During hisstay inCambridge,Ramanujandevelops tu-berculosisandgoesbacktoIndiawherehediesattheageof32.Theactingthroughoutisfirstclass.JeremyIrons is outstanding as Hardy and he evenlooks like him. Dev Patel is convincing asRamanujan.Unfortunately,hedoesn’t looklike him; Ramanujan was short and fatwhereas Patel is quite tall.We particularlyliked Toby Jones as Littlewood, providingsomeofthe lightermoments. Inshort, thisisperhapsthebestfilmaboutmathematicsevermade!

ArmandoMartinoandDavidSingermanUniversityofSouthampton

The Man Who Knew InfinitywillbereleasedintheUKon8AprilandintheUSon29April.


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1865 - 2015

Inaugural Hirst Lecture & Society Meeting

St Andrews, 20 April 2016

3.30 pm: Opening of the meeting

3.45 pm: Mark McCartney (Ulster) Title TBA

4.45 pm: Tea

5.15 pm: Hirst Lecture, Edmund Robertson (St. Andrews) Title TBA

6.15 pm: Meeting closes. Wine reception.

The Inaugural Hirst Lecture & Society Meeting celebrates the joint award of the Hirst Prize & Lectureship, in the 150th Anniversary year of the London Mathematical Society, to Professor Edmund Robertson (St. Andrews) and the Dr John O’Connor (St. Andrews) for their creation, development and maintenance of the MacTutor History of Mathematics web site.

The prize and lectureship are named after Thomas A. Hirst, 5th President of the London Mathematical Society from 1872-1874. The prize is awarded in recognition of original and innovative work in the history of mathematics, which may be in any medium.

These lectures are aimed at a general audience. All interested, whether LMS members or not, are most welcome to attend this event. For further details and to register please email [email protected]

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 Elizabeth Fisher ([email protected]).


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News

MATHEMATICAL SCIENCES RESEARCH DISpLAYED IN pARLIAMENTThreemathematicianswonmedalsandawardsatacompetitionintheHouseofCommonsonMonday 7March 2016 for the excellence oftheirmathematical science research,walkingawaywitha£3,000,£2,000and£1,000prizeforGold(sponsoredbytheClayMathematicsInstitute),SilverandBronze(sponsoredbytheBankofEngland)respectively.Dr Philip Pearce (University ofManchester),Dr Tom Montenegro-Johnson (University ofCambridge) and Weijian Zhang (Universityof Manchester) each presented research todozens of politicians and a panel of expertjudgesaspartofthepostercompetitionSETforBritain.Dr Philip Pearcewas awardedGold for hisresearch on building a virtual placenta, DrTom Montenegro-Johnson won Silver forhis research on microrobotic swimming andWeijian Zhang won Bronze for his researchon time-dependent network modelling forminingscientificliterature.

Thethreewinnerswere judgedagainst29other shortlisted mathematicians and cameoutontop.Sir Adrian Smith, Chair of the Council fortheMathematical Sciences (CMS) said: ‘TheCMS is delighted, once again, to showcasetheimportanceofthemathematicalsciencesto a wider audience. It is paramount toencourage early-career research scientists,engineers, technologists and mathemati-ciansandtheSETforBritainevent isaveryeffectivewayofdoingthis.Wehavebeenen-couragedby theenthusiastic response fromearly-careerresearchersinthemathematicalsciencesandfeelsurethiswill thiscontinueinthefuture’.StephenMetcalfeMP,ChairmanofthePar-liamentaryandScientificCommittee,said:‘This annual competition is an importantdateintheparliamentarycalendarbecauseitgivesMPsanopportunitytospeaktoawiderange of the country’s best young research-

(ltor)DrStephenBenn(RoyalSocietyofBiology),SylajaSrinivasan(BankofEngland),ProfessorNickWoodhouse(ClayMathematicsInstitute),WeijianZhang(BronzeAwardWinner),DrPhilipPearce(GoldAwardWinner),DrTomMontenegro-Johnson(SilverAwardWinner),ProfessorSirAdrianSmith(CMS),StephenMetcalfeMP


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ers.Theseearlycareerengineers,mathemati-ciansandscientistsare thearchitectsofourfutureandSETforBritainispoliticians’bestopportunity to meet them and understandtheirwork’.TheParliamentaryandScientificCommitteerunstheeventwithsupportfromtheRoyalAcademy of Engineering, the Royal Societyof Chemistry, the Institute of Physics, the

Royal Society of Biology, The PhysiologicalSocietyandtheCouncilfortheMathematicalSciences.The eventwasmade possible this year bythe prize sponsors, who are Essar, the ClayMathematics Institute,WarwickManufactur-ingGroup(WMG),theInstituteofBiomedicalScience,theBankofEnglandandtheSocietyofChemicalIndustry.

MATHEMATICS pOLICY ROUND-UpMarch 2016

HIGHER EDUCATION

BIS Committee publishes assessing quality in HE report

The Business, Innovation and Skills SelectCommittee has published its report -The Teaching Excellence Framework: Assessing quality in Higher Education.‘TheCommittee supports the Universities Min-ister’s desire to improve teaching qualityat universities, widen participation, andincreasethefocusongraduateemployabil-ity but the Committee’s report recognisesgenuine concerns about the implementa-tion of the new teaching framework andthe pace of its introduction’. The full

report is available at http://tinyurl.com/h6xavd8.

RESEARCHConsultation on Mathematics for Horizon 2020The European Commission has launchedan open consultation on Mathematics in H2020. The objective is to collect a largequantity of concrete proposals that cansubsequentlybeusedtoinformthefuturework programmes (2018-19-20)with inno-vativemathematicalcontent.Theconsulta-tion isopenuntil 30April 2016. More in-formationisavailableathttp://tinyurl.com/h8n6xt2.

VOICE OF THE FUTURE 2016The Council for Mathematical Sciences (CMS)onceagainsentyoungmathematicalscientiststothisyear’sVoice of the Futureevent.Theeventisanopportunityforscientistsaged16-35toputtheirquestionstoanassembledpanelofMPsattheHouseof Commons. The event, organisedbytheSocietyofBiology,tookplaceatPortcullisHouseonTuesday1March2016.This year’s CMSnominatedparticipantswereRosannaCretney(OpenUniversity),EllenDowie(University of Kent), Hannah Muit (Ernst &Young)andMariaSudell(UniversityofLiverpool).MPsattendingtheeventincludedtheMinister

for Universities and Science, Jo Johnson MP;ShadowMinisterforScience,YvonneFovargueMP;NicolaBlackwoodMPandmembersoftheHouseofCommonsSelectCommitteeforScience&Technology;andSirMarkWalporttheGovern-mentChiefScientificAdviser.Avideomessagewas also received fromTimPeake aboard theInternationalSpaceStation.Moreinformationabouttheeventisavailableat https://www.rsb.org.uk/policy/policy-events/voice-of-the-future. The event was alsobroadcast on Parliament TV http://tinyurl.com/zcpgtmj.


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News

SCHOOLS AND COLLEGES

OECD Report

AreportpublishedbyOECD-Low-perform-ing Students: Why they Fall Behind and How to Help them Succeed -examines lowperformance at school by looking at lowperformers’ family background, educationcareer and attitudes towards school. Thereportalsoanalysestheschoolpracticesandeducationalpolicies thataremore stronglyassociated with poor student performance.Theevidenceprovidedinthereportrevealswhatpolicymakers,educators,parentsandstudents themselves can do to tackle lowperformanceandsucceedinschool.Morein-formation is available at http://tinyurl.com/gu6ba48.

Tough Choices Report

YourLifehaslaunchedareporttitled-Tough Choices: The real reasons A-level students are steering clear of science and maths.

Theskillsgapissettogrownotdiminish,demonstrating that huge challengesremain. This report aims to help inspirechange by providing an insight intostudents’ thinking and the choices theyface.Thereportlooksatthedecision-mak-ingprocessofthosestudentsthatchooseto move away from science and math-ematicsbeforeA-level. The full report isavailableathttp://tinyurl.com/gshcqmk.

OTHER

New Director General Business and Science

GarethDavieshasbeenappointedto theroleofDirectorGeneral forBusiness andScience, at the Department for Business,Innovation and Skills (BIS). More infor-mation is available at http://tinyurl.com/za89jwd.

DrJohnJohnstonJointPromotionofMathematics

Tony Yue Yu receivedhis PhD in 2016 fromUniversitéParisDiderotunderthesupervisionofMaxim Kontsevich andAntoine Chambert-Loir.Tony works on non-archimedean geometry,tropical geometry and mirror symmetry.He aims to build a theory of enumerativegeometry inthesettingofBerkovichspaces.Suchatheorywillgiveusanewunderstand-ingof the enumerativegeometry of Calabi-Yau manifolds, as well as the structure oftheirmirrors. Itisalsointimatelyrelatedtothetheoryofclusteralgebrasandwall-cross-ingstructures.TonyhasbeenappointedasaClayResearchFellowforatermoffiveyearsbeginning1September2016.Formore information visit www.claymath.org.

CLAY RESEARCH FELLOWS 2016The Clay Mathematics Institute is pleasedto announce that Simion Filip and TonyYueYuhavebeenappointedClayResearchFellows.

Simion Filip willreceive his PhD inJune 2016 fromthe University ofChicago under thesupervision of AlexEskin. Simion is in-terested in the con-nections betweendynamical systemsand algebraic geometry, in particularbetween Teichmüller dynamics and Hodgetheory. His recent interests also involve K3surfacesandtheirspecialgeometricproper-ties. Simionhas been appointed as a ClayResearch Fellow for a term of five yearsbeginning1July2016.


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ThefollowingitemsarefromtheEuropeanMathematicalSociety(EMS)webpagewww.euro-math-soc.eu/recent-news.

Meeting of presidents in BudapestThenextmeetingofpresidentsofmembersocieties of the European Mathemati-cal Society will take place in Budapest,Hungary, during the weekend 2 to 3April 2016. The meeting is hosted by theJános Bolyai Society and the Alfréd RényiInstitute of Mathematics. Among otherissues,problemsofmathematicaleducationthroughoutEuropewillbeafocalpointforthemeeting.

Crafoord Prize The Royal SwedishAcademyofScienceshas awarded the2016CrafoordPrizein Mathematics toYakov Eliashberg,Stanford University,USA,“for the devel-opment of contact and symplec-tic topology and groundbreaking discoveries of rigidity and flexibility phenomena”.Yakovwasbornin1946 in St Petersburg, Russia, obtaining aPhDat Leningrad StateUniversity in 1972.He is the Herald L. and Caroline L. RitchProfessor ofMathematics at Stanford Uni-versity.

Turkish academics persecuted Turkish academics who have openly criti-cizedTurkey’smilitarycrackdownonethnicKurdish communities are now feeling thewrathof theirgovernment. In recentdaysthe government arrested 33 academics.Although all have since been released,15 have been fired from their universityposts. The course of action started on 11January,whena letter protesting violencein Turkey's ethnically Kurdish Southeast-

EUROpEAN NEWS

ProfessorYakovEliashberg

ernregion,andcallingonthegovernmentto make peace with Kurdish rebels, waspostedonline.Meanwhile,morethan2,200academics in Turkey andmore than 2,300abroadsignedthe letter (seehttp://tinyurl.com/z968vqj).

