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Newsletter (Pacific Institute for the Mathematical Sciences) : vol. 5, issue 2, Summer 2001 Pacific Institute for the Mathematical Sciences 2001

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Newsletterfor the Mathematical SciencesInstitutePacific http://www.pims.math.capims@pims.math.capiSummer 2001Vol. 5 Issue 2TheContentsBanff Research Station . . . . . . . . . . . . . . . . . . . . . 1,3Frontiers in Mathematical Physics . . . . . . . . .1,10Month of Industrial Math . . . . . . . . . . . . . . . . 1,5,9Director’s Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Nominations for PIMS Prizes . . . . . . . . . . . . . . . . 2MITACS News . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4,7Industrial Activities . . . . . . . . . . . . . . . . . . . . . . . 5–9Scientific Activities . . . . . . . . . . . . . . . . . . . . . . 10–15Call for BIRS Proposals . . . . . . . . . . . . . centrefoldPredator-Prey Equation and Developmentof HIV/AIDS in Canada . . . . . . . . . . . . . . . . .16–19PIMS Distinguished Chairs . . . . . . . . . . . . . . . . . 19Industrial and Scientific Training . . . . . . . . 20–21PIMS PDFs for 2001/02 . . . . . . . . . . . . . . . . . . . . 21Education Activities . . . . . . . . . . . . . . . . . . . . .22–28Contact List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28APCTP, Perimeter and PIMSCollaborate on Frontiers inMathematical PhysicsThe newly established Perimeter Institute forTheoretical Physics has joined the Asia PacificCenter for Theoretical Physics (APCTP) andPIMS in sponsoring the Frontiers in MathematicalPhysics (FMP) workshop held annually in Van-couver.The Asia Pacific Center for Theoretical Physics(www.apctp.org) is an international organiza-tion based in Seoul, South Korea. The membercountries or regions of the institute are Australia,China, Japan, Malaysia, Philippines, Singapore,Taiwan, Thailand and Vietnam.Please see Frontiers, page 10.NSF and ASRA Join NSERC SiteVisit for Banff Research StationSite visit team (from left to right): Alan Mackworth (Director, Lab-oratory for Computational Intelligence, UBC), Arvind Gupta (Direc-tor, MITACS), Joe Buhler (Deputy Director, MSRI), Robert Moody(Scientific Director, BIRS), David Gross (Director, ITP), Nassif Ghous-soub (Director, PIMS) and David Eisenbud (Director, MSRI). Missingfrom photo: Michael Lamoureux (Managing Director, BIRS) and SteveHalperin (Dean of Science, Univ. of Maryland).Please see Banff Site Visit, page 3.Month of Industrial Math at PIMS: Awealth of opportunities for Canadian andUS graduate studentsThe month of June 2001 wit-nessed a succession of sci-entific events in industrialmathematics at PIMS. Morethan 300 researchers, gradu-ate students and senior un-dergraduates came from 25Universities in Canada andthe US to learn, research,interact, network and solveindustrial problems at sev-eral interrelated events. Thetimetable was configured sothat visiting students couldparticipate in more than oneof the worskhops.Please see IndustrialMath, page 5.Lisa Korf (U. of Washington) speakson Web Hosting Agreements at thePIMS Industrial Graduate Camp.Paci£c Institute for the Mathematical SciencesDirector’s NotesNassif Ghoussoub, FRSCThe messages of support for the establishment of the BanffInternational Research Station poured in from all conti-nents. Hundreds of people took the time and made theeffort to write us a few lines of support, of encouragementand of their wishes for the station’s success. The soli-darity of the world’s most prominent research mathemat-ics institutes was overwhelming and particularly appreci-ated: Oberwolfach, Luminy, IHES, Isaac Newton, Steklov,IPAM, IMA, DIMACS, Fields and others.Most mathematicians spoke of it with Oberwolfach andLuminy in mind, the physicists with Aspen and the com-puter scientists with Schloss Dagstuhl. Musicians amongus shared their childhood memories playing the violin atthe Banff Music School. Some recalled their youthfulhikes in the heavenly surroundings. Many spoke fondly ofthe impact of similar institutions on their early researchand on how their professional lives were formed in suchplaces. They wrote about the moments where mathemat-ical truths eased into their consciousness and about theintensely productive times they experienced at compara-ble European centers.Nigel Horspool, Head of Computer Science at the Uni-versity of Victoria, wrote that he always wondered “whyI had to travel all the way to Germany for a meetinglike that” (Dagstuhl’s). Ragnar-Olaf Buchweitz, Head ofMathematics at the University of Toronto, spoke aboutthe “dream coming true”. George Elliott stated “that it isa sign that our country is approaching maturity, that lead-ership on such a scale should be coming from the West”.Carl Amrhein, Dean of Arts and Science at the Universityof Toronto wrote about “the splendid opportunity to raisethe international profile of the mathematical sciences inCanada even higher” before generously pledging a finan-cial contribution as a concrete statement of support fromhis faculty. Vitali Milman, President of the Israel Math-ematical Union commented that, “The choice of Banff isabsolutely the best place I could think of in your part ofthe world”. Arthur Carty, President of the National Re-search Council (NRC) writes, “I expect that we [NRC] willbe able to participate in activities of the Research Stationincluding workshops and roundtables”. A proud Albertanwrote, “Until now, I’ve had to describe the University ofAlberta to foreigners as the place where Bob Moody is.Soon I’ll be able to add: and it’s close to BIRS! This is awonderful project!”.I hope that this show of support for the Banff Stationis only the first chapter in the history book of a hugelysuccessful institution.Call For NominationsThe Pacific Institute for the Mathematical Sciences isaccepting nominations for the following prizes:1. PIMS Research Prize: Awarded for a particu-lar outstanding contribution to the mathematicalsciences that was disseminated during the five-yearperiod prior to the award being given. Open toCanadian citizens, permanent residents of Canadaand residents of Pacific Rim countries who main-tain academic ties to the Canadian mathematicalsciences community.2. PIMS Education Prize: Awarded to a mem-ber of the PIMS community who has made a sig-nificant contribution to education in the mathe-matical sciences. This prize is intended to recog-nize individuals from the PIMS member univer-sities or other educational institutions in Albertaand British Columbia, who have played a majorrole in encouraging activities which have enhancedpublic awareness and appreciation of mathematics,as well as fostering communication among variousgroups and organizations concerned with mathe-matical training at all levels.3. PIMS Industrial Outreach Prize: Awardedto an individual who has employed mathematicalanalysis in the resolution of problems with directindustrial, economic or social impact. This prizeis intended for individuals from the academic,private and government sectors. This prize will begiven to individuals who at the time of nominationare Canadian citizens or permanent residents ofCanada.Nominees for each prize should be nominated by threesponsors. They are to provide a cover letter explain-ing the nominee’s contribution, impact and relevancefor the prize. The nomination should also include aCV of the nominee, a publication list, a list of creativeworks or list of industrial products, and relevant sam-ples of the nominee’s work, such as reprints, patentsor educational materials.Nominations should be sent to:Attention: PIMS PrizesPIMS Director’s Office1933 West MallUniversity of British ColumbiaVancouver BC V6T 1Z2CanadaNominations must be received by Sept. 15, 2001.For more information, please see the webpagehttp://www.pims.math.ca/prizes.Vol. 5, Issue 2 Paci£c Institute for the Mathematical Sciences2Joint NSF, ASRA, NSERC Site visit for Banff Research StationContinued from page 1.The BIRS Executive, David Eisenbud (Director, MSRI), Robert Moody (Scientific Director,PIMS) and Nassif Ghoussoub (Director, PIMS) discuss outside Corbett Hall in Banff.On June 15, 2001 there was asite visit at the Banff Centreat which three major grantingagencies were present: the Nat-ural Sciences and EngineeringResearch Council of Canada,the National Science Founda-tion of the United States, andthe Alberta Science and Re-search Authority. The com-mittee was profoundly affectedby the world-wide enthusiasticsupport for the BIRS initiative,as illustrated by more than 500letters of support which werereceived from all over the worldand by the obvious need for afacility such as this in NorthAmerica.The site visit was coor-dinated by Nassif Ghoussoub(Director of PIMS and Princi-pal Applicant for the NSERCproposal), David Eisenbud (Di-rector of MSRI) and Robert Moody (Scientific Director of BIRS), with considerable help from Arvind Gupta (MITACSScientific Director), Michael Lamoureux (Deputy Director of PIMS and Managing Director of BIRS) and Joe Buhler(Deputy Director of MSRI). The site visit received a huge boost from the presence and active participation of SteveHalperin (Dean of Science at the University of Maryland), David Gross (Director of ITP in Santa Barbara) and AlanMackworth (Director of the Laboratory for Computational Intelligence at UBC).Several senior administrators from the PIMS institutional universities also made the effort to participate in person:Mike Boorman (Dean of Science, University of Calgary), Dick Peter (Dean of Science, University of Alberta), KeithArcher (VP-Research, University of Calgary), Bruce Clayman (VP-Research, Simon Fraser University), Martin Taylor(VP-Research, University of Victoria), Indira Samarasekera (VP-Research, University of British Columbia) and RogerSmith (VP-Research, University of Alberta).The visiting reviewers also heard, through conference calls, from more than fifteen heads of departments of mathe-matics, computer science and statistics in Canada and the USA: R. Buchweitz (Math, University of Toronto), D. Gross(Math, Harvard), N. Circone (Computer Science, University of Waterloo), R. Goebel (Computer Science, University ofAlberta), H. Rossi (Math, University of Utah), H. Brunner (Math, Memorial University), W. Rundell (Math, TexasA & M), D. Marshall (Math, University of Washington), E. Saab (Math, University of Missouri), P. March (Math, OhioState University), G. Benkart (Math, University of Wisconsin at Madison), E. Campbell (Math, Queen’s University),N. Kamran (Math, McGill University), K. Taylor (Math, University of Saskatchewan), Doug Arnold (Director of theInstitute for Mathematics and Its Applications, Minnesota) and N. Reid (Statistics, University of Toronto).The site visit concluded with a tremendous show of support from Mary Hofstetter (President and CEO of the BanffConference Centre) and from Robert Church (President of the Alberta Science and Research Authority).®­©ªA Call for Proposals for BIRS is available inthe centrefold of this newsletter. Please visitthe webpage www.pims.math.ca/birs formore information about BIRS.Every piece of information that we have re-ceived from each of the funding agencies hasbeen extremely encouraging and we are nowconfident that BIRS will become a reality. Atthe time of the site visit we had received closeto 75 letters of intent to run programs at BIRS,showing yet again the enthusiasm of the com-munity for the project. The selection processwill be highly competitive, as it should be!Paci£c Institute for the Mathematical Sciences Summer 20013MITACS NewsMathematicians Gather in Montre´al for 2nd MITACS AGMContributed by Donald Bilodeau,MITACS Communications Officer.On May 11th and 12th, MITACS (The Mathematics of In-formation Technology and Complex Systems) held its 2ndAnnual General Meeting and Poster/Demo Exhi-bition at McGill University in Montreal. Dubbed NovelUses of Mathematics in the Biomedical Sector, the annualevent offered attendees a wide array of plenary and ses-sional presentations.Prof. Terry SpeedAmong the invited plenaryspeakers, Terry Speed (Univer-sity of California) presented adynamic talk on Statistics &DNA Microarray Data, whereinhe outlined two interesting casestudies that displayed some ofthe novel challenges that thistechnology poses.Ivar Ekeland (Paris-Dauphine University) presenteda riveting discussion on TheMathematics of InformationAsymmetry. In the session,Prof. Ekeland discussed thetwo types of information asymmetry in economic theory:moral hazard and anti-selection. While focusing on thelatter, he described how the design of incentive-compatiblecontracts leads to new problems in the calculus of vari-ations, for which he gave some mathematical resultsand stated some open problems. Later that evening,Prof. Ekeland also captivated the audience during hisbanquet address.Prof. Ivar EkelandChristos Papadim-itriou (University ofCalifornia) presentedanother dynamic plenarysession on the subjectof Algorithmic ProblemsRelated to the Inter-net. He surveyed somerecent research donein collaboration withJoan Feigenbaum, DickKarp, Elias Koutsou-pias and Scott Shenker.According to Prof. Pa-padimitriou, the internethas arguably supersededthe computer as the most complex cohesive artifact and isthe source of a new generation of foundational problemsfor theoretical computer science. These new challengesstem from two novel aspects of the internet: (a) its novelnature as a computer system that intertwines a multitudeof economic interests in varying degrees of competitionand (b) its history as a shared resource architecture thatemerged in a remarkably ad hoc yet gloriously successfulmanner.More than 300 MITACS members, post-doctoral fel-lows, graduate students, and media representatives at-tended this annual event. The Poster and Demo Exhi-bition attracted 56 entries, highlighting research break-throughs from several MITACS projects. Graduate stu-dents and Ph. D.’s from across Canada presented their re-search for judging by academic and industrial profession-als. Prizes were awarded during Friday night’s Banquetheld at the prestigious McGill Faculty Club.The first place winners were from left: Nicolas Chapados(University of Montreal), High-Dimensional Data Inferencefor Automobile Insurance Premia Estimation and JulienArno (University of Victoria), Reproduction Numbers forCompartmental Models of Disease Transmission.The second place winners were from left: Joanna Bier-nacka (University of Toronto), A Genetic Model in whichMultiple Gene Weighting does not improve Gene Localization;Alexandra Chavez-Ross (University of British Columbia),Application of Chemotaxis Models to Alzheimer’s Disease;Magdaleana Luca (member of Alexandra’s team); IchiroTakeuchi (University of Montre´al), A Robust LearningMethod for Regression with Asymmetric Heavy-Tail Noise;Radu Bradean (Simon Fraser University), Modelling ofHeat and Mass Transfer in Porous Fuel Cell Electrodes.Please see MITACS AGM, page 7.Vol. 5, Issue 2 Paci£c Institute for the Mathematical Sciences4Industrial ActivitiesPIMS Month of Industrial Mathematics: A wealthof opportunities for Canadian, US graduate studentsContinued from page 1.The program started by the PIMS-MITACS-Ballard Inc.Workshop on Computational Dynamic Fuel Cells at SimonFraser University held on June 4–8. This was organizedby the MMSC-MITACS team led by Brian Wetton (Uni-versity of British Columbia) and Keith Promislow (SimonFraser University) in conjunction with the PIMS Centerfor Scientific Computing led by Bob Russell (SimonFraser University). (See page 20.)This was followed on June 9-10, by a PIMS-NSF-MITACS Workshop on Inverse Problems andImaging at the PIMS facility at the University ofBritish Columbia. The workshop was organizedby the POTSI-MITACS team led by Michael Lam-oureux and Gary Margrave (University of Calgary) inJohn Chadam (University ofPittsburgh) speaking to graduatestudents on Portfolio Analysis.conjunction with thePIMS Center for In-verse Imaging andApplications led byGunther Uhlman(University of Wash-ington). (See page 6.)Between June 11–15, the 4th PIMSGraduate IndustrialMathematics Mod-elling Camp was heldat the University ofVictoria. This year,20 US graduate stu-dents were admittedto the program in ad-dition to the custom-ary 40 Canadian par-ticipants (See page 7.). As usual, it was followed by the5th PIMS Industrial Problem Solving Workshop held thisyear at the University of Washington in Seattle betweenJune 18–22.The last 2 events were superbly organized by ChrisBose (University of Victoria), Randy LeVeque (Universityof Washington), Huaxiong Huang (York University), MarkPaulhus (University of Calgary), Keith Promislow (SimonFraser University) and Ian Frigaard (University of BritishColumbia).John Chadam wrote to the organizers: “Just wantedto thank you all for your efforts in organizing three won-derful workshops. All three were intellectually stimulatingand exceptionally well run. Hope I see you all soon in theeast.”A student participant in both GIMMC and IPSW,Theodore Kolokolnikov, wrote to the Director: “These twoChris Bose (University of Victoria), an organizer of theIndustrial Graduate Camp and the Industrial Problem SolvingWorkshop.weeks, in many ways, exceeded my expectations. Weworked not just on ‘toy examples’, but on real problemswith enough interest to the industry that they were will-ing to pay money to participate. On the other hand,these problems were also very interesting from a math-ematician’s point of view. They required a variety ofskills from the participants; and thanks to different back-grounds, many different approaches were tried.Graduate students doing numerical simulations.“For example, in my group (Canadian National Se-curity agency), we used various techniques from graphtheory as well as probability theory. All of these methodsinvolved interesting mathematical results, such as theo-rems about random graphs or how to catch a robber onPlease see Industrial Math, page 9.Paci£c Institute for the Mathematical Sciences Summer 20015Report on PIMS-MITACS InverseProblems and Imaging WorkshopUniversity of British ColumbiaJune 9–10, 2001Contributed by Michael Lamoureux (Univ. of Calgary).On June 9 and 10, PIMS welcomed over 30 researchers tothe Inverse Problems and Imaging Workshop 2001, held atthe UBC campus in Vancouver. This meeting was the firstgathering of the newly formedPIMS Centre for InverseProblems and Imaging and the third Inverse ProblemsSeminar of the Pacific Northwest (IPSPN), which buildson the successes of the 1999 IPSPN in Seattle, and 2000IPSPN in Corvallis. With support from the NSF, PIMS,and the POTSI project of MITACS, the purpose of thenew PIMS Centre and this seminar series is to bring to-gether mathematicians and other scientists in the PacificNorthwest working on different aspects of the field, to ap-praise the current status of development and to encourageinteraction with researchers working directly on applica-tions.This year’s workshop featured a baker’s dozen of speak-ers presenting talks on a wide range of topics in in-verse problems and imaging, including medical tomogra-phy, seismic exploration, synthetic aperture radar, statis-tical image recovery, and parameter estimation of ODEsand PDEs. Real applications include such things as form-ing three-dimensional “pictures” of the human body viaelectrical, magnetic, or X-ray transmission measurements;forming images of the earth’s subsurface by measuring thepropagation of seismic waves or the electrical conductivityof soil; taking aerial photographs of a landscape via a singlepass of an aircraft/spacecraft dragging a microwave trans-mitter. Mathematical techniques presented included mi-crolocal analysis of pseudo-differential operators, Fourierintegral operators, sampling techniques, least square meth-ods applied to inversion and imaging, and many others.A particularly valuable result of this series of semi-nars is the initiation of new collaborative links betweenresearchers at various PIMS universities as well as at otherPacific-linked institutions, including one as far away asNew Zealand. One clear message learned at the meetingis that the various mathematical techniques developed forany one application in inverse problems and imaging canhave a direct impact on several of the other applicationsdue to the similarities in the theoretical formulation of theproblems. Forging links between the various researchersis essential to the rapid dissemination of these powerfultechniques, and we are pleased to see this year’s workshopplaying a role in these emerging collaborations.The organizers, Michael Lamoureux (U. Calgary),Gary Margrave (U. Calgary) and Gunther Uhlmann(U. Washington) would especially like to thank the ad-ministrative staff of PIMS at UBC and PIMS at UCalgaryfor their excellent assistance in coordinating the organisa-tional details of this workshop, which was key to makingthis event a pleasant success.PIMS-MITACS-Ballard Workshop onComputational Fuel Cell DynamicsSimon Fraser UniversityJune 4–8, 2001Contributed by Keith Promislow (SFU).The PIMS-MITACS-Ballard Workshop on ComputationalFuel Cell Dynamics (CFCD) was held June 4–8, 2001 at Si-mon Fraser University. This workshop addressed the mod-elling and numerical resolution of the processes of phasechange, multi-phase transport, electro-chemistry, and in-terface dynamics in the porous electrodes of Proton Ex-change Membrane (PEM) fuel cells.The world’s major automotive manufacturers are en-gaged in an historic race to develop PEM fuel cells as al-ternatives to internal combustion engines for automotivepower. Ballard Power Systems, based in Burnaby BC, isbroadly recognized as the world leader in this technology,which holds out the promise not only of a highly efficient,environmentally friendly automobile, but also of an ex-tremely versatile power generation system with a broadspectrum of possible applications.PEM fuel cells convert oxygen and hydrogen into wa-ter and useful electric potential in a highly efficient catal-ysed reaction. An effective model of water managementin fuel