Horizon 2020 consultationIn 2014 the European Commissionorganized an online consultation Math-ematics and Digital Science that wasfollowed up by a workshop in Brussels inNovemberthatsameyearandresultedinareportwithrecommendationsfortheincor-porationofvariousmathematicalareasandmethodologies into future programmeswithintheHORIZON2020programme.TheEMS participated in both the consulta-tion and theworkshop very actively. Thisyear,asimilaronlineopenconsultationhasbeen started and has received a numberof reactions already. The EMS urges itsmembers(bothsocietiesandindividuals)totakeupthechallengeandthusgivemathe-maticiansbetteroptionsforapplicationsinfuture work programmes under HORIZON2020.Theconsultationwillstayopenuntil30April2016.Forfurtherinformationseehttp://tinyurl.com/h8n6xt2.

Hermann Weyl PrizeThe 2016 Hermann Weyl Prize has beenawarded to Vasily Pestun of IHES (France)forhisgroundbreakingresultsinthestudyof supersymmetric gauge theories, suchas his ingenious computation of partitionfunctions that led to the discovery of richconnectionsbetweenfour-dimensionalandtwo-dimensional quantum field theories.Theawardceremonywilltakeplaceduringthe International Colloquium on Group Theoretical Methods in Physics to be heldinRiodeJaneiro,Brazil,from19to25June2016. For further information see http://icgtmp.blogs.uva.es/.

DavidChillingworthLMS/EMSCorrespondent


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News

The Heilbronn Institute for MathematicalResearchhasjustcelebrateditsfirst10yearsinoperation.Itisanationalinstitutethatsupportsmathematics across the UK. Its members splittheirtimebetweentheirownpersonalresearchand fundamental mathematical problemssuggestedbytheUKGovernmentCommunica-tionHeadquartersinCheltenham.AtanyonetimetheInstitutetypicallyhasover40members,rangingfromhighlydistinguishedseniormathematicianstoearlycareerResearchFellows; it supports over 25 postdoctoralResearchFellowships.TheHeilbronnInstituteisbasedinBristolandLondon. Fellowsare currentlyhosted in seven

UKMathematicsDepartments,andthisnumberissettoincrease.Overthepast10yearsover150mathematicianshavebeenmembers,includingover60ResearchFellows.Thesemembershavecomefrommorethan20universitiesintheUK.Aswellassupportingmathematiciansthroughsabbatical secondments and Research Fellow-ships,theInstitutefundsarangeofconferences,workshops and focused research events. Forexample,itfundsanAnnualDistinguishedLectureSeries,whichin2016willbegivenbyProfessorPeter Sarnak (IAS, Princeton), and an AnnualConference at which recent speakers includeProfessors Nalini Anantharaman,Jean-Francois Le Gall, Bryna Kra, KristinLauter, Henrik Lenstra, WendelinWernerandDonZagier. ItalsosupportsmanyothermathematicaleventsacrosstheUK.FormoreinformationabouttheworkoftheInstituteseeheilbronn.ac.uk.

CHALKDUSTChalkdust Issue 3 is now available. It includes an interview withProfessor Ian Stewart, the legacy of Fibonacci, an article aboutfractional calculus and much more. If you would like to readyour maths-horoscope or find out what the half derivative ofa function is, you can read it online for free at www.chalkdustmagazine.com, where you can also order a printed copy ofthe magazine, read a weekly blog and subscribe to a monthlynewsletter.


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1865 - 2015

General Society Meeting &Hardy Lecture 2016

Friday 8 July 2016 JZ Young Lecture Theatre, UCL, Gower Street (nearest tube stations: Euston and Euston Square)

3.30 Opening of the meeting and LMS business, including the announcement of the 2016 Prize winners (open to all) Tony Scholl (Cambridge) TITLE TBA4.45 Tea/Coffee5.15 Jacob Lurie (Harvard) – Hardy Lecture Weil's Conjecture for Function Fields Abstract: Let q be a positive definite quadratic form with integer coefficients. We say that another such quadratic form q' is in the genus of q if, for every positive integer n, the quadratic forms q and q' differ by a change of variable when reduced modulo n. Up to a change of variables, there are only finitely many quadratic forms in a genus. Moreover, there is a formula (the "mass formula" of Smith-Minkowski-Siegel) which counts the number of quadratic forms within a genus. This mass formula was reformulated by Tamagawa and Weil as a statement about the volume of certain adelic homogeneous spaces for the special orthogonal group SO(n). This led Weil to conjecture an analogous statement for the volumes of homogeneous spaces for other groups, which he verified in a number of cases and has subsequently been proven by Langlands, Lai, and Kottwitz. In this lecture I'll describe joint work with Dennis Gaitsgory which establishes the function field analogue of Weil's conjecture, using techniques inspired by algebraic topology

6.30 Reception at De Morgan House7.30 Society Dinner to be held at VENUE TBC

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 for your place at the meeting, please email Elizabeth Fisher ([email protected]). If you would like to attend the Society Dinner, please email Elizabeth Fisher ([email protected]). The cost to attend the Society Dinner is £35.00 per person (inclusive of wine).


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LMS LIBRARY AT UCLRegistering, Renewing, Visiting

Members of the Society are reminded thattheymay register as users of theUniversityCollege London (UCL) Library, where theLondonMathematicalSocietyLibraryisheldandwhichcontainsacollectionof:• periodicalspublishedbyothermath-ematicalsocietieswhicharereceivedinexchangefortheSociety'spublications

• copiesofbooksandjournalspublishedbytheSociety

• itemsacquiredbytheSocietyasreviewcopiesorgiftsThe Society’s Library is housed in the UCLScienceLibrary.Membersmayalsouseallthematerialavailableinthereadingroomsandstores of the UCL family of libraries. Theseprivilegesinclude:• borrowinguptotenitemsatanyonetime• placinguptothreeconcurrentreserva-tionsonmaterialalreadyonloan.

• borrowingbooksbypostwithoutservicecharge(costsforreturningthebooksmustbecoveredbytheuser)

• accesstoMathSciNetandspecificelec-tronicjournalsfromdesignatedterminalsintheScienceLibrary

• useoftheExploreaccesspointstosearchforandviewelectronicpublicationsandsavesinglecopiesofarticles(nomorethanonearticleperjournalissue)foryourownpersonaluse–youcansavearticlestostandardUSBsticks,notethatUSBstickscontainingencryptedsoftwaredonotworkontheExploreaccesspoints

• useofphotocopyingfacilitiesatUCLlibraries(chargedatthesamerateasUCLstaff)

• rapidphotocopyingservicebypost-Pho-tocopyRequestandCopyrightDeclarationFormFor licensingreasons,useoftheLibraryatUCLdoesnotincluderemoteelectronicaccesstojournalsandarticles.Tocheckthelistingsof electronic journals available to visitors,beforeyour visit to theLibrary,useExplore(http://sfx.ucl.ac.uk/sfx_local/az/walkin).

To Register/Renew (in person)

Complete the application form (downloadfrom www.ucl.ac.uk/library/docs/borrower-form)andbringthefollowingitemswithyou:• passport-sizephotograph• proofofidentitye.g.passport,photocarddrivinglicence

• proofofaddresse.g.utilitybill,recentbankstatement,validphotocarddrivinglicence

• proofofmembership–aletterofconfir-mationcanbeobtainedfromtheSociety–[email protected]

To Register/Renew (by post)Toregisterbypost,completetheapplicationform (download fromwww.ucl.ac.uk/library/do–cs/borrowerform)andreturnitwith:• apassport-sizephotograph• proofofmembership–aletterofconfir-mationcanbeobtainedfromtheSociety–[email protected]: Head of Membership, UCL LibraryServices, University College London, GowerStreet,LondonWC1E6BT(tel:02076797953,fax: 020 7679 7373, email: [email protected]).

When registering by post, library cards will be posted back to the address given on the application form.

Library cards are valid for 12 months from date of issue and will need to be renewed each year.No charge is made for the initial registra-tionorforrenewingexpiredlibrarycardsorcardswhicharewithinonecalendarmonthofexpiring.Reminders to renew - to receive remindersto renew by email from the Library at UCL,remember to include an email address onthe form when registering and renewing.TheUCLLibrarywillsendoutreminderstwoweeksbeforeyourlibrarycardisduetoexpire.Forgotten cards – if you forget your librarycard, you will not be admitted to any UCLLibrary.Thisruleisstrictlyapplied.

LMS Items


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Visiting the Library

New: checking seat availabilityYoucannowcheckonlinefortheavailabilityofseatsinthereadingroomsandcomputerclusterattheScienceLibrary:www.ucl.ac.uk/library/sites/science/#current

New: self-guided tourYou can now familiarise yourself with the

layout of the Science Library by viewingthe self-guided touronline:http://www.ucl.ac.uk/library/docs/floor-plans/science-self-guide.

24 hour openingTheScienceLibraryisopen24hoursforUCLLibrary card holders and has extended theopeninghoursoftheassistancedesk.

Opening hours

Help point and Collection Point

Self Service Reading Rooms

Monday 09:30–21:00 Openfrom08:45 Openfrom08:45

Tuesday 09:30-21:00 24houropening 24houropening

Wednesday 09:30-21:00 24houropening 24houropening

Thursday 09:30-21:00 24houropening 24houropening

Friday 10:00-21:00 24houropening 24houropening

Saturday 11:00-18:00 Closeat20.45 Closeat21:00

Sunday Closed 11:00-20:45 11:00 -21:00 (holdersofUCLLibraryCardsonly)

• Duringtheweekendsandevenings,theLibraryisopenprincipallytoofferbookloansandtohandlerelatedqueries.Forallotherqueries,pleasecontactamemberofstaffduringofficehours(www.ucl.ac.uk/library/help)

• Duringtheyear,theopeninghoursmaychange.PleasechecktheScienceLibrarywebsitebeforetravelling(www.ucl.ac.uk/library/sites/science#open)

Visit www.lms.ac.uk/library/lms-library forfurther information about the Society’sLibrary.

LMS GRANT SCHEMESNext Closing Date for Research Grant Applications: 15 May 2016

Applications are invited for the followinggrants:

Conferences (Scheme 1)Grantsofup to £7,000areavailabletoprovidepartial support for conferences held in the

UnitedKingdom.Thisincludesamaximumof£4,000forprincipalspeakers,£2,000tosupporttheattendanceof research studentswhoarestudyingatuniversities intheUK,and£1,000tosupporttheattendanceofparticipantsfromScheme5orformerSovietUnioncountries.


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LMS Items

LMS COUNCIL DIARY5 February 2016A personal view

As thenewCouncilDiarist, thisentrymarksmyfirst contribution to theLMS Newsletter inthatrole.Iwouldliketobeginbyexpress-ingmysincerethanksonbehalfofallCouncilmembers to Francis Clarke, who recentlystepped down as Diarist, for his excellentserviceinthatregard.The February meeting of Council markedthefirstmeetingforournewPresidentSimonTavaré in his role as Chair. The Presidentmade some introductory remarks based onhis experience observing previous meetingsintheroleofPresident-Designate, includingan expression of enthusiasm about the

Society’s support for youngmathematicians.The President updated Council on his activi-tiesundertakenonbehalfoftheSocietysincethepreviousmeeting; these included a visittoFudanUniversityinChinaandaHouseofCommons launch event for the Council forMathematicalSciences(CMS).The Council also heard the First QuarterFinancial Review from the Treasurer, whonoted a large donation from an individualtotheSocietyasaresultofitsdevelopmentwork. A few possible uses for these fundshadbeencarefullyconsidered,andatalaterstage in themeetingCouncil agreed touse

Celebrating new appointments (Scheme 1)Grantsofup to £600areavailabletoprovidepartial support for meetings held in theUnited Kingdom to celebrate the new ap-pointmentofalecturerataUKuniversity.