cells, which predicts condensation and subsequentmotion of liquid water, must include the effects of multi-species, multi-phase transport, and electro-chemistry. Theporous electrodes of PEM fuel cells are treated with Teflonwhich renders the liquid-solid surfaces a high-energy in-terface, and traditional models of two-phase flow breakdown in this context. The interconnected physical pro-cesses underlying PEM fuel cell dynamics require sophis-ticated models to predict performance under a bewilderinghost of operating conditions, and transient modes, includ-ing start-up and shut-down. The numerical resolution ofthe models poses significant problems, including movingboundary layers and a tremendous range of interconnectedtime-scales for differing physical processes spanning over10 orders of magnitude.The CFCD workshop was multi-disciplinary, unitingworld class experimental, model building, and computa-tional scientists with industrial researchers. It was an ex-tremely lively event with an extended, and occasionallyheated, discussion session after each of the more than 25talks. The 40 plus participants came from General Motors,Bristol Univ., Univ. of Southampton, Univ. of Notting-ham, National Research Council, Motorola, SaskatchewanResearch Council, National Science Foundation USA andUniv. of Bath, as well as various North American Univer-sities and Ballard Power Systems.The workshop was broadly acknowledged to have beenan exceptional event, and plans are underway for a sequelat the new BIRS centre in Banff.The organizers were Keith Promislow (Mathematics,SFU) and Brian Wetton (Mathematics, UBC).Vol. 5, Issue 2 Paci£c Institute for the Mathematical Sciences64th PIMS Graduate Industrial Math Modelling CampUniversity of Victoria, June 11–15, 2001Contributed by Chris Bose (University of Victoria).From June 11–15, the University of Victoria hosted thefourth annualPIMS Graduate Industrial Math Mod-elling Camp (GIMMC). The students followed up witha second week of industrial mathematics at the IPSW inSeattle, June 18–22. A record 58 students attended theCamp, led by 8 academic mentors on a selection of in-dustrial problems. Our sincere thanks to this year’s hard-working mentors:Sergei Bespamyatnikh (UBC, Watchtower Placement)John Chadam (Univ. of Pittsburgh, Portfolio Analysis)Ian Frigaard (UBC, Metal Spray Casting)Lisa Korf (U. Washington, Web Hosting Agreements)Hedley Morris (San Jose State, Imaging Problem)Tim Myers (Univ. of Capetown, Modeling Ice Accretion)Miro Powojowski (Algorithmics Corp., Risk Neutral Mea-sures)Moshe Rosenfeld (Univ. of Washington, Control of Street-light Networks)As with previous camps, students from all regions ofCanada were eligible to attend. This year the programmewas expanded to include 60 invited participants, up fromthe usual cap of 40. Further, in recognition of our newestPIMS institution, University of Washington, a special ef-fort was made to attract students from US universities. Inall, we had more than 130 applicants to the Camp, andwe accepted participants representing 25 North AmericanUniversities. Thirty-nine participants were from Canadaand the remaining 19 were from the United States. Manyfavourable comments were collected from our mentors at-testing to the excellent academic preparedness and to theenthusiasm of the students.Increased exposure throughout North America given tothis year’s Camp will result in even more applications nextyear. Students wishing to attend GIMMC 2002 shouldwatch for an announcement this fall on the PIMS websiteand apply as soon as possible.Detailed problem descriptions and a photo al-bum may be found on the GIMMC website athttp://pims.math.ca/industrial/2001/gimmc/.Proceedings from the workshop will be available fordownload from the PIMS website later this summer.MITACS AGMContinued from page 4.Arvind Gupta (Scientific Director of MITACS) statedthat, “I’m very pleased with the overwhelming atten-dance and I’m proud to announce that since its in-ception, MITACS’ partners and research groups havepublished more than 60 preprints, 400 research pa-pers, and co-sponsored more than 75 workshops andseminars. Moreover, MITACS has trained more than300 students for new employment opportunities inthe following sectors: biomedical, commercial & in-dustrial, information technology, manufacturing, andtrading & finance.” On behalf of MITACS, Dr. Guptasincerely thanks Drs. Speed, Ekeland, and Papadim-itriou and all of the poster judges for their con-tribution to the success of the MITACS AGM andPoster/Demo Exhibition.Visit the website www.mitacs.math.ca, for alisting of upcoming workshops.Participants at the 4th annual PIMS GIMMC enjoyed dry days and summer sunshine in Victoria.Paci£c Institute for the Mathematical Sciences Summer 200175th PIMS Industrial Problem Solving WorkshopUniversity of Washington, June 18–22, 2001Contributed by Randy LeVeque (U. Washington), Marc Paulhus (U. Calgary) and Chris Bose (U. Victoria).Participants in IPSW 2001 outside the Miller Building at the University of Washington.This year’s Industrial Problem Solving Workshop(IPSW) was held at the University of Washington in Seat-tle. About 100 people registered for the event, includingthe 58 graduate students who had taken part in the grad-uate modelling camp the week before. Faculty from anumber of universities around the world were also in-volved. Participants split up into six groups to attack theindustrial problems brought to the workshop, spanning abroad range of applications and mathematical techniques.Most of the industrial participants were able to stay allweek this year, and were actively involved in workingwith the groups. A brief description of the problems andsome of the progress made is given below. More completeproblem descriptions may be obtained from the website,http://www.pims.math.ca/industrial/2001/ipswand proceedings papers are being written by each group.Representing local Seattle industry, John DeTrevillebrought a problem from Microsoft on optimizing the lay-out of files on a disk, given an expected order in whichthe files will be accessed. The group learned a great dealabout the complex details involved in hard drive technolo-gies. They also quickly established that the problem wasequivalent to the intractable Travelling Salesman Problem.After building some one- and two-dimension disk models,they applied various heuristic techniques to try to findthe optimal solution for some sample data that Microsoftprovided. It was concluded that the heuristic methods ap-pear to provide better solutions more quickly using the2-D model than with the 1-D model, suggesting that themore realistic 2-D (or the even more realistic 3-D modelnot studied) should be used when disk performance is criti-cal. Current hardware limitations make the 1-D model theVol. 5, Issue 2 Paci£c Institute for the Mathematical Sciences8industry standard.Many of the participants who specialize in continu-ous modelling were attracted to the problem presentedby Bill Micklethwiate of Firebird Semicondutors,arising from growing large single crystals of Indium Anti-monide (InSb) from a melt. These crystals, about the sizeof a wine bottle, may develop imperfections due to ther-mal stresses as they cool. This problem contained some-thing for everyone in continuum mechanics – fluid dynam-ics coupled with convective, diffusive, and radiative heattransfer, Stefan problems for the moving phase boundary,and temperature-dependent stress analysis within the solidphase. This group split into several subgroups to tacklevarious aspects of the problem by both analytical and nu-merical approaches. Some new insights were gained intothe expected shape of the moving boundary and the rela-tive importance of different heat-transfer mechanisms.Allan Douglas from the Communications Secu-rity Establishment brought a problem relating to com-puter security on the large computer networks, such asthe internet. Mobile software objects that move aroundbetween computers are becoming more common and theproblem concerns the ability of the “good guys” to trackdown malicious software of this form. This led to an exten-sive literature search on problems of graph searching andrandom walks. The group discovered a vast and richlydeveloped literature that was directly applicable to theproblem at hand. They then expanded on that literatureand established some new results based on the particularsof the problem.Ron Forth presented a problem from the AlbertaEnergy Company on decline analysis, attempting to ex-trapolate trends in production rate data from oil and gaswells to forecast future production. The current practiceis for a petroleum engineer to perform the extrapolationusing visual curve fitting biased heavily by personal ex-perience. The data is typically very noisy and has theadditional feature that physical parameters in operationduring the period of data collection are randomly chang-ing (changes to pumping schedules, shutdowns, productionenhancement, etc) so no one model can be expected to fitthe entire time series. The workshop group concentratedon three aspects of the problem. First, the partitioningof the time series into intervals over which one physicalmodel may be applied. Moving average and wavelet tech-niques were investigated; both seemed sufficient to per-form the partition, provided reasonable thresholding val-ues were used. Second, a curve fitting over each subintervalwas performed. This was fairly straightforward as physicalconsiderations lead to a parametric family of model curvesand a simple, weighted, least-squares fit within that familyappears to suffice. Finally a weighting of the various ex-trapolations obtained in the previous step determines thefinal decline curve estimate. A heuristic weighting schemewas proposed and tested with reasonable results on a re-stricted data set. The possibility that this last step wouldlend itself to a neural-net approach was discussed.Alan King of IBM brought a problem on properlypricing web-hosting service agreements. A web-hostingservice provider may have a large number of clients withdifferent needs, and a finite amount of computer resourcesto distribute amongst those customers in order to satisfycertain Quality-of-Service (QoS) agreements. However,the web-hosting service can also dynamically reallocateits resources based on the observed needs of its clientsat any given time. The team tackled this extremely com-plex problem and built a very realistic model taking intoaccount a wide range of complexities such as requests ofdifferent size with different priorities, time-lag in the hard-ware re-distribution, as well as penalties for failing to meetthe QoS agreements.The final problem came from Algorithmics, a finan-cial mathematics firm. Alex Kreinin presented a prob-lem on measuring the credit risk of a given portfolio, basedon the credit ratings of the obligors. Standard Monte-Carlo techniques do not work very well since the interest-ing events (default by the obligors) are very rare and hencerequire a large number of simulations. Algorithmics cameto the workshop with a very well thought out model andeveryone was pleasantly surprised that the group discov-ered an analytical solution based on using the Lindberg-Feller Theorem (basically the Central Limit Theorem inthis context) to approximate the credit risk of all counter-parties in a single (credit driver) scenario. This resultedin approximating the risk across scenarios by a mixtureof Gaussians, the latter being one of the current methodsfor treating distributions with long tails. The group thenproceeded to test this fast, approximate solution againstmuch more time-consuming full Monte Carlo simulationsfor one time step. They found reasonable agreement andexpect much better results for longer time horizons sincethe CLT is better suited when the number of independentrandom variables increases. This was viewed as a signifi-cant development in the important area of credit risk, andwe look forward to seeing it developed further.Month of Industrial MathContinued from page 5.an n-dimensional cube. In addition, we simulatedsome results to verify their correctness. Most of themethods we used were new to most members of thegroup.“Part of the success came from working togetherwith other dedicated students. Not only did we man-age to make progress on posed problems, but we hadlots of fun doing it, and made friendships that willlast well beyond the workshops.“Overall, this workshop was an excellent experi-ence and I will gladly go back next year.”Paci£c Institute for the Mathematical Sciences Summer 20019Scienti£c ActivitiesAPCTP, Perimeter Institute and PIMS Collaborate onFrontiers in Mathematical PhysicsContinued from page 1.From left, Michael Stevenson (President, Simon Fraser University), Nas-sif Ghoussoub (Director, PIMS), Taejin Lee (Programme Coordinator,APCTP), K. S. Viswanathan (Simon Fraser University), Hugh Morris(Chairman, Board of Directors, PIMS), Gordon Semenoff (University ofBritish Columbia) and B. K. Chung (Executive Director, APCTP) aftersigning the APCTP-PIMS Coopertaive Agreement at the Diamond Univer-sity Centre, Simon Fraser University.The APCTP has a mandate to promote andfoster high level research in theoretical physics.Since its inception in 1996 it has maintainedan active programme of international meetingswhich has earned it a worldwide reputation forexcellence.Since 1998, APCTP has cooperated withPIMS on jointly organizing and funding theFrontiers in Mathematical Physics workshopswhich have taken place in Vancouver everysummer. This year’s workshop was used anoccasion to sign a cooperative agreement be-tween PIMS and APCTP, which formalizes analready strong record of scientific collaborationand cements future plans for cooperation. Pro-fessor B. K. Chung, Executive Director of theAPCTP, and Professor Nassif Ghoussoub, Di-rector of PIMS joined SFU President MichaelStevenson and more than fifty participants ofthe workshop to celebrate this unprecedentedcollaborative event.The Perimeter Institute for TheoreticalPhysics (http://www.perimeterinstitute.com) is based in Waterloo, Ontario, Canada. It was founded in 2000through a personal donation by Mike Lazaridis, President and Co-Chief Executive Officer of Research In Motion Limited(RIM) to “serve as a state-of-the-art Canadian physics institute dedicated to bold, provocative research of the funda-mental aspects of the physical world...”. Both PIMS and APCTP welcome the involvement and support of the PerimeterInstitute to the Frontiers in Mathematical Physics series.This year, the fifth workshop in the Frontiers in Mathematical Physics Series focused on the consequences of re-cent breakthroughs in the rapidly developing areas of superstring theory and nonperturbative gauge field theory. Theworkshop was held from July 16–27 at the PIMS facility at Simon Fraser University. The organizing committee wasK. S. Viswanathan (chair, Simon Fraser University), Taejin Lee (Kangwon University, Korea), Yuri M. Makeenko (NielsPresident Michael Stevenson of SFU witnessing the sign-ing of The APCTP-PIMS Cooperative agreement by PIMSDirector Nassif Ghoussoub and APCTP Executive DirectorB. K. Chung (at right).Bohr Institute, Copenhagen and ITEP, Moscow), JohnNg (TRIUMF), Alexander Rutherford (PIMS) and Gor-don W. Semenoff (University of British Columbia).Many of the lectures were video taped and willbe made available from the PIMS streaming videoweb page (http://www.pims.math.ca/video). Formore information on the workshop please seehttp://www.pims.math.ca/science/2001/fmp.Planning has already begun for next year’s workshop,which will focus on supersymmetry and the physics of extradimensions. This subject contains some very important newideas which have revolutionalized our thinking on some ofthe long-standing problems in theoretical particle physics.This is particularly timely, as particle physics experimentswill finally achieve the next energy threshold within the nextfive years. Many questions about nature at the high en-ergy frontier could well be answered by these experiments.The organizing committee for next year’s workshop is be-ing chaired by John Ng (TRIUMF). Further informationon the workshop and online registration are available fromhttp://www.pims.math.ca/science/2002/fmp.Vol. 5, Issue 2 Paci£c Institute for the Mathematical Sciences10PIMS Hosts the 9th Canadian Conferenceon General Relativity and RelativisiticAstrophysics at the University of AlbertaContributed by Eric Woolgar (University of Alberta).Co-sponsored by PIMS, the Perimeter Institute for Theo-retical Physics and the Canadian Institute for TheoreticalAstrophysics (CITA), the Canadian Conference on Gen-eral Relativity and Relativisitic Astrophysics (CCGRRA)was held at the University of Alberta on May 24–26. Thiswas the ninth in the series of CCGRRA meetings, whichhave been held every two years since 1985. This year’sCCGRRA was organized by Hans Kunzle (University ofAlberta), Sharon Morsink (University of Alberta), andEric Woolgar (University of Alberta). It was held in con-junction with the Black Holes III meeting in Kananaskison May 19–22, which was also supported by PIMS. Therewere 82 participants for CCGRRA, with approximately 60participants from Canadian universities.The first day was devoted to developments in math-ematical relativity and related areas of quantum grav-ity. After opening remarks by University of Alberta The-oretical Physics Institute Director Wojciech Rozmus,Fields Medalist Shing-Tung Yau (Harvard University)discussed Conditions for the Existence of Black Holes us-ing the Mean Curvature Flow. Amanda Peet (Universityof Toronto) presented a talk on Recent Progress in Super-string/M Theory, while John Baez (University of Cal-ifornia at Riverside) spoke about Spin Networks in LoopQuantum Gravity. The day’s final plenary talk, byKristinSchleich of UBC, surveyed Topological Censorship.The second day’s plenary speakers concentrated on as-trophysics. Eric Poisson (University of Guelph) spoke onGravitational Radiation Reaction Calculations, while Vir-ginia Trimble (University of California at Irvine) gave alively discussion of Observations of Compact Objects. Nu-merical relativity was also represented, with Saul Teukol-sky (Cornell University) speaking on Numerical Simula-tions of Black Holes.On the final day, Kip Thorne (California Institute ofTechnology) gave an outline of Progress in the Construc-tion of the LIGO Gravitational Wave Observatories whichare due to begin scientific data collection at the beginningof 2002. Viqar Husain (University of New Brunswick)spoke on Dualities and Wilson Loops. The closing talk ofthe conference was given by J. R. Bond (Director, Cana-dian Institute for Theoretical Astrophysics) who gave a lec-ture on the state of our knowledge of cosmological param-eters, incorporating the latest data from the Boomerangexperiment.A detailed list of lectures given at the conference andscanned copies of the slides for many of the lectures areavailable from the conference website:www.math.ualberta.ca/∼ccgrra.Further information on the related Black Hole IIImeeting is available from the website:fermi.phys.ualberta.ca/∼gravity/bh3conference.Wave Phenomena III: Cornerstone of thePIMS Thematic Programme on FluidDynamicsContributed by T. Bryant Moodie (University of Alberta).PIMS at the University of Alberta hosted the workshopWave Phenomena III on June 11–15. This workshopis the third event in the PIMS Thematic Programme onFluid Dynamics, which also features the Third PIMSFluid Dynamics Summer School, held May 27 –June 8 at the University of Alberta, and The Interna-tional Conference on Theoretical and NumericalFluid Mechanics II, to be held August 20–24 at theCoast Plaza Hotel in Vancouver.The wave concept is probably the most widely used sin-gle notion in all of physical science. It links together suchdiverse disciplines as geophysics, oceanography, meteorol-ogy, astrophysics, physiology, and biology. In geophysicalcontexts, waves are a primary method by which energyis transported in fluids and they are thus responsible forglobal circulation of the atmosphere, the oceans, and theearth’s mantle. In biological contexts, waves are used inthe study of haemodynamics, neural networks, and respi-ratory flows. Waves are also studied intensively for theiruse in remote sensing and have been exploited to map ouratmosphere from space, to explore and see the deep oceans,and to detect disease by non-invasive methods. The enor-mous range of spatial scales spanned by waves is indicativeof their relevance to many disciplines.The previous two Wave Phenomena meetings were alsosuccessful and focused on wave propagation phenomena ina wide spectrum of applications. For the third Wave Phe-nomena Meeting, we chose to focus on the fluid mediumfor wave transmission. We did this first because of thegeneral importance of the subject at this time with its re-lation to world climate change and our concerns with thischange and second in order to better mesh with the topicsof the 3rd PIMS Summer School in Fluid Dynamics,which immediately preceded the conference.Waves III was attended by 145 delegates fromCanada, Mexico, USA, Turkey, Ghana, France, Germany,The Netherlands, Scotland, Italy, India, Denmark, China,Japan, Sweden, New Zealand, Taiwan, Australia, and Rus-sia. There were a total of 23 plenary talks that were givenin the morning session each day. These were then followedby the contributed talks that were held in 5 parallel ses-sions during the afternoons.The plenary talks were given by Peter Baines (CSIRO),David Benney (MIT), Jerry Bona (U. of Texas, Austin),Carlo Cercignani (Politecnico di Milano), Harindra JosephFernando (Arizona State), Roger Grimshaw (Loughbor-ough), Richard Lindzen (MIT), Michael Longuet-Higgins(UCSD), Andrew Majda (Courant Institute), MichaelMcIntyre (Cambridge), James McWilliams (UCLA),Robert Miura (UBC), Alan Newell (U. of Arizona, Tuc-son), Richard Peltier (U. of Toronto), George Philander(Princeton), Raymond Pierrehumbert (U. of Chicago),Please see Waves III, page 12.Paci£c Institute for the Mathematical Sciences Summer 