Postgraduate Research Conferences (Scheme 8)Grantsofup to £4,000areavailabletoprovidepartial support for conferences held in theUnitedKingdom,whichareorganisedbyandareforpostgraduateresearchstudents.

Research in Pairs (Scheme 4)Grantsofup to £1,200areavailabletosupportavisitforcollaborativeresearcheitherbythegrant holder to another institution abroad,orbyanamedmathematician fromabroadtothehomebaseofthegrantholder.Grantsofup to £600areavailabletosupportavisitforcollaborativeresearcheitherbythegrantholder toanother institutionwithin theUK,or by a namedmathematician fromwithintheUKtothehomebaseofthegrantholder.

International Short Visits (Scheme 5)Grants of up to £3,000 are available tosupport a visit for collaborative researchby

a named mathematician from a country inAfrica (or countries where mathematics isin a similar position) to the home base ofthegrantholder.Grantsofup to £2,000areavailable to supportavisit for collaborativeresearchbythegrantholdertoacountryinAfrica(orcountrieswheremathematicsis inasimilarposition).Forfulldetailsofthesegrantschemes,andto download application forms, please visitthe LMS website: www.lms.ac.uk/content/research-grants.• Applicationsreceivedby15 May 2016willbeconsideredatameetinginJune.

• Applicationsshouldbesubmittedwellinadvanceofthedateoftheeventforwhichfundingisrequested.

• Normallygrantsarenotmadeforeventswhichhavealreadyhappenedorwhereinsufficienttimehasbeenallowedforprocessingoftheapplication.Queries regarding applications can beaddressed to the Grants AdministratorAnthony Byrne (0207 927 0807, [email protected]) who will be pleased to discussproposals informally with potential appli-cantsandgiveadviceonthesubmissionofanapplication.

[email protected]

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No.457April2016

LMS FUNDING FOR UNDERGRADUATE MATHEMATICAL SOCIETY MEETINGS 2016

In 2016, the LMS Research MeetingsCommitteehassupportedoneUndergradu-ateMathematicalSocietyMeeting:VarsityEvent between the Mirzakhani Society(Oxford) and the Emmy Noether Society(Cambridge)(seereportonpage22).

Applications for Future Undergraduate Mathematical Society Meetings

The LMS considers requests from Under-graduateMathematical Societies tohostameetingandoffers fundingofup to £500foreither fullorpartial support for travelandsubsistenceofaspeaker(s),andreason-ablecostsforcatering.Applicationscanbemadeatanytimebutthedeadlineforapplicationsinthecurrentfinancial year is Friday 1 July 2016. Thereis limited funding and applications willbe consideredon afirst-come,first-servedbasis.ApplicantsshouldcontactElizabethFisher

([email protected]) for an applica-tionform.Applicationsshouldbecounter-signedbytheLMSDepartmentalRep.ForalistofLMSRepresentatives,visitthewebsitewww.lms.ac.uk/membership/lms-representatives. If your department does not haveaLMSRep,pleasecontactElizabethFisher([email protected]).

LMS-sponsored Undergraduate Mathematical Society Meetings 2014 & 2015

In 2014 and 2015, the LMS supported thefollowing ResearchWorkshops Undergrad-uateMathematicalSocietyMeetings:• Application of Fluid Dynamics to

Atmosphere and the Ocean,Durham• Juggling: Theory and Practice,StAndrews

• Mathematics in the World of Gaming,King’sCollegeLondon

thegift to supportUndergraduateResearchBursaries.Accordingtousualpractise,theCouncilheardseveral committee reports. TheProgrammeCommitteeproposed,andCouncilagreed,toseektohosta‘LondonMathematicalSocietyLecture’ as part of future programmes ofthe International Congress of Mathemati-cians (ICM). Vice-President Brown updatedthe Council on Research Policy Committeeactivities, including efforts to gather dataabout the lackof funding formathematicalsciences postdoctoral fellowships and abouttheallocationof fundingwithin institutionsfor Doctoral Training Programmes (DTPs) inthemathematicalsciences.Healsonotedthecompletion of a survey about departmentalviewsontheResearchExcellenceFramework(REF),withdatayettobeprocessed.Healsoreportedthat thematterofgenderbalance

ofEPSRCfellowshipswouldberaisedatthenextStrategicAdvisoryTeam(SAT)meeting.Theresultsofthe2015electionswerenoted,andtheScrutineerpresentedhis reportandreviewoftheseelections.Councilalsoagreedseveralappointments tovarious committees,andnotedthatthePresidentialSearchPanelwould be initiating its search for the nextPresident.The Council also agreed a list of 54 newmemberstobeelectedattheSocietymeetinglaterinFebruary.A final item of note was a proposal tosupportmathematiciansoutsideofacademia,for example retirees, or early career math-ematicianswhohavenotyetsecuredapost;Council agreed that this is an importantareaofactivityandthat the ideashouldbedevelopedfurther.

TaraBrendle


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TheSchoolofMathematics isseekingtoappointaChairofAnalysis intheDepart-mentofPureMathematics,inordertodevelopourstrengthinthisarea.TheSchoolhas traditionally been strong in functional analysis and operator theory, but wewelcomeapplicationsinallareasofanalysis.ItislikelythatthisappointmentwillbefollowedbyafurtherappointmentofaLecturerinAnalysis,anditishopedthattheappointedProfessorwillparticipateintheselectionofthelatter.

The salary, which is negotiable, will be within the Professorial range - minimum£60,512p.a.(pro rata).

Informal enquiriesmay bemade to ProfessorDugaldMacpherson, tel +44 (0)1133435166,[email protected],HeadofSchool,tel+44(0)1133435161,[email protected].

Pleaseapplyonlineat:http://www.jobs.ac.uk/job/ANE334/chair-in-analysis/

Closing date: 9 May 2016

UNIVERSITY OF LEEDSChair in Analysis

Full time (part time hours will be considered)

SIR ANDREW WILES AWARDED 2016 ABEL pRIZE

The NorwegianAcademy of Scienceand Letters hasawarded the 2016AbelPrizetoProfessorSirAndrewWiles,Uni-versity of Oxford, ‘forhis stunning proof ofFermat’sLastTheoremby way of the modu-

larityconjectureforsemi-stableellipticcurves,openinganewerainnumbertheory’.WileswillreceivehisawardfromHisRoyalHighnessCrownPrinceHaakonattheUniversityofOsloon24May2016.Wilesisoneofveryfewmathematicians–ifnottheonlyone–whoseproofofatheoremhasmadeinternationalheadlinenews.In1994hesolvedFermat’sLastTheorem,whichatthetimewasthemostfamous,andlong-running,unsolvedprobleminthesubject’shistory.Hisproofwasnotonlythehighpointofhis

careerbutalsotheculminationofaremarka-blepersonaljourneythatbeganthreedecadesearlier.Wilesrecallsthathewasintriguedbytheproblemthatheasayoungboycouldun-derstand, and yet it had remained unsolvedfor three hundred years. ‘I knew from thatmomentthatIwouldneverletitgo’,hesaid.‘Ihadtosolveit’.TheAbelCommitteesaid,‘FewresultshaveasrichamathematicalhistoryandasdramaticaproofasFermat’sLastTheorem’.SirAndrewwasawardedanLMSWhiteheadPrize in 1988 and was elected an HonoraryMemberoftheLMSin2001.On behalf of the LMS, and the UK math-ematical communitymore broadly, ProfessorSimon Tavaré FRS, the President of the LMS,congratulates Sir Andrew on his remarkableachievementsthathaveledtothe2016AbelPrize.More information is available at www.abelprize.no/

News


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The David Crighton LectureProfessor Frank Kelly CBE FRS

Thursday 12 May 2016 at 6.15 p.m. followed by a reception

at The Royal Society, Carlton House Terrace,

London, SW1Y 5AGRegistration will open at 5.45 p.m.

Mathematics and Financial MarketsAbstract:A substantial proportion of mathematics graduates, at both first degree and doctoral level, enter the financial services sector. This is hardly surprising given the importance of the sector to the economy, and the role of mathematical modelling in the valuation of instruments and the assessment of risk. What is striking is that, with some notable exceptions, few math-ematicians have been actively engaged in the design of financial markets. This is undoubtedly a serious challenge with parallels from other large-scale complex networks: to design a dis-tributed system, linking self-interested and intelligent agents, so that the outcome is effective and efficient.

How would an ideal market operate, to allow liquidity between long-term investors to be provided by short-term traders? In the second part of the talk I outline some preliminary work, joint with Elena Yudovina, on this question. I describe a simplified and analytically tractable model of a limit order book where the dynamics are driven by stochastic fluctuations between supply and demand. The model has a natural interpretation for a highly traded market on short time scales where there is a separation between the time scale of trading, represented in the model, and a longer time scale on which fundamentals change.

There has been considerable discussion recently of the effects of competition between multiple high-frequency traders, and of proposals aimed to slow down markets. A key issue is that traders may compete on the speed with which they can snipe an order rather than compete on price, and a proposed regulatory response is to use frequent batch auctions. Our model is clearly a caricature of a real limit order book, but it does provide insight into various high-frequency trading strategies (for example market-making, sniping and mixtures of these) and the impact on Nash equilibria when a market in continuous time is replaced by frequent batch auctions.

ProfessorFrankKellywillbepresentedwiththeDavidCrightonMedalwhichisawardedbien-nially,forservicesbothtomathematicsandtothemathematicalcommunity,bytheInstituteofMathematicsanditsApplications,andtheLondonMathematicalSociety.

Admission tothelectureandreceptionisbyticketonly.ForticketspleasecontactAlisonPenryattheIMA,CatherineRichardsHouse,16NelsonStreet,Southend-on-Sea,SS11EForemailalison.penry@ima.org.ukby24April2016.Ticketsarefreeofchargeandwillbeallocatedonafirstcome,firstservedbasis.Pleaseconfirmwhetheryouwishtoattendthelectureandreception,orthelectureonly.


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The London Mathematical Society is a registered charity for the promotion of mathematical knowledge.

CECIL KING TRAVEL SCHOLARSHIP The London Mathematical Society annually awards a £5,000 Cecil King Travel Scholarship in Mathematics, to a young mathematician of outstanding promise. The Scholarship is awarded to support a period of study or research abroad, typically for a period of three months. Study or research in all areas of mathematics is eligible for the award. The award is competitive and based on a written proposal describing the intended programme of study or research abroad, and the benefits to be gained from such a visit. A shortlist of applicants will be selected for an interview during which they will be expected to make a short presentation on their proposal. Applicants must be nationals of the UK or the Republic of Ireland, either registered for or having completed a doctoral degree within 12 months of the closing date. Applications should be made using the form available on the Society's website (www.lms.ac.uk/prizes/cecil-king-travel-scholarship) or by contacting [email protected]. The closing date for applications is Monday 6 June 2016. It is expected that interviews will take place in London in late June or early July. The Cecil King Travel Scholarship was established in 2001 by the Cecil King Memorial Fund. The award is made by the Council of the London Mathematical Society on the recommendation of the Cecil King Prize Committee, nominated by the Society's Research Meetings Committee.