200111Summer 2001 in Vancouver: Place to be for Nonlinear PDEMore than 500 researchers from 15 countries are partic-ipating in the PIMS Thematic Programme on NonlinearPDE, which is being held at PIMS-UBC from July 2 toAugust 18. This programme deals with several interre-lated topics originating in finance, physics, chemistry, bi-ology and material sciences, as well as in geometry. Thecommon feature of these topics is that they involve theinterplay between nonlinear, geometric and dynamic com-ponents of partial differential equations. The focal pointof each workshop is a series of minicourses given by someof the best world experts in the field. For further details,see http://www.pims.math.ca/pde.1. Minicourse Lecturers in the Workshop on Vis-cosity Methods in Partial Differential Equations:Xavier Cabre´ (Universitat Politecnica de Catalunya)2 lectures on Nonconvex Fully Nonlinear Elliptic Equa-tions: C2,α Regularity for some Bellman-Isaacs Equa-tions.Craig Evans (Berkeley): 2 lectures on Hamilton-Jacobi Equations and Dynamical Systems.Robert Jensen (Loyola): 2 lectures on VariationalProblems in L∞.Panagiotis Souganidis (Austin): 2 lectures on FullyNonlinear Stochastic PDEs.Andrzej Swiech (Georgia Tech): 5 lectures on Viscos-ity Solutions in Infinite Dimensional Spaces and Opti-mal Control of PDEs.Thaleia Zariphopoulou (Austin): 2 lectures on Vis-cosity Solutions in Finance.Waves IIIContinued from page 11.Peter Rhines (U. of Washington), Colin Rogers (U. ofNew South Wales), P. L. Sachdev (Indian Instituteof Science), Ted Shepherd (U. of Toronto), MelvinStern (Florida State), Steve Thorpe (SouthamptonOceanography Centre) and John Whitehead (WoodsHole).Waves III was organized by Andrew Bush, BryantMoodie, Bruce Sutherland, and Gordon Swaters, allof the University of Alberta, with the very able assis-tance of Lisa and Lina from the University of AlbertaPIMS office. The opening address was given by DickPeter (DEan of Science, University of Alberta) whoemphasized the important role that has been playedin the mathematics community by The Pacific Insti-tute for the Mathematical Sciences and how meetingsof this calibre would not be possible without the sup-port of PIMS.Interested readers may view a complete listof speakers together with their abstracts, con-tact information, and pictures on the websitewaves3.math.ualberta.ca.2. Minicourse Lecturers in the Workshop on PhaseTransitions:Henri Berestycki (Paris): 4 lectures on Propagationof Fronts in Excitable Media.David Kinderlehrer (Carnegie-Mellon): 4 lectures onTopics in Metastability and Phase Changes.3. Minicourse Lecturers in the Workshop on Con-centration Phenomena and Vortex Dynamics:Fang-Hua Lin (Courant Institute): 4 lectures on Vor-tex Dynamics of Ginsburg-Landau and Related Equa-tions.Wei-Ming Ni (Minnesota) and Changfeng Gui(UBC): 4 lectures on Diffusions, Cross-diffusions andtheir Steady States.Michael Struwe (ETH): 4 lectures on Wave Maps.4. Minicourse Lecturers in the Workshop on Varia-tional Methods and their Applications in PDEs,Hamiltonian Systems & Mathematical Physics:Yann Brenier (Paris): 4 lectures on Variational prob-lems related to fluid and plasma modelling.Maria Esteban (Paris): 3 lectures on VariationalProblems in Relativistic Quantum Mechanics: Dirac-Maxwell Equations.Eric Se´re´ (Paris): 3 lectures on Variational Problemsin Relativistic Mechanics: Dirac-Fock Equations.5. Minicourse Lecturers in the Workshop on Geo-metric PDEs:Clifford Taubes (Harvard): 4 lectures on Pseudo-holomorphic geometry as a tool to study smooth 4-dimensional manifolds.Gang Tian (MIT): 4 lectures on Recent progress inComplex Geometry.Rick Schoen (Stanford): 4 lectures on GeometricVariational Problems.Changfeng Gui (UBC), Fang Hua Lin (Courant Institute),Michael Struwe (ETH) and Wei-Ming Ni (Minnesota), theminicourse lecturers for the Workshop on Concentration Phe-nomena and Vortex Dynamics.Vol. 5, Issue 2 Paci£c Institute for the Mathematical Sciences12PIMS Thematic Programmes for 2002Thematic Programme (A):Asymptotic Geometric Analysis,PIMS at UBCOrganizing committee: Vitali Milman (co-chair, TelAviv), Nicole Tomczak-Jaegermann (co-chair, U. Alberta),Nassif Ghoussoub (PIMS and UBC), Robert McCann(U. Toronto), Gideon Schechtman (Weismann Inst.).Advanced Graduate Camp, June 15–30: Lectureson subjects connected with the whole program directed toyoung participants, advanced Ph.D. students and PDFs.Conference on Convexity and Asymptotic Theoryof Normed Spaces, July 1–5: Organised by Erwin Lut-wak (Warsaw) and Alain Pajor (Marne-La-Valle´e). Topicsinclude classical convexity, Radon transform and Fouriermethods in convexity, asymptotic theory of high dimen-sional convex bodies, geometric functional inequalities andprobabilistic methods in convexity, isoperimetric-type in-equalities.Concentration Period on Measure Transportationand Geometric Inequalities, July 8–12: Organized byRobert McCann (U. Toronto). This concentration periodwill focus on transportation of measure methods and theirapplications, concentration of measure phenomenon, ge-ometric functional inequalities (Brascamp-Lieb, Sobolev,entropy, Cramer-Crao, etc), “isomorphic” form of geomet-ric inequalities and probabilistic methods.Workshop on Phenomena of Large Dimensions,July 14–20: Organized by Vitali Milman (Tel Aviv),Michael Krivilevich, Laszlo Lovasz (Microsoft Research)and Leonid Pastur (U. Paris VII). Topics include differ-ent phenomena observed in complexity theory, asymptoticcombinatorics, asymptotic convexity, statistical physicsand other theories of very high parametric families (orlarge dimensional spaces).Focused Research Groups on Random Methodsand High Dimensional Systems, July 21–August 5:Coordinated by Vitali Milman (Tel Aviv) and NicoleTomczak-Jaegermann (U. Alberta).Workshop on Non-commutative Phenomena andRandom Matrices, August 6–9: Organized by GillesPisier (U. Paris VI and Texas A & M) and StanislawSzarek (U. Paris VI and Case Western Reserve). Top-ics include the distribution of eigenvalues of random ma-trices, norms of such matrices, some aspects of free andquantum information theories, applications in many fields,quantized functional analysis and operator spaces and non-commutative Lp spaces.Workshop on Banach Spaces, August 12–15: Or-ganized by Bill Johnson (Texas A & M and Ted Odell(U. Texas, Austin). This workshop will focus on theasymptotic theory of Banach spaces and other applicationsof local theory to the geometry of infinite dimensional Ba-nach spaces.Thematic Programme (B):Selected Topics in Mathematical andIndustrial StatisticsWorkshop on the Role of Statistical Modelling inthe 21st Century, May 4–6, PIMS at Simon FraserUniversity: Organized by Richard Lockhart and Char-maine Dean (SFU) and Peter Guttorp (U. Washington).This workshop will bring together leading practitionersand philosophers of scientific, Bayesian and frequentistmodelling statistics with leading researchers in model as-sessment, validation and goodness-of-fit. The goals are toidentify opportunities and challenges for model develop-ment and criticism and to begin to outline approaches toassessment of complex models.International Conference on Robust Statistics(ICORS 2002), May 12-18, UBC: The Scientific Com-mittee is Luisa Fernholz (Temple Univ.), Ursula Gather(Dortmund), Chris Field (Dalhousie) and R. H. Zamar(UBC). This conference will be a forum for new develop-ments and applications of robust statistics and statisticalcomputing. Experienced researchers and practitioners, aswell as younger researchers, will come together to exchangeknowledge and to build scientific contacts. The confer-ence will centre on methods designed for processing largedatasets of uneven quality (databases containing outliers,gross errors, missing data, etc.). This conference expectsto touch upon many different aspects of data analysis in afashion which integrates theoretical and applied statistics.Design and Analysis of Experiments, July 14–18,Coast Plaza Suites Hotel, Vancouver: Organized byRandy Sitter (SFU), Derek Bingham (Michigan), BruceAnkenman (Northwestern) and Agnes Herzberg (Queen’sU.). Many industrial problems are not well-explored inthe statistical literature. To help North American indus-try compete globally, advanced statistical methods suit-able for real applications need to be further developed.Statistical experimental designs, developed by Sir RonaldFisher in the 1920’s, largely originated from agriculturalproblems. Although the design of experiments for indus-trial and scientific problems may have the same basic con-cerns as design for agricultural problems, there are manydifferences: (i) industrial problems tend to require investi-gation of a much larger number of factors and usually in-volve a much smaller total number of runs (observations),(ii) industrial results are more reproducible, (iii) industrialexperimenters are obliged to run their experimental pointsin sequence and are thus able to plan their follow-up ex-periments guided by previous results, unlike agriculture, inwhich all results are often harvested at one time, and (iii)models can be very complicated in industrial and scientificexperimentation, sometimes requiring the need for nonlin-ear models or for computer modelling and finite elementanalysis.Paci£c Institute for the Mathematical Sciences Summer 200113Second Canada-China Mathematics CongressAugust 20–23, 2001 in Vancouver, BC, CanadaThis initiative builds on the success of the first Congress held at Tsinghua University, Beijing, in August 1999, and isaimed at developing further the collaborative research effort between the two countries. It is sponsored by the 3 × 3Canada-China initiative, the Centre de Recherches Mathe´matiques, the Fields Institute for the Mathematical Sciences,the Pacific Institute for the Mathematical Sciences and the MITACS Network of Centres of Excellence.Organizing Committee: Nassif Ghoussoub (National Math. Coordinator for 3x3 Canada-China Initiative), Dale Rolfsen (PIMSUBC-Site Director), JingYi Chen (UBC), Xiao Jiang Tan (Peking University), Lizhong Peng (Peking University), Dayong Cai (Tsing HuaUniversity), XingWei Zhou (Nankai University), JiaXing Hong (Fudan University).Officers of the Chinese Delegation• Zhi Xing Hou (President of Nankai University, Director of Math-ematical Centre of Chinese Education Ministry)• Wang Jie (Vice director of Chinese Nature Scientific Foundation)• Zhiming Ma (President of the Mathematical Society of China)• L.Z. Peng (Secretary of the Mathematical Society of China)• K.C. Chang (Director of the Mathematical Centre of ChineseEducation Ministry)Officers of the Canadian Delegation• Tom Brzustowski (President of NSERC)• Barry McBride (Vice-President Academic, UBC)• Luc Vinet (Vice-President Academic, McGill University)• Nassif Ghoussoub (PIMS Director and National Math. Coor-dinator for 3x3 Canada-China Initiative)• Arvind Gupta (MITACS program leader)• Ken Davidson (Director, Fields Institute)• Jacques Hurtubise (Director, CRM)• Jonathan Borwein (President, Canadian Math Society)Plenary Speakers:• Weiyue Ding (Director of the Institute of Mathematics, PekingUniversity), On the Schrodinger Flow• Jie Xiao (Tsinghua), Hall Algebras and Quantum Groups• Yiming Long (Director of the School of Mathematical Sciences,Nankai University), Iteration theory of Maslov-type index withapplications to nonlinear Hamiltonian systems• Xiaoman Chen (Fudan), On the Structure, K-theory of Roe Al-gebras• Zhiming Ma (Academic Sinica), Some New Results/Directionsin Probability Theory• Gordon Slade (UBC): Statistical Mechanics• Mark Lewis (Alberta): Mathematical Biology• Ian Putnam (Victoria): Operator algebras and hyperbolic dy-namical systems• Luc Vinet (McGill): Mathematical Physics• Catherine Sulem (Toronto): PDE• Henri Darmon (McGill): Number Theory• Gang Tian (MIT): Complex GeometrySession SpeakersI. Algebra and Number Theory:• Qingchun Tian (Peking): Iwasawa Theory for p-adic Represen-tation• Xingui Fang (Tsinghua): On 1-arc Regular Graphs• Weisheng Qiu (Peking): Completely Settling of the MultiplierConjecture for the case of n = 3p3• Yonghui Wang (Capital Normal): Some Results on AnalyticNumber Theory• Jim Carrell (UBC)• Abraham Broer (Montreal)• Kai Behrend (UBC)• Terry Gannon (Alberta)• Zinovy Reichstein (UBC)• Jim Bryan (UBC)• Kumar Murty (Toronto)• Tony Geramita (Queens)• Robert V. Moody (Alberta)II. Mathematical Physics and PDE:• Yunbo Zeng (Tsinghua): Two binary Darboux transformationsfor KDV hierarchy with self-consistent sources• Peidong Liu (Peking): Entropy and Iyapunov Exponents forStationary Random Maps• Chengming Bai (Nankai): Puzzle Degeneracies and Yangian• Songmu Zheng (Fudan): Maximal attractor for some non-linearPDEs• Jiayu Li (Fudan): Geometric Analysis• Li Ma (Tsinghua): New results about mean field equations• Shuxiang Huang (Shang Dong): Global Solutions and Asymp-totic Behaviour for Reaction-diffusion Equations• Dmitry Jakobson (McGill): Geometric Analysis• Jia Quan Liu (Peking): On Quasilinear Elliptic Equations• Shoulin Zhou (Peking): On a Singular Equation• Shenghong Li (Zhejiang): Second Boundary Problem forParabolic Equations with Gradient Obstacle• S. Gustafson (UBC)• Victor Ivrii (Toronto)• Peter Greiner (Toronto)• G. Semenoff (UBC)• I. ÃLaba (UBC)• JiQuang Bao (PIMS)• Richard Froese (UBC)• Changfeng Gui (UBC)• Peter Orland (CUNY, visiting UBC) SU(2)×SU(2) gauging ofintegrable XXX models• John Harnad (CRM, Concordia): Math. PhysicsIII. Probability and Statistics:• Guanglu Gong (Tsinghua): Iterative Systems• Yongjin Wang (Nankai): A probabilistic analysis to one classof non-linear differential equations on unbounded domains andits application to superprocesses• Tianping Chen (Fudan): Unified stabilization approach to prin-cipal minor components extraction algorithms• Runchu Zhang (Nankai): Optimal Blocking of 2n−k and 3n−kFractional Factorial DesignsVol. 5, Issue 2 Paci£c Institute for the Mathematical Sciences14• Martin Barlow (UBC)• Ed Perkins (UBC)• Jonathan Taylor (McGill)• Gordon Slade (UBC)• Remco Van der Hofstad (Microsoft, Delft U of Tech)• Peter Hooper (Alberta)• Harry Joe (UBC)IV. Wavelets and their Applications:• Xingwei Zhou (Nankai): Some results on Wavelet frames• Lizhong Peng (Peking): Orthogonal Wavelets on the HeisenbergGroup• Heping Liu (Peking): The Joint Spectral Multipliers on Heidel-berg Groups• Ding-Xuan Zhou (Hongkong City): Wavelet Analysis• Hoi Ling Cheung (Hongkong City): Wavelet Analysis• Serge Dubuc (Montreal)• Bin Han (Alberta)• Rong-Qing Jia (Alberta)• Jean-Marc Lina (Montreal)• Remi Vaillancourt (Ottawa)V. Computational, Industrial & Applied Analysis:• Houde Han (Tsinghua): The Numerical solutions of Heat Equa-tion on Unbounded Domains• Dayong Cai (Tsinghua): Multi-solution of Power System andits Fast Algorithm• Jianwei Hu (Nankai): Finite Element-Finite Volume TypeMethod for Nonlinear Convection-Diffusion Problems and its Ap-plications• Yongji Tan (Fudan): On some Inverse Problems• Zhongmin Wu (Fudan): Quasi interpolation for solving ordi-nary differential equations• Yangfeng Su (Fudan): Some problems on GTH algorithm forStochastic matrices• Xunjing Li (Fudan): On Optimal Control Theory for InfiniteDimensional Systems• Shufang Xu (Peking): Numerical Analysis of the Maximal So-lution of the matrix Equation X + A∗X−1A = P• Wenxun Xing (Tsinghua): Computational Applied Analysis• Yanren Hou (Xi’An Jiaotong): Full Discrete PostprocessingProcedure to the Galerkin Approximation Based on AIMD• Zheng Jian Hua (Tsinghua): Hyperbolic metric and its appli-cation in complex dynamics• Huaxiong Huang (York): Industrial Analysis• M. Fortin (Laval): Computational Analysis• H. Brunner (Memorial U. of Newfoundland)• J. Wu (York): Industrial and Applied Analysis• A. Peirce (UBC): Industrial and Applied Analysis• Brian Wetton (UBC): Industrial and Computational Analysis• Michael Ward (UBC): Applied Analysis• Uri Ascher (UBC): Computational Analysis• S. Ruuth (SFU): Computational AnalysisVI. Geometry/Topology:• Jinkun Lin (Nankai): Some new families of filtration six in thestable homotopy spheres• Lei Fu (Nankai): Weight Filtration and Monodromy Filtrationof Vanishing Cycles• Xiaojiang Tan (Peking): Petri Map for Rank 2 Vector Bundles• Shaoqiang Deng (Nankai): Dipolarizations in Lie Algebras andHomogeous ParaKaehler Manifolds• Hui Kou (Sichuan): Topology• K.C. Chang (Peking): An Evaluation of Minimal Surfaces• Youcheng Zhou (Zhejiang): Topology• Jacques Hurtubise (CRM/McGill)• Kunio Murasugi (Toronto)• McKenzie Wang (McMaster)• Eckhard Meinrencken (Toronto)• Denis Sjerve (UBC)• Rick Jardine (Western Ontario)• Olivier Collin (Universite´ du Que´bec a` Montre´al)• Maung Min-Oo (McMaster)• Dale Rolfsen (UBC)VII. Operator Theory/Functional Analysis:• Guanggui Ding (Nankai): Some Recent Advances and the OpenProblems on Perturbations and Extensions of Isometric opera-tors• Man Duen Choi (Toronto)• Kenneth Davidson (Waterloo)• George Elliott (Toronto)• Michael Lamoureux (Calgary)• James Mingo (Queen’s)• Andu Nica (Waterloo): Levels of operator-valued R-transformsin free probability• Sam Walters (UNBC)• Shuang Zhang (Cincinnati): Purely infinite simple C*-algebrasgenerated by an isometry and a bilateral shift• Allan Donsig (Nebraska)• Thierry Giordano (Ottawa)VIII. Mathematical Finance:• Duo Wang (Peking): Bifurcation of the ABS model of funda-mentals versus trend chasers with positive share supply• Junyi Guo (Nankai): Compound models and their ruin proba-bilities for risk processes with correlated aggregate claims• John Walsh (UBC)• Uli Haussmann (UBC)• Ali Lari-Lavassani (Calgary)• Abel Cadenillas (Alberta)IX. ODE and Dynamical systems:• Weigu Li (Peking): Planar Analysis Vector Fields with Gener-alized Rational First Integrals• Zhiming Zheng (Peking): Semi-uniform Ergodic Theory and itsApplication• Meirong Zhang (Tsinghua): The rotation number approach toeigenvalues of the one-dimensional p-Laplacian• Weinian Zhang (Sichuan University): Bifurcations of a Polyno-mial Differential System of Degree n in a Biochemical Reaction• Yun Tang (Tsinghua): Singularities of quasi-linear DAE in thesetting of real algebraic geometry• Lan Wen (Peking): A C1 Density Theorem• Oleg Bogoyavlenskij (Queen’s)• Florin Diacu (Victoria)• C. Rousseau (Montre´al)• J. Belair, (Montre´al)• B. Langford (Guelph)• W. Nagata (UBC)• M. Li (Alberta)• V. LeBlanc (Ottawa)• Leon Glass (McGill): Dynamics in High Dimensional Models ofGenetic NetworksPaci£c Institute for the Mathematical Sciences Summer 200115The Fascinating Predator-Prey Equation andDevelopment of HIV/AIDS in CanadaContributed by B. D. Aggarwala (University of Calgary)IntroductionModelling in mathematics is as old as mathematics it-self. Galileo Galilei (1564–1642), arguably the first modernmathematician, wrote down equations to ‘model’ the veloc-ity of a piece of stone as it fell down the Tower of Pizza.Sir Issac Newton (1642–1727) considered his model of theSolar System as a towering achievement of his life, whichindeed it was. In epidemiology, spread of childhood infec-tious diseases in constant populations was first modelledby Hamer [1] in 1906. In this article, we apply a sim-ple predator-prey model in epidemiology to the spread ofHIV/AIDS in Canada and arrive at some surprising con-clusions.In a predator-prey model, we look upon the HIV pos-itive people as the predators and the HIV negative onesas the prey. Now the usual ratio dependent predator-preymodel isx′(t) = αx(1− x)− xy/(x+ y) (1a)y′(t) = −ay + kxy/(x+ y) (1b)where x(t) and y(t) are the number of prey and the num-ber of predators respectively at any time t. In this model,in the absence of the predators, the prey multiply logis-tically according to the equation x′(t) = αx(1 − x). Inencounters with predators, the prey die according to theterm k1xy/(x+ y). We have non-dimensionalised the con-stant k1 to 1 in equation (1a). The constant k is called theconversion factor, so that a ‘sacrifice’ of xy/(x + y) preyadds kxy/(x+ y) to the population of predators (it takesmore than one mouse to keep one cat alive). In the ab-sence of the prey, the predators die according to the term‘−ay’, because they have no food. With this explanation,the equations (1) are the usual “rate of change = rate inminus rate out” equations, familiar from the first coupleof chapters of most texts on differential equations.If we write the equations (1) as x′(t) = F (x, y), y′(t) =G(x, y), then the points where F (x, y) = G(x, y) = 0 arecalled the points of equilibrium of these equations. Theidea is that you look upon (x, y) = (x(t), y(t)) as a movingpoint in the (x, y) plane and these are the points where itsvelocity is zero. If we know how the equations behave inthe ‘neighbourhood’ of these points, then there are theo-rems in mathematics which tell that for large values of t,the moving point will end up either at one of these equilib-rium points, or go to infinity, or ‘get stuck’ in a limit cycle.A limit cycle is simply a periodic solution of our equationswhich the moving point approaches for large values of t.It is possible to prove that, in our system, if x(0) > 0,and y(0) > 0, then the moving point will stay in a closedand bounded region of the first quadrant, so that infinityis ruled out. If we now define F (0, 0) = G(0, 0) = 0 (noticethat F (x, y) and G(x, y) have not been defined at the ori-gin so far), then the origin is an equilibrium point of thesystem and we want to know how the system behaves inthe neighbourhood of the origin. In the case of HIV/AIDSapplication, this point represents the annihilation of thesociety.The behaviour of such a system ‘near’ an equilibriumpoint can be investigated by expanding F (x, y) andG(x, y)near such an equilibrium point in Taylor series and retain-ing only the linear terms. If such an equilibrium point isthe origin, this leads to the equations X ′(t) = AX, whereA is a 2× 2 matrix, X =(xy)and the eigenvalues of thematrix A decide the behaviour of the system near the ori-gin. The trouble in our case is that F (x, y) and G(x, y) donot have Taylor series expansions near the origin. Whatdo we do?We start with an example. We arbitrarily take (a, k) =(.31, .62) and ask ourselves the question; starting fromwhich points in the (x, y) plane do we approach the ori-gin for large values of t? We notice that in addition toP1 = (0, 0), there are two other equilibrium points of ourequations, namely P2 = (1, 0) and P3 = (x1, y1), wherex1 = (kα − k + a)/(kα) and y1 = (k − a)x1/a, andthat the eigenvalues at these ‘other’ equilibrium points are(−α, k− a) and the two roots λ of λ2+Bλ+C = 0 whereB = (a+α− 1)−a2(k− 1)/k2 and C = a(k−a)(kα−k+a)/k2 respectively. In our example, we take B = 0 whichgives α = .595. We are now ready to go to the computer.On the computer, we arbitrarily assume that if x(t)2+y(t)2 is ‘small’ , less than 108 say, for some large valuesof t (we took t = 150), then we are aproaching the origin.After all, if we are approaching some other point, then wedo not expect to find ourselves near the origin for largevalues of t. Here is the diagram plotting all such pointsin the first quadrant. The square symbol in this diagramgives the location of P3 = (x1, y1).This does not throw much light on the problem. Whatis the bounding curve of the area in Fig. 1? We considerthe path of two solutions starting very close to the bound-ary of all these points in the above diagram. We tookA1(.9, .399) and A2(.9, .398 as examples. We found thatthe solution starting from A1 goes to the origin while theone starting from A2 comes very close to the origin, thenleaves the origin staying close to the x-axis (an eigenvectorat the origin), comes close to P2(1, 0) staying close to thex-axis (an eigenvector at this point as well), leaves P2(1, 0)along the other eigenvector at this point, and finally ap-proaches P3 along a spiral. We strongly suspect that thesame thing is happening at the origin. The bounding so-lution is approaching the origin along an eigenvector. Butwe cannot linearise our equations near the origin and wedo not know this eigenvector. What do we do?Vol. 5, Issue 2 Paci£c Institute for the Mathematical Sciences16Fig. 1: This diagram shows the area from where thepoints in the first quadrant go to the origin for (a, k, α) =(.31, .62, .595). The square symbol gives the location of P3.For problems in the plane, there is another, simplermethod for finding the eigenvalues and eigenvectors of ourdifferential equations. If the equilibrium point is the ori-gin, then the line y = mx is an eigenvector if the dif-ferential equation is satisfied along this line in the neigh-bourhood of the origin, i.e. if y′ = mx′ for “small” val-ues of x and y. For our equations, this gives m =(a + α − k)/(1 − a − α). Corresponding to this value ofm, the quantity λ = (α−m)/(1 +m) is the eigenvalue. Ifm > 0 and λ < 0, then the solution is approaching the ori-gin along y = mx for large values of t. In our example, weget m = 3 and λ = −.155. Since the solution is approach-ing the origin for positive values of t, it must be going awayfrom the origin for negative vaues of t. Here is the solutionimposed upon the above diagram and running from t = 0to t = −118. We conclude that this indeed is the solutionwhich bounds the area from where the solutions go to theorigin.Fig. 2: This diagram shows the points in the first quadrantfor (a, k, α) = (.31, .62, .595) from where the solutions go tothe origin and a solution of our equations running alongy = mx (see text) from t = 0, to t = −118.We conclude that in this example, there are three eigen-vectors through the origin as against two when the equilib-rium point is a ‘regular’ one with Taylor series expansionsof F (x, y) and G(x, y). In this example, the eigenvectorsat the origin are x = 0 (corresponding λ > 0, y = 0 (withλ < 0) and y = mx (with λ < 0). If m = tan(θ1) then theorigin is an unstable saddle point in the sector 0 < θ < θ1and a stable node in the sector θ1 < θ < pi/2.For other values of (a, k, α), m may be either positiveor negative and the corresponding λ may also be eitherpositive or negative. If m is negative, then there is nocorresponding eigenvector through the origin (because thesolution has to stay in the first quadrant) and withm posi-tive, if λ is also positive, then the solution runs away fromthe origin in positive time. However, it cannot go veryfar (the solution must be bounded) and it turns back andcomes back to the origin along the y-axis. We investigatedthe cases of B > 0 and B < 0 in a similar manner. Noth-ing unexpected was found. For m < 0, we can make thefollowing two important statements:Proposition 1 If a+α < min(1, k), then all solutions goto the origin.Proof: If we consider u = x/y and x as the two depen-dent variables, then equations (1) reduce tox′(t) = αx(1− x)− x/(1 + u) (2a)& u′(t) = −αu(1− x)− u1 + u + au−ku21 + u (2b)The desired result follows from the fact that u′(t) ≤αu + au − u × min(1, k), because writing m = min(1, k),this gives u(t) ≤ u(0)e(α+a−m)t, which implies that ifα + a < m, then u goes to zero, and therefore x goesto zero, as t goes to infinity. The only equilibrium pointwith x = 0 is the origin and therefore all solutions ap-proach this point. It is easy to see in this case that P2 andP3 are both unstable.Proposition 2 If a + α > max(1, k), then no solutiongoes to the origin.Proof: If, for large values of t, x < ² for some small posi-tive number ², then it is easy to see from equation (2b) thatu′(t) ≥ mu where m = min(a+α−1−α², a+α−k−α²).But then u(t) becomes arbitrarily large and consequentlythe second term in (2a) becomes arbitrarily small. Thisimplies that x must increase, which proves the statement.Also for m > 0, we can make the following two state-ments:Proposition 3 If k < a+α < 1, then there are solutionsof equations (1) which approach the origin.Proof: In this case m = (a+α−k)/(1−a−α) is a pos-itive number and as we have pointed out above, there aresolutions of our equations which approach the origin alongthe line y = mx. This happens if x′(t) < 0 along y = mxnear the origin, which is true if k < a/(1−α) < a+α < 1in this case. If for any value x1 of x, the value of sucha solution is y1, then any solution which starts at (x1, y2)where y2 > y1 must approach the origin, because these twosolutions cannot intersect each other except at the origin.Other solutions approach either P2 or P3 dependng uponother criteria.Proposition 4 If 1 < a+α < k, then there are solutionsof equations (1) which approach the origin.Paci£c Institute for the Mathematical Sciences Summer 200117Proof: In this case again, m is a positive number andthere are solutions which approach the origin. In this case,x′(t) < 0 along y = mx near the origin if 1 < a+ α < k <a/(1− α). There are other solutions which approach P3.Application to HIV/AIDSTo describe the spread of HIV/AIDS in a society, we writeour equations (1) asx′(t) = αx(1− x)− kxy/(x+ y) (3a)y′(t) = −αy + kxy/(x+ y) (3b)where x(t) and y(t) stand for the number of the HIV neg-ative and HIV positive individuals in our society, respec-tively. It is to be noted that in a random mating envi-ronment, the total number of mating partners to an x orto a y is x + y, so that an x may mate with a y with aprobability of kxy/(x+y). Hence the equations (3). Theseequations are equivalent to taking k = 1 in the foregoingdiscussion (k = 1 because if one HIV negative individualis lost, then one HIV positive individual is gained), butthen the time scale is different. We take one year to bethe unit of time in this section. Proposition 1 above nowstates that if a + α < k, then all solutions go to the ori-gin. The three points of equilibrium now are P1 = (0, 0),P2 = (1, 0) and P3 = (x1, y2) where x1 = (α−k+a)/α andy1 = (k−a)x1/a. These three points correspond to (a) thesociety being eliminated, (b) the disease being eliminatedand (c) the disease becoming endemic, respectively. It isof utmost importance for us to know which values of theparameters lead to these three equilibrium points and par-ticularly, to the annihilation of the society. This is whatwe have discussed so far.We have found that in many cases, where the popula-tion of a country is more than the environment will sup-port (i.e. x > 1), and k is large, as is the case in manydeveloping countries of the world today, even a relativelylow value of y, the number of infected people in the coun-try, may force the solution to eventually go to the origin,a state which represents annihilation of the society (seeFigure 1). In these cases, the number of infected peoplebecomes very large for a while, and then the society getsannihilated. Perhaps this is what is happening in somecountries in Africa today. In Botswana, according to TheEconomist, “the age-distribution of Botswana’s populationwill change from the “pyramid” that is typical of countrieswith rapidly growing populations, to a “chimney-shaped”graph from which the young have been lopped out. Tenyears from now, according to figures released at the con-ference by USAID, the American government’s agency forinternational development, the life expectancy of some-body born in Botswana will have fallen to 29. In 20 years’time, the old will outnumber the middle-aged” [2]. Mostof the old people in a situation like this are infected peo-ple so that the number of infected people has become verylarge, just as our theory predicts.Before we congratulate ourselves however, we shouldlook at Proposition 1 above which says that if a+ α < k,then all solutions go to the origin. We estimated the valuesof these constants for five consecutive years 1995, 1996,1997, 1998 and 1999 from the data provided by HealthCanada and Statistics Canada. In each year we foundthat a+α < k (though each one of these three numbers isgoing down). According to this model, therefore, the newsfor Canada is not good. The medical advances are buyingus time for sure, but we must further reduce the value ofk and/or increase the values of a and α. In addition toimproving the methods of treatment and encouraging safesex, a higher rate of increase of (healthy) population iscalled for. For more details see [3].For Canada (and for any other society as well), the val-ues of a, k, and α for any given year may be estimated fromthe data on HIV/AIDS published by Health Canada [4].Also the estimates for the population of Canada are avail-able from Statistics Canada [5]. We found, however, thatthere was no data available on the number of HIV positivepeople who are alive at any given moment. We assumedthat one percent of HIV positive people die before theydevelop the AIDS disease (from accidents and such). Con-sidering that the HIV positive people are living longer andlonger, this is perhaps a reasonable hypothesis. The num-ber alive at any moment t would then be the total numberof HIV positive cases reported up to the time t (which wasavailable) minus one percent minus the total number ofdeaths from AIDS reported (which number was also avail-able). Based upon this data in any given year and thepopulation figures for the succeeding year, we estimatedthe number of HIV positive people in the succeeding year.In this manner, we estimated the number of HIV positivepeople in Canada for the years 1996, 1997, 1998, 