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UNIVERSITY OF CAMBRIDGEFACULTY OF MATHEMATICS

ADAMS pRIZE

Statistical Analysis of Big Data

TheUniversityofCambridgehasannouncedthesubjectforoneifitsoldestandmostprestigiousprizes.TheAdamsPrizeisnamedafterthemathematicianJohnCouchAdamsandwasendowedbymembersofStJohn’sCollege.Itcommemo-ratesAdams’sroleinthediscoveryoftheplanetNeptune,throughcalculationofthediscrepanciesintheorbitofUranus.

TheChairmanoftheAdjudicatorsfortheAdamsPrizeinvitesapplicationsforthe2016-17prizewhichwillbeawardedthisyearforachievements inthefieldofStatisticalAnalysisofBigData.

Theprizeisopentoanypersonwho,on31October2016,willholdanappoint-ment intheUK,either inauniversityor insomeother institution;andwhoisunder40(inexceptionalcircumstancestheAdjudicatorsmayrelaxthisagelimit).Thevalueof theprize isexpected tobeapproximately£15,000,ofwhichonethirdisawardedtotheprize-winneronannouncementoftheprize,onethirdisprovidedtotheprize-winner’sinstitution(forresearchexpensesoftheprize-winner)andonethirdisawardedtotheprize-winneronacceptanceforpublica-tioninaninternationallyrecognisedjournalofasubstantial(normallyatleast25printedpages)originalarticle,ofwhichtheprize-winnerisanauthor,surveyingasignificantpartofthewinner’sfield.

Applications,comprisingaCV,alistofpublications,thebodyofwork(publishedorunpublished)tobeconsidered,andabriefnon-technicalsummaryofthemostsignificantnewresultsofthiswork(designedformathematiciansnotworkinginthesubjectarea)shouldbesenttotheSecretaryoftheAdamsPrizeAdjudicatorsviaemailtoadamsprize@maths.cam.ac.uk.

The deadline for receipt of applications is 31 October 2016.


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FROM SYMBOLIC DYNAMICS TO AppROXIMATION METHODS AT LSD & LAW 2016 Report

A part of the annual two-day London Strin-gology Day & London Algorithms Workshop(LSD&LAW2016)wasdedicatedthisyeartothe LMS sponsored research meeting From Symbolic Dynamics to Approximation Methods(SDAM). The meeting was intercalated withtheworkshop’sschedule,takingplaceonbothThursday4andFriday5February2016.Its programme included three invited talksandothershortinformaltalksandattractedallparticipantsof theLSD&LAW2016meeting.Thenumberof researchers thatattendedtheworkshopthisyearwasover60comingfrommorethan15countries.Theratiooffemalere-searchersamongtheparticipantswasofabout

25%,fiveofthempresentingtheirwork.TheSDAMmeetinghadasitsfocusthespacediscretizationofgeneraldynamicsystemswhichcomplemented the interests of the researchcommunitypresentatLSD&LAW2016.The invited talk given by Marie-PierreBéal (University of Marne-la-Vallée, France)discussedshiftsofsequenceswhicharesetsofbi-infinite sequencesof symbolsdefinedbyagiven set of forbidden patterns. The speakerpresented how rational expressions may beobtainedforthezetafunctionsoftheseclassesof shifts of sequences and showed formulasof the zeta functions for some shifts definedby non-regular constraints (zeta functions

Marie-PierreBéaltalksaboutanexampleofZetafunctionsforsub-shifts

FatimaVayanigivesanexampleofq-gramspresentinaDNAsequence

RituKundutalksaboutthebackgroundoftheSuperbubbleproblem

TizianadiMatteogivesexamplesofdifferentlevelsofmath-ematicalmodelsconsideredonnetworkfilteringforbigdata

Reports


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havebeencomputed forDyck shifts,Markov-Dyckshifts,andsofic-Dyckshifts).Someofthepresented applications of symbolic dynamicsreferredtocodingforconstrainedchannels.FilippoMignosi(UniversityofL'Aquila,Italy)exploredinhisinvitedtalkSturmianWords,or“Sturmian Trajectories”, which are a classicaltopicofSymbolicDynamics.Thetalkconsistedofbotholdandrecent“semantic”relationshipsbetweencombinatorialpropertiesofSturmianwordsandclassicalapproximationresults.Michael Soltys (California State UniversityChannel Islands,USA)proposed inhis invitedtalkseveralopenproblems.Amongthese,arel-ativelyrecentresultshowsthatSquareShuffleisNP-complete.ThisisoneofthesyntacticallysimplestNP-completeproblems.However,thisresultwasprovenforanalphabetofsixsymbolsandthequestionremainsopenfornon-unaryalphabetsofnomore thanfiveelements.Healsodiscussedanopenproblemrelatedtorep-etitions in strings over alphabet lists and anopenproblem related to theminimality of auniversalalphabetfortheseliststofulfilcertainintersectionproperties.

Several shorter contributing talks discussedvarious problems falling into the intersec-tion between symbolic dynamics, combina-torics and algorithms. Gabriele Fici (Univer-sity of Palermo, Italy) presented some newresultsrelatedtoalgorithmsonthepreviouslymentionedforbiddenwords,whichhavedirectapplicationsinbioinformatics(oneofthetradi-tionalfocusareasoftheLSD&LAWmeetings).The talkof TizianaDiMatteo,King'sCollegeLondon, presented amathematicalmodelingofnetworkfilterswithapplicationsintheeval-uationofstockmarkets,anarearepresentativeforthe“bigdatachallenge”.TheSDAMmeetingwassupportedbyanLMSConference grant and the Department of In-formaticsatKing’sCollegeLondon,whichalsoprovidedadditionalsupportfortheoverallLSD&LAW2016workshop.ThenextLSD&LAWmeetingwillbeheldatKing’sCollegeLondoninFebruary2017(exactdatestobeannouncedsoon).

MaximeCrochemoreRobertMercas

King’sCollegeLondon


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Reports

WHY BE NONCOMMUTATIVE?Report

The conference Why be noncommutative? was held on 8 February 2016, at ImperialCollege London, funded by an LMS Confer-encegrantcelebratingnewappointments,aswellasbyImperialCollegeLondon.Thecon-ferencewasattendedbyover50participants,includingatleast30PhDstudents,sometrav-ellingfromasfarasEdinburgh(andreceivingtravel support from the conference). Itwasgeared towards PhD students and postdocs,introducing aspects of noncommutativegeometryfromthepointofviewofalgebraandrepresentationtheory.Manyparticipants

gavepositivefeedback.Thefirsttalkwasbytheorganizer,DrTravisSchedler (Imperial College London), entitledPoisson and noncommutative geometry, ex-plainingtheideaofstudyingnoncommutativealgebras as functions on a noncommutativespace, the Kontsevich-Rosenberg approachvia representation varieties, andhowPoissongeometry and Hamiltonian flow enter viadeformation theory, ending with a discus-sion of deformation quantization and Kont-sevich's formality theorem. The second talkwas by Professor Iain Gordon (University of

MIRZAKHANI SOCIETYReport

The Mirzakhani Society of theUniversity of Oxford was es-tablished in October 2014 topromote the welfare of thoseidentifying as female or non-bi-narystudyingmathematics.TheSociety is named afterMaryamMirzakhani, thefirstwoman towintheFieldsMedal.OnSaturday27February2016,weheldaVarsityeventwiththeEmmy Noether Society of theUniversityofCambridge.Itwasa great experience where wewere able to discuss the issuessurrounding gender equality inmathematics from a perspec-tive stretchingbeyondourownuniversities.Thiseventinvolvedthree speakers; the first was Anne Davis, aProfessor of Mathematical Physics and theUniversity Gender Equality Champion forSTEMM subjects at Cambridge; the secondspeakerwasPerlaSousi,aLecturerintheSta-tisticsLaboratoryatCambridge;andthethirdspeaker was Christie Marr, Deputy DirectoroftheIsaacNewtonInstitute.Wealsowere

abletoexploreCambridge.TheLMSfundingwasusedtocaterthiseventforourmembers.We’dliketotakethisopportunitytothanktheLMSforthefunding;itwasmuchappre-ciated.

HelenRyan(President)RebeccaLowiss(Treasurer)

EmmaBeer(Secretary)

MembersoftheMirzakhaniSocietywiththePresidentoftheEmmyNoetherSociety


23INTEGRABLE SYSTEMS IN NEWCASTLEReport

ThethirdoccurrenceoftheworkshopIntegra-ble Systems in Newcastletookplacefrom5to

6February2016attheUniversityofNorthum-briaatNewcastle.Themeetingwashostedby

AttendeesattheIntegrable Systems in Newcastleworkshop

Edinburgh),entitledWhy be noncommutative with algebraic combinatorics?, which beganwith the classic theorem of Shepherd-ToddandChevalley that quotients of linear spacesbygroupsaresmoothifandonlyifthegroupisgeneratedbycomplexreflections(andtheirclassification),and thenproceeded toexplaintheintricatecombinatoricsarisingwhentakingaquotientoftwocopiesofthereflectionrepre-sentation,involvingconjecturesandtheoremsofHaiman,Gordon,andothers.Thethirdandfinal talkwas by Toby Stafford (University ofManchester),entitledNoncommutative projec-tive algebraic geometry, and focussedon theproblemsofclassificationofnoncommutativeprojectivespacesoflowdimension,beginningwithclassicresultsofArtin,Tate,andVanden

Bergh for curves and surfaces, leading upto birational classification of noncommuta-tive surfaces, includingArtin's conjectureandresults of Rogalski, Sierra, and Stafford onsubalgebrasoftheSkylaninalgebra.Alltalkspresentedopenquestionsinthefieldandledto lively discussions with the audience thatcontinuedintotwobreaksforteaandcoffeeaswellaslunch.The conference dinner, attended by 30 par-ticipants (and subsidized for PhD students),washeldatOlivesRestaurantinKensington,ashortwalkfromtheconference,andwasfullof interesting discussionswhich continued af-terwardsuntillateatanearbybar.

TravisSchedlerImperialCollegeLondon


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theNonlinearWavesandIntegrableSystemsgroupandfocusedoninvestigatingnewcon-nectionsbetweenintegrabilityandphysics.The success of the event is due in greatpart to the excellent contributions of thespeakers Martina Balagović (Newcastle),Pierre-Philippe Dechant (York), Gennady El(Loughborough), Katrin Leschke (Leicester),Davide Proment (East Anglia), Noel Smyth(Edinburgh), and Iain Stewart (Strathclyde).The topics ranged from liquid crystals androgue waves to new constructions in Liealgebras and surface theory. A workshop

dinnerwas held on the Friday evening andwaswell attended.Wewould like to thankallparticipants,withaspecialmentiontotheresearchstudentsforfurtherstimulatingthediscussionsduringthecoffeebreakswithveryinterestingposters.It is a great pleasure to acknowledge thegenerous support from the London Math-ematical Society and the Department ofMathematicsandInformationScienceswhichmakesthisseriespossible.

BenoitHuardNorthumbriaUniversity

VISIT OF DR JYUN-AO LIN

Dr Jyun-Ao Lin (Institute of Mathematics,AcademiaSinica)isvisitingVanessaMiemietzattheUniversityofEastAngliafrom2to30April2016. DrLinworksongeometric representa-tiontheory,especiallyontheHallalgebrasofcurves.His visitwill be devoted to the studyof the categorification of the spherical Hallalgebra of a projective line defined over afinitefield.ThestructureoftheassociatedKLRalgebra relies on the computation of exten-sionsbetweentheEisensteinsheavesandwillprovide another approach to the representa-tiontheoryofquantumaffinealgebrasaswellasthegeometricLanglandsprogram.Hewillgiveatalkatthepuremathematicsseminar atUEAon 25April at 3 pmonThe spherical Hall algebra of a weighted projec-tive curve,inwhichhewillalsopresentsomerecentapplicationsofthiswork.For further information contact VanessaMiemietz ([email protected]). This visit issupportedbyanLMSscheme5grant.

VISIT OF YONG HOUDr Yong Hou (Institute for Advanced Study,Princeton) will be visiting the UK between25Mayand10June2016. DrHouworksonhyperbolic 3-manifolds and his recent workhas focused on properties of the HausdorffdimensionofthelimitsetofSchottkygroups

acting on hyperbolic 3-space. Details of DrHou’stalksduringhisvisitare:• Friday27May,UniversityofSouthampton

Measure decompositions on Cayley graph of free group(contactJimAnderson:[email protected])

• Thursday2June,UniversityofWarwickRigidity of Kleinian groups(contactSaulSchleimer:[email protected])

• Monday6June,OxfordUniversityHausdorff dimension and complexity of Kleinian groups(contactMarcLackenby:[email protected])Further details may be obtained from JimAnderson ([email protected]). ThevisitissupportedbyanLMSScheme2grant.

VISIT OF CHRISTIAN LOMpProfessorChristianLomp(UniversityofPorto)willbevisitingtheUKbetween4Mayand11June 2016. Professor Lompworks on Hopfalgebras, quantum groups and ring theory.Details of Professor Lomp's talks during hisvisitare:• Tuesday17May,SwanseaUniversity

Actions of semisimple Hopf algebras on semiprime rings(contactTomaszBrzezinski:[email protected])

Reports, Visits

[email protected]

25

No.457April2016

• Wednesday1June,QueenMaryUniversityofLondonIntegral Calculus on Quantum Exterior Algebras(contactShahnMajid:[email protected])

• Wednesday8June,UniversityofGlasgowActions of semisimple Hopf algebras on iterated Ore extensions(contactGwynBellamy:[email protected])Further details of these arrangementsmay be obtained from Tomasz Brzezin-ski([email protected]).ThevisitissupportedbyanLMSScheme2grant.

VISIT OF DANA SCOTTProfessor Scott's visit to theUK, from7 to28May2016,wasannounced intheMarchissueoftheLMS Newsletter.Belowarepro-visional titles of lectures/seminars he willgive,togetherwithemailaddressesoflocalcontacts who will supply further informa-tiononrequest,closertothedate.

Oxford: 7-11 MayPhilosophyofMathematicsSeminar,9Mayat16.30Does Mathematics Need a Foundation?ComputerScienceSeminar,10Mayat14.00Stochastic Lambda CalculusLogicSeminar,11Mayat11.00Can Modalities Save Naive Set Theory?Contact:DanIsaacson([email protected])

Birmingham: 11-15 May Seminartitleanddatetobeannounced.Contact:MartinEscardo([email protected])

Leeds: 15-19 MayMathLogicSeminar,17Mayat16.00Lambda Calculus and Type TheoryTheLöbLecture,18Mayat16.30Does Mathematics Need a Foundation?Contact:StanWainer([email protected])

Cambridge: 19-24 MayTheMordellLecture,20Mayat17.00Does Mathematics Need a Foundation?PSSLWorkshop21-22MayStochastic Lambda Calculus Contact:PeterJohnstone([email protected])

London: 24-29 MayUCL,25or27MayLambda Calculus and Type TheoryImperial,26MayStochastic Lambda CalculusBCSlecture26MayeveningLambda Calculus: Then and NowQueenMary,25or27MayTitle:TobeannouncedContacts:AlexandraSilva([email protected])IvanTomasic([email protected])

VISIT OF TOBIAS KUNADrTobiasKuna(UniversityofReading)willbe visitingDrDimitriosTsagkarogiannisatthe University of Sussex during the week16to20May2016.Thisvisit,togetherwitha previous one (14 to 18 March) will bedevoted to the study of the convergencepropertiesandremainderestimationofper-turbativeexpansionsforinteractingparticlesystems.Theconvergenceanalysis requiresthe identification of massive cancelationsbased on a deep understanding of theunderlying combinatorial and graph theo-retical structure. These singular perturba-tionexpansionsallowafinecontroloftheinfluenceofsmalleronlargerscales.During his visit, on Tuesday 17 May, DrTobias Kuna will also give a talk on Con-trolled cluster expansion, graphical repre-sentation and convergenceinwhichhewillalso present the recent developments inthiswork.For further information contactDr Dimitrios Tsagkarogiannis([email protected]). The visitissupportedbyanLMSScheme4ResearchinPairsgrant.


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LMS HARDY LECTURE TOUR 2016

The2016LMSHardyFellowisProfessor Jacob Lurie(Harvard).TheHardyLectureshipwasfoundedin1967 inmemoryofG.H.Hardy inrecognitionofoutstandingcontributiontobothmathematicsandtotheSociety.TheHardyLectureshipisalecturetouroftheUKbyamathematicianwithahighreputationinresearch.

JacobLuriewillvisittheUKinJuneandJuly2016andhewillgivetalksat:

Oxford20JuneOrganiser: Ulrike Tillmann

Southampton21/22JuneOrganiser: Jelena Grbic

Glasgow27JuneOrganiser: Andy Baker

Aberdeen28JuneOrganiser: Assaf Libman

Leicester30June/1JulyOrganiser: Frank Neumann

Sheffield4/5JulyOrganiser: John Greenlees

Cambridge6/7JulyOrganiser: Julius Ross

Hardy Lecture, London

Weil's Conjecture for Function Fields 8Julyat3.30pm,London

Organiser: London Mathematical Society

For further information on attending each lecture, please contact the local organisers.For general enquiries about the Hardy Lectures, please contact Elizabeth Fisher ([email protected]).

G.H.Hardy,LMSPresident1926–1928and1939–1941PhotoCourtesyofMasterandFellowsofTrinityCollege

Cambridge

JacobLurie(Harvard)HardyLecturer2016


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THE LONDON MATHEMATICAL SOCIETY JOINTLY WITH GRESHAM COLLEGE

Tuesday, 24 May 2016 6:00pm at The Museum of London

Mathematics, Measurement and Money

Professor Norman Biggs London School of Economics

Throughout its brief history, mathematics has been closely linked with measurement and money. In the ancient settlements the rules of arithmetic and geometry were used to solve problems about the allocation of food and resources. When life became more complex, the use of coined money led to computational problems that required good algorithms for their solution.

Nowadays we rely on mathematics for security, and the links between information and money have become blurred. Can mathematics keep us safe?

ADMISSION FREE

NO RESERVATIONS REQUIRED – FIRST COME, FIRST SERVED

Museum of London, London Wall, London EC2Y 5HN

Nearest underground stations: Barbican, St Paul’s, and Moorgate

020 7831 0575 [email protected] www.gresham.ac.uk


29

1865 - 2015

Combinatorics and Operators in Quantum Information Theory

LMS Research SchoolQueen’s University, Belfast5-9 September 2016Organisers: I. G. Todorov (QUB) and S. Severini (UCL)

Course outlineIn the past decade, progress on zero-error quantum information has not only strength-ened the existing links with graph theory, but has also uncovered new and unexpected connections with operator algebras and optimisation. This has led to the formation of a new area on the crossroad of quantum computing, combinatorics, operator theory and mathematical programming. The purpose of the School is to introduce PhD students and young researchers to both its methods and problems, discussing topics such as zero-error capacities, graph entropy, quantum graph parameters, games for quantum players, quantum correlations, conic optimisation and communication complexity.

The three main lecture courses are:• Graphs and information theory (Andreas Winter, Barcelona/Bristol) • Non-commutative order in quantum games (Vern Paulsen, Waterloo) • Optimisation methods in quantum information theory (Monique Laurent, Amsterdam/Til-

burg and Jop Briët, Amsterdam)

These lecture courses will be supplemented by tutorial sessions. For further information please visit: http://www.qciao.org

Apply by Friday 27 May 2016 using the registration form available at: https://www.surveymonkey.co.uk/r/RS-23ApplicationForm Research students, post-docs and those working in industry are invited to apply. Numbers will be limited and those interested are advised to make an early application. Registration Fees: Graduate Students(£150); Early Career Researchers (£250)


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Meetings

SCOTTISH pARTIAL DIFFERENTIAL EQUATIONS COLLOQUIUM

The fourth Scottish Partial Differential Equations Colloquium(4thSPDEC2016)willbe held at the University of Dundee from9to10June2016.TheaimofthismeetingistobringtogetherresearcherswhoseworkfeaturesPDE’sandtheiranalysis,toprovidea platform for early career researchersto exhibit their recent work and researchinterests, as well as to create an opportu-nity to discuss in an informal setting withinternationally leading researchers. Plenaryspeakersare:• JohnBall(Oxford)• WilliJäger(Heidelberg)• CharalambosMakridakis(Sussex)• BarbaraNiethammer(Bonn)Theorganisersof4thSPDECareIreneKyzaand Mariya Ptashnyk. For more informa-tionvisitthewebsiteatwww.maths.dundee.ac.uk/spdec2016/.The Colloquium is supported by an LMSConference grant, the Edinburgh Mathe-maticalSocietyResearchSupportFund, theGlasgow Mathematical Journal LearningandResearchSupportFund,andtheUniver-sityofDundee.

COMBINATORICS AT OXFORDAone-daymeetinginCombinatoricswillbeheld inOxfordonWednesday1 June2016.The meeting will take place at theMathe-maticalInstitute,withtalksstartingat11.00am and coffee available beforehand from10.30am.This year's speakers are Leslie Goldberg(Oxford),PennyHaxell(Waterloo),MihyungKang (Graz), János Pach (Lausanne) andGáborTardos(Budapest).Anyone interested is welcome to attend.Somefundsmaybeavailabletocontributeto the expenses of research students whowishtoattendthemeeting.Furtherdetails

canbeobtainedfromthewebpage,whichcan be found at http://people.maths.ox.ac.uk/scott/Pages/one-day_meeting.htm.Themeeting is supportedbyanLMSCon-ferencegrantandtheBritishCombinatorialCommittee.

COMpUTATIONAL AND ANALYTIC pROBLEMS IN SpECTRAL THEORY

AconferenceonComputational and Analytic Problems in Spectral Theorywill takeplaceatCardiffUniversityfrom6to9June2016.The topics include spectral theoryofdiffer-ential operators, inverse problems, blockoperator matrices, periodic and quasiperi-odicdifferentialoperators,quantumgraphsand networks, modern sampling methodsandcomputations,andnumericalanalysis.The organisers are B.M. Brown (Cardiff)and I. Wood (Kent). Further information,including registration and contact details,canbe foundon thewebsite atwww.cs.cf.ac.uk/spectral.There is some financial support availableforUKbasedresearchstudents.Themeetingis supported by an LMS Conference grantandtheCardiffSchoolofComputerScienceandInformatics.

QUANTUM pHYSICS AND LOGICThe 13th international conference onQuantum Physics and Logic (QPL) will behosted by the University of Strathclyde inGlasgowbetweenMonday6andFriday10June 2016.QPL is a conference that bringstogether researchers working on math-ematical foundations of quantum physics,quantum computing, and related areas,witha focuson structuralperspectivesandthe use of logical tools, ordered algebraicand category-theoretic structures, formallanguages, semantical methods, and othercomputersciencetechniquesappliedtothestudyofphysicalbehaviouringeneral.

[email protected]

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No.457April2016

Invitedlectureswillbegivenby:• ElhamKashefi(UniversityofEdinburgh)• TomLeinster(UniversityofEdinburgh)• KrystaM.Svore(MicrosoftResearch)• StephanieWehner(TUDelft)Additionally,tutoriallectureswillbegivenby:• KoheiKishida(UniversityofOxford)

Sheaves and contextuality• AleksKissinger(RadboudUniversityNijmegen)Process theories and graphical languages

• ConorMcBride(UniversityofStrathclyde)Logic and functional programming

• DanielOi(UniversityofStrathclyde)Quantum foundations and Bell experiments

• OgnyanOreshkov(UniversityLibredeBruxelles)Causality in quantum theory

• PeterSelinger(DalhousieUniversity)Quantum programming languagesOn Saturday 11 June, there will be a co-locatedworkshoponSemantic SpacesattheIntersection of NLP, Physics, and CognitiveScience. Invited speakers are Hans Briegel(University of Innsbruck), Peter Gardenfors(Universityof Lund) andDominicWiddows(MicrosoftResearch).For registration and more information,see http://qpl2016.cis.strath.ac.uk. The con-ference is partially funded by an LMS Con-ference grant to support attendance byresearch students. See the website abouthowtoapplyforsupport.

RANDOM INTERACTING SYSTEMSTheschoolandworkshoponRandom Inter-acting Systemswilltakeplacefrom19to24June2016inBath,withfocusonrecentde-velopments on random interacting systems,including (but not restricted to) interact-ing and self-interacting particle systems,randomgrowthprocesses,percolation,spinsystems,randomwalksandotherstochasticprocessesinrandomenvironments,randomandevolvinggraphs,randominterlacements,

and random polymers. The meeting willcomprisethefollowingtwomini-courses:• MichaelDamron(GeorgiaInstituteofTechnology)Geodesics in first-passage percolation

• RonPeled(TelAvivUniversity)The spin and loop O(n) models andinvitedtalksbythefollowingspeakers(*tobeconfirmed):• KrzysztofBurdzy(UniversityofWashington)

• ManuelCabezas(PUCChile)• ElisabettaCandellero(UniversityofWarwick)

• PietroCaputo(UniversitàRomaTre)• ShirshenduGanguly*(UniversityofWashington)

• JackHanson(CityCollegeofNewYork)• DmitryIoffe(Technion)• ElenaKosygina(BaruchCollege,CUNY)• FabioMartinelli(UniversityàRomaTre)• AllanSly*(UCBerkeley)• YinonSpinka(TelAvivUniversity)• Alain-SolSznitman(ETHZürich)• VincentTassion(UniversitéGenève)• BálintTóth(Bristol&TUBudapest)• DanielUeltschi(UniversityofWarwick)There is a £70 registration fee, and somefunding is available to contribute to localexpenses of some participants,with prefer-ence given to PhD students, post-docs andyoungresearchers.Therewillbeslotsforasmallnumberofcontributedtalks.Formoreinformation,includinghowtoregister,visithttp://people.bath.ac.uk/ados20/ris2016/.Themeeting is supportedbyanLMSCon-ference grant, the Marie Curie Actions,Prob-L@BandUniversityofBath.

BSDES, SpDES AND THEIR AppLICATIONSThe University of Edinburgh will hostfrom 3 to 7 July 2017 the internationalworkshop on Backward Stochastic Differ-ential Equations (BSDE), Stochastic PartialDifferential Equations (SPDE) and their ap-plications.Themeetingprovidesaplatformforresearcherstoshowcasestate-of-the-art


32

Meetings

developments and to identify and exploreconverging research directions within Sto-chastic Analysis, Numerical ApproximationsandapplicationsinFinanceandPhysics.Theconfirmedspeakersinclude:• EmmanuelGobet,ÉcolePolytechnique)• IstvánGyöngy(UniversityofEdinburgh)• PeterImkeller(HumboldtUniversity)• MoniqueJeanblanc(UniversityofEvry)• NicolaiV.Krylov(UniversityofMinnesota)• JinMa(UniversityofSouthernCalifornia)• AnnieMillet(UniversityofJussieu)• EtiennePardoux(UniversityofMarseille)• MichaelRöckner(BielefeldUniversity)• MartaSanz-Sole(UniversityofBarcelona)• NizarTouzi(ÉcolePolytechnique)• ShigePeng(ShandongUniversity)The meeting offers an ample opportu-nity forparticipants to interactwithworldleadersinthesefieldsandtogeneratenewideasandreinforceexistingcollaborations.ThemeetingisbeingorganizedbyGonçalodos Reis (Edinburgh), Lukasz Szpruch(Edinburgh), Samuel Cohen (Oxford), DanCrisan (Imperial College), Michela Ottobre(Heriot-Watt) and Anke Wiese (Heriot-Watt).Thereisagranttosupportyoungresearch-ers, more information on thewebsite. Par-ticipants should register at this website or,incaseofdifficulty,emailtheorganisersatBSDE.SPDE.2017@gmail.com.Findoutmoreatwww.ed.ac.uk/maths/bsde-spde-2017.Themeeting is supported by the Interna-tional Centre for Mathematical Sciences(ICMS),theUniversityofEdinburgh,theHe-riot-Watt University and the LondonMath-ematicalSociety(LMSConferencegrant).

GROUpS ST ANDREWS 2017Groups St Andrews 2017 will be held inBirmingham fromSaturday5 to Sunday13August2017.Thetalkswilltakeplacefrom6to12Augustinclusive.

Main Speakers:• MichaelAschbacher(CaliforniaInstitute

ofTechnology)• RadhaKessar(CityUniversity,London)• Pierre-EmmanuelCaprace(UniversiteCatholiquedeLouvain)

• GunterMalle(TUKaiserslautern)

Plenary Speakers:• TimBurness(UniversityofBristol)• VincentGuirardel(UniversitedeRennes1)

• HaraldHelfgott(UniversityofGottingen)• AndreiJaikin-Zapirain(UniversidadAu-tonomadeMadrid)

• DonnaTesterman(ÉcolePolytechniqueFederaledeLausanne)The conference website is available at:www.groupsstandrews.org/2017/index.shtml.Theorganisersencouragethoseinter-estedinattendingtheconferencetoregisteronthewebsitetoreceivefurtherupdatesontheconference. ConferenceorganisersareColinCampbell,ChrisParker,MartynQuick,EdmundRobertsonandColvaRoney-Dougal.

REpRESENTATION THEORY OF ALGEBRAIC GROUpSIn Honour of Stephen Donkin

A conference on Representation Theory of Algebraic Groups in honour of StephenDonkinwillbeheldatKing'sManorattheUniversityofYork from13 to15 July 2016.Professor Donkin has been a leading lightin the world of algebra for many years;his huge contribution to representationtheory in particular is evidenced by thedistinguished list of speakers at the confer-ence. Themeetingwill offer participants afantasticopportunitytoreflectonthedevel-opmentofthesubjectandtolookaheadtonewproblemsandnewideas.Alistofspeakersandfurtherinformationis available at www.math.unipd.it/~taylor/RAGS/.Hereparticipantscanalsofindalinktotheregistrationform.Thereisa£30reg-istrationfee.Themeeting is supportedbyanLMSCon-ference grant, the Heilbronn Institute and


33

the Royal Commission for the Exhibition1851.TheLMSfundingalsoprovideslimitedsupportforUKPhDstudents.Contacttheor-ganisersatharalampos.geranios@york.ac.ukformoreinformation.

ECSTATIC 2

Following the greatsuccess of last year, therewill be a second editionof ECSTATIC (Early CareerStage Topologists atImperialCollege).Thisisatwo-day workshop aimed

at young researchers (ie PhD students andpostdocs) interested in topology. As thename suggests, the workshop will be atImperial College London, fromMonday 13to Tuesday 14 June 2016. The two invitedspeakersare:• AndrásJuhász(Oxford)• SarahWhitehouse(Sheffield)The main aim of the workshop is toencourage young researchers to give talksthemselvesontheirareaofresearch.Somefundingisavailablefortravelandaccommo-dation.Forfurtherdetailsvisitthewebsiteat http://wwwf.imperial.ac.uk/~th2109/ecstatic/.The conference is supported by an LMSScheme 8 Postgraduate Research Confer-encegrant,anIMAsmallgrant,TCCOxford,andImperialCollegeLondon.

pOSTGRADUATE GROUp THEORY CONFERENCE 2016The 18th Postgraduate Group Theory Con-ference (PGTC) will be held at ImperialCollege London from Tuesday 28 June toFriday 1 July 2016. The PGTC is an annualstudent-organised conference which aimsto bring together postgraduates workinginmathematicsandwhohaveaninterestingroup theoryor relatedareas. Theplenarytalksintheopeningandclosingofthecon-ferencewillbegivenby:• TimBurness(UniversityofBristol)

• RowenaPaget(UniversityofKent)Theconferencewillconsistmainlyoftalksby participants, where the environment isintended to be relaxed and stimulating. Itwill be a great opportunity to meet andexchange ideas with other students fromaroundtheUKandabroad.Registration and more information isavailable at www.imperial.ac.uk/pgtc-2016/.For any queries contact the organizers atpgtc2016@imperial.ac.uk.TheconferenceissupportedbyanLMSScheme8PostgraduateResearch Conference grant, the HeilbronnInstituteforMathematicalResearch,theTCCand Department of Mathematics, ImperialCollegeLondon.

MODELLING, ANALYSIS AND SIMULATIONA European Summer School onModelling, Analysis and Simulation: Crime and Image ProcessingwillbeheldattheMathematicalInstitute,Oxford,from4to8July2016.Thefocusisonthemathematicaltopicsofcrimemodelling and image processing, whichcurrently attract a lot of attention but arerarely taught together. It combines a tra-ditionalresearchschoolthatintroducestheparticipants tomathematical topics, theoryand techniques of current interest with atypical modelling week, where the par-ticipants apply these techniques to specificreal-worldproblemsduring several daysofhands-on group work. Two types of tech-niques will be taught for each topic, onebased on partial differential equations(PDEs)andtheotheronadiscreteapproachsuchasnetworks.Thelecturersare:• AndreaBertozzi(UCLA)• MasonPorter(Oxford)• GabrielPeyré(Paris)• CarolaSchönlieb(Cambridge)The organisers areAndreasMünch, JaredTanner,GittaKutyniokandBarbaraWagner.For more information visit the website athttp://tinyurl.com/zrge5vu. The event issupported by the EMS and theMathemati-calInstitute.


34

GRApH LIMITS AND STATISTICS11 – 15 July 2016

inassociationwiththeIsaacNewtonInstituteprogrammeTheoretical Foundations for Statistical Network Analysis

(11July–21December2016)

Theopeningworkshopwillbefocusedonmergingideasfromcombinatorics,prob-abilityandstatistical theorywithmethodology, startingfromthenotionofgraphlimitsandnonparametricstatisticalmodels.Thiswillbethemeansto:

i.identifythemethodologicalandtheoreticalchallengesinestablishingthefounda-tionsofnetworks;

ii. highlight the state of the art in relevant branches of mathematics, includingin-depthtalksandoverviewpresentationsinthetopics.

Furtherinformationavailablefromthewebsitewww.newton.ac.uk/event/snaw01.

Closing date for receipt of applications 11 April 2016

BAYESIAN METHODS FOR NETWORKS25 - 27 July 2016

inassociationwiththeIsaacNewtonInstituteprogrammeTheoretical Foundations for Statistical Network Analysis

(11July–21December2016)

Bayesianmodels of networks and of relational data have a long history in statis-ticsandmachinelearning.TheBayesianapproachprovidesanaturalframeworktoconstruct statistical networkmodels from structuredparametric or nonparametricprobabilisticmodels,andinferitsparameters.

ThepurposeofthisworkshopistobringtogetherexpertsontopicssuchasBayesianinferenceofnetworkparameters,exchangeablemodelsofnetworksandrelationaldata, latentvariablemodelsofuserpreferences,andotheraspectsof thisdiversefield.

Furtherinformationavailablefromthewebsitewww.newton.ac.uk/event/snaw05.

Closing date for receipt of applications 2 May 2016


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DATA LINKAGE AND ANONYMISATION: SETTING THE AGENDA

5 – 8 July 2016

inassociationwiththeIsaacNewtonInstituteprogrammeData Linkage and Anonymisation(4July–21December2016)

The openingworkshop sets the agenda for theData Linkage and Anonymisa-tion programme.Itwillbringtogetheradiverserangeofparticipants,includingmathematicalscientistsfromstatisticsandcomputerscienceaswellasresearchersanddatausersfromotherdisciplinesanddomainsofapplication.Viewingdatalinkageandanonymisationasfieldsofmethodologicalresearchinthemathemat-icalsciences,theobjectivesoftheworkshopare:

i.tointroducetheprogrammetopicstoparticipantswithvarieddegreesoffamili-aritywiththesefields,includinginductionofjuniorresearchers,andpromotionofcommunicationbetweenparticipantsworkingindifferentmethodological/disciplinarytraditions;

ii. to identify key challenges which these research fields address; to map outanddiscussrecentdevelopmentsandresearchfrontiers;toclarifyconnectionsbetweendifferentareasofresearch;

iii. to activate participants to identify common interestswith a view to initiat-ingfurtherdiscussionandtopotentialcollaborationandtodevelopafuturetimetableofeventstofacilitatecollaboration.

Attheendoftheworkshop,participantswillbeabletoidentifyotherparticipantswithcommoninterests,organisethemselves into informalworkinggroupsandcollaborateonresearchactivities,seminars,etc.astheprogrammecontinues.

Furtherinformationavailablefromthewebsitewww.newton.ac.uk/event/dlaw01

Closing date for receipt of applications 14 April 2016


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1865 - 2015

Northern Regional Meeting

The University of Manchester23 June 2016

12.50 pm - Opening1.00 pm - Plenary speaker 1: Professor Sanju Velani (The University of York)2.00 pm - coffee break2.30 pm - Plenary speaker 2: Professor Julien Barral (Paris 13) 3.30 pm - minibreak3.45 pm - Public lecture: Henna Koivusalo (The University of York)4.45 pm - Wine reception (Alan Turing Building)7.00 pm - Dinner at EastZeast

These lectures are aimed at a general mathematical audience. All interested, whether LMS members or not, are most welcome to attend this event. For further details and to register and to reserve a place at the dinner, please visit http://personalpages.manchester.ac.uk/staff/jonathan.fraser/LMSregionalmeeting16.html The meeting forms part of a workshop on Dynamical systems, ergodic theory and applications from 23-24 June 2016. There will talks on Thursday morning and all day Friday with plenary lectures from Ian Melbourne and Dejun Feng.For further details visit: http://personalpages.manchester.ac.uk/staff/jonathan.fraser/LMSregionalmeeting16.html or contact the organisers. (Jonathan Fraser; [email protected]) 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.

The London Mathematical Society is the UK’s learned society for mathematics. Founded in 1865 for the promotion and extension of mathematical knowledge, the Society has a membership of over 2500 drawn from all parts of the UK and overseas. Its principal activities are the organisation of meetings and conferences, publication of journals and books, provision of financial support for mathematical activities, and contribution to public debates on issues related to mathematics, research and education.London Mathematical Society, De Morgan House, 57-58 Russell Square, London WC1B 4HS. Tel +44 (0)20 7637 3686; Fax: +44 (0)20 7323 3655; Email: [email protected]; Web: www.lms.ac.uk; Registered charity no. 252660


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1865 - 2015

Society Meeting & Reception

At the 7ECM, Berlin, GermanyThursday 21 July 2016

Lecture Theatre, Main Building, TU Berlin

4.30 Opening of the meeting, Terry Lyons (Oxford) From Hopf Algebras to Machine learning via Rough Paths

Rough path theory aims to build an effective calculus that can model the interactions between complex oscillatory (rough) evolving systems. At its mathematical foundations, it is a combination of analysis blended with algebra that goes back to LC Young, and to KT Chen. Key to the theory is the essential need to incorporate additional non-commutative structure into areas of mathematics we thought were stable. At its high points, there are the regularity structures of Martin Hairer that allow robust meaning to be given to numerous core nonlinear stochastic pdes describing evolving interfaces in physics.

Classic results, by Clark, Cameron and Dickinson, demonstrate that a nonlinear approach to the data is essential. Rough path theory lives up to this challenge and can be viewed as providing fundamentally more efficient ways of approximately describing complex data; approaches that, after penetrating the basic ideas, are computationally tractable and lead to new scalable ways to regress, classify, and learn functional relationships from data. One non-mathematical application that is already striking is the use of signatures on a daily basis in the online recognition of Chinese Handwriting on mobile phones.

6.00 Reception (Ticket required)

LMS members will have the opportunity to sign the Membership Book which dates back to 1865.For a ticket to the reception, please email Elizabeth Fisher ([email protected])

The London Mathematical Society is the UK’s learned society for mathematics. Founded in 1865 for the promotion and extension of mathematical knowledge, the Society has a membership of over 2500 drawn from all parts of the UK and overseas. Its principal activities are the organisation of meetings and conferences, publication of journals and books, provision of financial support for mathematical activities, and contribution to public debates on issues related to mathematics, research and education.London Mathematical Society, De Morgan House, 57-58 Russell Square, London WC1B 4HS. Tel +44 (0)20 7637 3686; Fax: +44 (0)20 7323 3655; Email: [email protected]; Web: www.lms.ac.uk; Registered charity no. 252660


38

Reviews

EXpERIMENTAL MATHEMATICS byV.I.Arnold,translatedbyDmitryFuchs&MarkSaul,2015,MSRIMathematicalCirclesLibrary,Vol.16,158pp,£25.50,US$29.90,ISBN978-0821894163.

Thisshortbookisthewrite-upoffourlecturesdeliveredbyV.I.Arnoldtoparticipantsofthe2005DubnaSummerSchool"ContemporaryMathematics." The style is very direct andinformalwithappealstothelisteners/readertogetinvolvedinthesubjectmatter.V.I. Arnold was very well known for hisengagingstyleoflecturingandwritingandhis general enthusiasm for conveying howmathematicsshouldbedone.Hismainpointisthatone'sownengagementwithexamplesleadsto insightsandintuition—oftengeo-metrical in nature— via the search for un-derlying structures and patterns. This thenallows for the formulation of a hypothesisorconjecturethatmaybeprovedor,ifthatappearstobeverydifficult,exploredfurtherbymoreexperimentation. Inthecontextofthe book, mathematical experimentationreferstoworkingoutanincreasingnumberofexamplesoftheconceptunderconsidera-tion.Arnold'sapproachis literallyhands-on,and he presents results of quite extensivecalculations — mostly of combinatorialobjects—thatwereperformedbypencilandpaper.Arnoldmentionsonseveraloccasionsthat such calculations can and should beperformed for larger examples with thehelpofcomputersanddirectlyappealstohisaudienceforhelpindoingthis.I found it refreshing to read a book onmathematics that not only contains somewell-defined open problems, but statesseveraltimesthatthecorrectquestionshavenot even been formulated yet. Hence, thereader gets a glimpse of the coal-face ofmathematics where problems are activelyexplored, defined and put into a widercontext.Eachchapter(orlecture)startswithexamples that can be followed and repro-ducedquitereadily,butArnoldthenquicklydevelopsmore fundamental points of view,invoking different kinds of advancedmath-ematics as he goes along. In this way, heprovidesnumerousexamplesofunexpected

connections andinsights. Itwillbehelpful to have abrief look at thetopics covered inthefourlectures.The first lecture,entitled The Sta-tistics of Topology and Algebra, con-cerns quite classi-calmaterialassoci-atedwithHilbert's16th problem: the number and possible ar-rangements of ovals of an algebraic curveof a given degree and the enumeration ofdifferenttypesofMorsefunctions(overthesphere). Starting from the basic configura-tions with one saddle and three maxima/minima— referred to by Arnold asMountElbrus and Mount Vesuvius — the Morsefunctions are represented by properlyorderedtrees,whichnaturallyleadstoacom-binatorialcountingproblemforwhichupperandlowerboundsarederived.Alsodiscussedare Morse functions over the torus, whichgiverisetographswithasinglecycle.Finally,afour-parameterfamilyofperiodicfunctionsispresented,whichisshowntogiverisetoatmost12ofthe550possiblegraphswithfourtriplebranchpointsandfourendpoints.Anopenproblemistoshowthatall12casesareactuallyrealisedbythisfunction.Lecture 2, The Combinatorial Complex-

ity of Randomness, considers the operationof taking differences between successivedigitstomapthesetofbinarysequencesoflength n into itself. This operation resultsinasinglecyclewithtreesattachedtoeachvertex of the cycle (of preperiodic points).Thesegraphsaredeterminedfornupto12,which is already a considerable task whenperformedwithout a computer. Interestingproperties of the structure of the graphsemerge,forexampleregardingthelengthof


39

the largestcycleasa functionofnandthefact that their sum is always a power of 2.The remainder of the chapter discusses thecomplexityofthediscretenumbertheoreticlogarithm and the complexity and random-nessofp×ptablesofGaloisfields(wherepisaprime).Thereader is invitedtoexploreinthesamewaysequencesofthreeormoresymbols,ratherthanbinarysequences.Lecture3,Random Permutation and Young

Diagrams of their Cycles,considerstherepre-sentationofapermutationof thenumbers1 tonby its cycles,whichcanbepresentedconvenientlyastheYoungdiagramassociat-edwiththepartitionofn.Arnoldconsidersthelength(ofthelongestcycle),theheight(number of cycles) and the number of rep-resentativesofagivenYoungdiagram.Theexperimentalpartofthischapterconsistsofprovidingtablesofthesenumbersuptoandincludingn=7.ThisallowsArnoldtoconsiderthe average length and height, as well asthe average covered area of the minimalrectangle containing the Young diagram.Given the fact that the number of permu-tations is n!, such tables quickly becomeimpractical for increasing n, even whenusinga computer. So togain insight in theaboveaveragesArnolddevisesamethodtogeneraterandompermutations;hisexamplesareforn=100andforn=169.ThelectureendswithaconsiderationofFibonacciauto-morphismsofthetwo-torus,themostfamousexampleofwhichisArnold'scatmap.Thesemapspermuteasetofn2pointsandtheas-sociatedYoungdiagramsfornupto20aretabledandseveralobservationsaremade.Thefourthandfinallecture,The Geometry

of Frobenius Numbers for Additive Semi-groups, is effectively a discussion of whatvalues one can represent with a system ofn given coins (positive base integers withgreatest commondivisor1); themotivatingexample is coins of 3 cents and of 5 cents.The Frobenius number is the integer fromwhere all integers canbe represented. Thecase of two coins is covered by a classicalresultofSylvester,andthelectureconsidersFrobeniusnumbersofthreebaseintegersa,

bandc.Whens=a+b+cisfixed,thesecanbearranged ina trianglewithobvious symme-triesofexchangingtheintegers;thetrianglesfors=19ands=41aregivenandpropertiesofFrobeniusnumbers, includingbounds, theiraveragesforfixedsandcontinuedfractions,arediscussedatconsiderablelength.As may be clear from the very shortsummary above, each lecture or chapter isverydenseandquiteatourdeforce.Itwilldefinitely help the reader to know alreadyquite a bit about different areas ofmathe-matics,includingtopology,geometry,graphtheory, combinatoricsandgroup theory.Al-ternatively or additionally, the reader mayusetheopportunitytolearnmoreabouttheconceptscoveredwhileworkingthroughtheexamples,argumentsandproofsinthebook.This brings me to the question of whoto recommend this book to. I believe thatfellow professional mathematicians willenjoy reading it because of its numerousconnections between different fields, andbecause itprovidesan insight intothewayof thinking of one of the toweringfiguresofmodernmathematics.However,Arnold'starget audience is young mathematicaltalent. Participants of the Dubna SummerSchool have been selected as the beststudents throughout Russia from the lasttwo years of high school and the first twoyears at university. I can imagine verywellthatsuchanexceptionalaudiencewillhavebeen inspired by Arnold's lectures, whichaccording to the School's website (www.mccme.ru/dubna/eng/)aretolastexactly74minuteseach!In fact, as the book and the very helpfulfurthernotesbytranslationeditorMarkSaulshow, several problems have subsequentlybeen solved by participants. On the otherhand, the book is clearly intended for awider readership of young mathematicaltalent.Readingachapterofa lecture is,ofcourse, not the same as listening to it live:thecoveredmaterial isextensiveandtherearejumpsinmathematicaldepth.The reader should be prepared to spendconsiderably more than 74 minutes per


40

Reviews

chapter.Arguablythebestwayofapproach-ing this book is indeed to perform one'sown experiments and computations, andthis requires time. In fact, eachof the four

chapterswould provide amplematerial forseveralweeksofagraduatecourse.

BerndKrauskopfAuckland,NewZealand

THE GEOMETRY OF THE OCTONIONSbyTevianDrayandCorinneA.Manogue,WorldScientific,2015,pp228,£63.00,$95.00,ISBN978-981401814..

Itwason16October1843thatHamiltontookhis famous walk along the Royal Canal inDublinandinamomentofinspirationdiscov-eredthealgebraofquaternionswhichhadabasis1,i,j,k,wherei,j,kweresquarerootsof -1. The next day, Hamilton wrote to hisgoodfriendJohnTGravesabouthisdiscoveryandthisledGravestothinkthatitmightbepossible to inventmoresquarerootsof-1.On26December he wrote toHamilton describing an8-dimensional algebrawith basis 1, e1,…e7whereeiaresquarerootsof-1.Hecalledhisnewnumbersoctavesthoughtoday they are calledoctonions. Hamiltonoffered to publicizeGraves’ discovery butsomehow never gotround to it. Twoyearslater, Cayley also discov-ered the octonions andpublishedhis result andoctonions were calledCayley numbers. (Whilewriting this review IwantedtofindoutmoreaboutJohnGraves.IlookedattheMactutorhistoryofmathssiteandfoundthathewasnot even listed. Norwas he listed inAIMM,the annals of Irish Mathematics and Math-ematicians.SonotonlydidJohnGraveshavehisbrilliantdiscoverynamedaftersomebodyelse,buthehadbeenwrittenoutofhistory!IhavewrittentoboththeseorganizationsandIampleasedtoreportthatthishasnowbeencorrected. ) It turns out that octonions are

notonlyanimportanttopicinalgebra,beingone of four normed division algebras overthe real numbers, but important in Physicstoo.AsIanStewartwroteinhisNewScientistarticleWhat seems like a pointless piece ofVictorianwhimsyturnsouttobeanessentialpartofthetheoryofeverything[IS]; anditsayssaysintheprefaceofthisbookthatthe

authorsbelievethattheoctonionswillultimatelybe seenas the key to aunified field theory ofPhysics.QuiteaclaimforJohnGraves’discovery!Thus this book onOctonions is verywelcome. One othertext in which octonionsplay the major part isOn Quaternions andOctonions by ConwayandSmith[CS].Howeverthisconcentratesonthearithmetic of octonionswhereas the bookunderreviewtacklesthegeometry of octonionsand goes on to discusstheir applications toPhysics. Also [CS] does

notreallypresentanelementaryconstructionoftheOctonions.Therearethreeparts.PartIiscalledNumberSystems,PartIIiscalledSymmetryGroupsandpartIIIiscalledApplications.The octonions are actually constructed inchapter 4. The most straightforward wayof constructing theoctonions is by buildinganalgebrawithbasis1,e1,…..e7,where theeiaresquarerootsof-1andwriteoutthe


41

multiplicationtable.Thisisquitecomplicatedbutamazingly this canbedonebydrawingan oriented Fano plane where the sevenvertices represent theei andtheedges tellyouhowtomultiply.ToseethisexplicitlygototheexcellentarticleonoctonionsbyJohnBaez [JB]. In this book the authors take adifferentapproachbasedontheCayley-Dick-sonprocesswhichconstructsa2k-dimension-al algebra from a k-dimensional one. Theybeginwiththequaternionsandthenadjoinanothersquarerootof-1whichwecallλ(inthebook theyuseahandwritten"l"). Theythenwritethatitiseasytoseethatλi,λj,λkaresquarerootsof-1sowehaveoursevensquarerootsof-l;i,j,k,λ,λi,λj,λk.Unfortu-nately,it isnoteasytoseethatλi,λj,λkaresquare rootof -1,butwecouldaddaxiomssuch as (λi)2=-1, etc., and then everything isfine.Because the octonions have a norm Nwhich obeys N(ab)=N(a)N(b) we get theeightsquarestheoremwhichtellsusthattheproductoftwonumberseachofwhichisthesumofeightsquares is itselfasumofeightsquares. This works if we replace eight byfourortwo,becauseofthequaternionsandcomplexnumbersbutnotifwereplaceeightby16orhigherpowersoftwo.PartIIisaboutmatrixgroupsandoctonionsdisappear for a short time. An elementarydescription is given of the matrix groupsSO(n) for low values of n and also of somegroupsof the formSO(p,q).Thisenable theauthorstodescribesomeideasthatoccurInphysicssuchasLorentzgroups,Paulimatricesand Gell-Mann matrices. They then get ontounitaryandsymplecticgroupsanddiscussmatrixgroupsoverthecomplexnumbers.Octonions reappear in chapter 9 wherematrix groups over other division algebrasare discussed, these other division algebrasbeing the quaternions and octonions. Firstthe well-known quaternionic description ofSO(3)isgivenshowingthatrotationscanbedescribed by quaternion conjugation andthen a quaternionic description is given ofSO(4). They then go on to give octionic de-scriptionsofSO(7)andSO(8).Chapter10isa

verybriefintroductiontoLiegroupsandLiealgebrasand then fromchapter11, the funreallystarts!The automorphism groups of the divisionalgebras are described. The automorphismgroupoftheoctonionalgebraisthesmallestoftheexceptionalLiegroupsG2whichisshowntobe14dimensional.Inordertodiscusstheremaining four exceptional Lie groups thealgebraof3×3octionicHermitianmatricesunder the Jordan product A°B=1/2(AB+BA).(This isnamedaftertheGermanmathemati-calphysicistPascuel Jordan,who introducedthem to study quantum mechanics.) Thisalgebra is called theAlbert algebraH3(0), 0here being the algebra of octonions. Theythen go on to describe the exceptional LiegroupsE6andE7usingoctonions.PartIIIonapplicationsisthemostadvancedpartof thebook. Ithas sectionsonoctionicprojective planes, octionic eigenvalueproblems,arithmeticofoctonionsandphysics,Thesectiononarithmetic isofmost interesttopuremathematicianswheretheydescribehow the E8 lattice can be described usingoctionicintegers.FormoredetailsaboutthisseethebookofConwayandSmith.Themostintriguing part of this study is connectionswithphysics. It is certainly true that somemathematicalphysicistsuseoctonionsintheirwork (e.g. see [GD]). Will they be used todescribe“thetheoryofeverything”?Thejuryisstillout!Tosumup,thisisareallyinterestingbook.Itdoescontainsomeerrorsandsomeofitcouldbemoreclearlyexplainedbut ithasencour-agedme to further explore this fascinatingtopic.

DavidSingermanUniversityofSouthampton

References[JB]JohnBaez,The Octonions,Bull.AmericanMaths.Soc.Vol.39,no.2,145-205,2001.[CS]JohnH.ConwayandDerekSmith,On quaterni-ons and octonions.A.K.PetersLtd,2003.[GD]GeoffreyM.Dixon,Division algebras, Lattices, Physics, Windmill Tilting.Amazon.co.uk(2011).[IS] Ian Stewart. The missing link, New Scientist,November2002,30-33.


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THE MAN WHO KNEW INFINITY(reviewonfrontpage)

BertrandRussell(JeremyNortham),Hardy(JeremyIrons)andLittlewood(TobyJones)

Hardy(JeremyIrons)andLittlewood(TobyJones)

Ramanujan(DevPatel),Hardy(JeremyIrons)andLittlewood(TobyJones)

Ramanujan(DevPatel)

Ramanujan(DevPatel)andSirFrancisSpring(StephenFry)

Hardy(JeremyIrons)addressingTheRoyalSociety

THE MAN WHO KNEW INFINITY - London Mathematical Society · 2018-01-16 · THE MAN WHO KNEW INFINITY...

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