1999, andthe year 2000. Thus the estimate for 1997 is based uponthe HIV data for 1996 and the population figure for 1997,similarly for all other years. In Table 1, we give theseestimates along with the actual numbers and the conse-quent error for the years 1995–1999. The actual numbersfor the year 2000 are not available at the time of writing(May 2001). We have assumed the population of Canadato be 30.7501 million in the year 2000 [5]. If the actualpopulation were different, then this estimate has to be re-vised. It should be noted that the error in any given yearis less than one half of one percent. Thus our estimatesare highly accurate.We also estimated the number of HIV positive peoplein Canada in 1996, 1997, 1998, 1999 and the year 2000based upon the HIV data for 1995 only and the popula-tion figure for each year. The results are given Table 2.The estimates are still highly satisfactory but not as goodas the previous ones.y 1996 1997 1998 1999 2000Estimate 26130 28005 30278 32306 34411Actual 26190 28110 30181 32253 n/a% Error .23 .37 .32 .16 n/aTable 1Vol. 5, Issue 2 Paci£c Institute for the Mathematical Sciences18y 1996 1997 1998 1999 2000Estimate 26130 27812 29603 31508 33536Actual 26190 28110 30181 32253 n/a% Error .23 1.06 1.92 2.31 n/aTable 2Acknowledgement: Computer programming help fromArunas Salkauskas (University of Calgary) is gratefully ac-knowledged.References:1. W. H. Hamer, “Epidemic disease in England”, Lancet,Vol. 1, pp.733–739.2. “A turning point for AIDS?”, The Economist, (July 15,2000)3. B. D. Aggarwala, “On two ODE models for HIV/AIDSdevelopment in Canada and a logistic seir model”, Re-search Paper #811, Departemnt of Mathematics andStatistics, University of Calgary, (May 2001).4. Surveillance Report to June 2000, Centre for Infec-tious Disease Prevention and Control, HIV and AIDSin Canada, (Nov. 2000).5. Cansim Retrieval Output, Quarterly estimates of popu-lation for Canada (2000).Vladimir Turaev and Gang Tian: PIMS Distinguished Chairs for 2001Vladimir Turaev (Strasbourg)Professor VladimirTuraev (Research Di-rector, CNRS IV,Strasbourg) is thePIMS DistinguishedChair at the Univer-sity of Calgary for themonths of July andAugust. He is givinga series of 6 lectureson Torsion Invariantsof 3-manifolds.Turaev has madeseveral seminal con-tributions to quan-tum invariants of 3-manifolds and topological quantumfield theory. His recent research has been motivated bythe development of topological quantum field theory byEdward Witten in 1988. Witten used the Feynman pathintegral in his construction, even though there is no rigor-ous mathematical justification for the path integral in thiscontext. Following the publication of Witten’s work, Tu-raev and Reshetikhin proved that a system of topologicalinvariants of 3-manifolds could be developed using the rep-resentation theory of quantum groups. In their work theyexploited a relationship between the representation theoryof quantum groups and solutions of the Yang-Baxter equa-tion of statistical mechanics. This allowed them to use thetheory of representations of the quantum group Uq(sl2(C))to define invariants of 3-manifolds. They then went on togive a rigorous construction of a topological quantum fieldtheory in dimension 3.Professor Turaev’s work has led to many advances inmathematics and physics. In particular, an understandingof the topological and geometric nature of quantum invari-ants is viewed by many to be essential for the deveopmentof a quantum theory of gravity.More information on Professor Turaev’s lec-tures at PIMS-UC is available on the webpagewww.pims.math.ca/science/2001/distchair/turaev.Gang Tian (MIT)PIMS is looking forwardto hosting Gang Tianas PIMS DistinguishedChair at UBC duringthe month of August,2001. Professor Tianis the Simons Professorof Mathematics at theMassachusetts Instituteof Technology. While atUBC, he will lecture onRecent Progress in Com-plex Geometry.Professor Tian’s re-search covers such di-verse areas as differential geometry, algebraic geometry,geometric analysis and partial differential equations. Hehas made fundamental contributions in each of these areas.In particular, he is well known for his work on the questionof existence and obstructions for Ka¨hler-Einstein metricson complex manifolds with positive first Chern class, forhis proof that the qantum cohomolgy ring is associative(joint with Y. Ruan) and for his work on higher dimen-sional dimensional gauge theory.Tian received the 19th Alan Waterman Award from theNational Science Foundation in 1994, the Oswald VeblenPrize in 1996 and was an Alfred P. Sloan Research Fellowfrom 1991–93.He has been invited to give many prestigious lec-tures around the world. A partial list includes the In-ternational Congress of Mathematicians in Kyoto (1990),the Bergmann Memorial Lecture at Stanford University(1994), the Courant Lecture at New York University(1996), Distinguished Visiting Lectures at the Univer-sity of Wisconsin (1996), Nachdiplomvorlesung Lectures atETH, Zu¨rich (1997), Myhill Lectures at New York StateUniversity, Buffalo (1998) and the Andrejewski Lecturesat Go¨ttingen University (1999).The lectures of both Professor Turaev and ProfessorTian will be videotaped and made available from the PIMSstreaming video webpage, www.pims.math.ca/video.Paci£c Institute for the Mathematical Sciences Summer 200119Industrial and Scienti£c Training ActivitiesIAM-CSC-PIMS Senior UndergraduateMath Modelling WorkshopPIMS-UBC and PIMS-SFUFebruary 17–18, 2001The annual SFU-UBC-PIMS Senior Undergraduate MathModelling Workshop was held on February 17 and 18, withSaturday’s portion organized by UBC’s Institute for Ap-plied Mathematics and Sunday’s by SFU’s Centre forScientific Computing. The students came from acrossCanada — Acadia, University of Western Ontario, Uni-versity of Alberta, University of Calgary, University ofBritish Columbia, Memorial University of Newfoundland,McGill University, University of Toronto, York University,and SFU.On Saturday, the students were given the choice ofworking on one of three projects: Nonlinear Heat Conduc-tion in the Microwave Heating of Ceramics with MichaelWard (Math, UBC), An Analytical and Numerical Study ofSolitary Waves (Solitons) with Bernie Shizgal (Chemistry,UBC and Director of the Institute for Applied Mathemat-ics) or Modelling the Flight Path of a Softball with DouwSteyn (Earth and Ocean Science, UBC).On Sunday, the students were given the choice of par-ticipating in one of two projects: Liquid Mobility in FuelCells run by Keith Promislow (Math, SFU) with help fromRon Haynes (Math Ph. D. student at SFU) or Visualiz-ing A Snowstorm run by Dave Muraki (Math, SFU) andTorsten Moeller (Computing Science, SFU).Both days of the workshop were highly successful, withthe mentors being rewarded by an enthusiastic and livelyresponse from the students. For more information, seewww.pims.math.ca/industrial/2001/suimw.Participants in the IAM-CSC-PIMS Senior UndergraduateMath Modelling Workshop.3rd PIMS Fluid Dynamics Summer SchoolPIMS at the University of AlbertaMay 27 – June 8, 2001Eighteen graduate students from all over the world at-tended a comprehensive series of lectures, and were givenhands-on experience performing and analyzing experi-ments in the Environmental and Industrial Fluid Dynam-ics Laboratory, as well as running numerical simulationsusing research-level codes. Topics included fluid dynam-ics fundamentals, industrial and environmental flows, geo-physical fluid dynamics, turbulence modelling and com-putational fluid dynamics. Subjects were all taught at agraduate level.This year’s summer school was particularly reward-ing for the students since it was held in conjunction witha PIMS Thematic Programme on Wave Phenomena andFluid Dynamics. Special invited speakers were T. G. Shep-herd (Univ. of Toronto) who spoke on The Fluid Dynam-ics of the Middle Atmosphere and H. J. S. Fernando (Ari-zona State) who spoke on Turbulence and Mixing in StablyStratified Fluid Layers.The Core Lecturers for the courses were JohnC. Bowman (Univ. of Alberta), Turbulence Modelling ;Andrew B. G. Bush (Univ. of Alberta), Climate Mod-elling ; Peter Minev (Univ. of Alberta), ComputationalFluid Dynamics; T. Bryant Moodie (Univ. of Alberta),Wave Theory ; Bruce R. Sutherland (Univ. of Alberta),Stratified Flows and Gordon E. Swaters (Univ. of Al-berta), Physical Oceanography.PIMS/MITACS UndergraduateIndustrial Case Study WorkshopCentre for Operations Excellence at UBC,October 25–29, 2001Selected students in the summer preceding their se-nior year are invited by PIMS and MITACS to com-pete in a 3-day industrial case study competition. Fif-teen students from across North America, in under-graduate programmes such as Engineering, Mathe-matics, Statistics, Computer Science and Economics,will be chosen for this intensive three-day industrialcase study competition. Business problems will beselected to require mathematical analyses, comple-mented with problem formulation, problem solving,and presentation skills.This workshop is designed to:• Introduce students to current research initiativesand industrial problems in the operations researchsector.• Provide a unique opportunity for students to workin teams to solve challenging problems with math-ematical and business content.• Allow industry executives the opportunity to be-come acquainted with students and evaluate themfor potential future employment.• Inform students of the exciting opportunities forgraduate studies in applied math and operationsresearch.For more information and registration please seehttp://pims.math.ca/industrial/2001/uicsw.Vol. 5, Issue 2 Paci£c Institute for the Mathematical Sciences20Statistical Genetics and Computational Molecular BiologyUniversity of Washington, December 16–18, 2001The programmes in Statistical Genetics and Compu-tational Molecular Biology at the University of Wash-ington will host a Workshop in Statistical Genetics andComputational Molecular Biology. The workshop is aimedat students from the mathematical, computational, andstatistical sciences who may be considering graduate studyand research in these areas of mathematical and compu-tational biology. The intended participants are primarilyundergraduate seniors or first-year graduate students atColleges and Universities of the Pacific Northwest Regionor Western Canada. PIMS will provide support for grad-uate students from the PIMS universities.Topics will be in computational molecular biology,genomics, statistical genetics, and bioinformatics. Lec-tures will be given by: David Baker (Biochemistry,Univ. of Washington) Protein Structure Prediction; JoeFelsenstein (Genetics, Univ. of Washington); JinkoGraham (Statistics and Actuarial Science, SFU) Test-ing and Estimation of Recombination Breakpoints in a Setof Aligned Sequences; Phil Green (Molecular Biotech-nology, Univ. of Washington) Analyzing Genome Se-quences; Kathleen Kerr (Biostatistics, Univ. of Wash-ington) Gene Expression Microarrays: Classical Statisticsand Modern Genomics; Leonid Kruglyak (FHCRC);John Mittler (Microbiology, Univ. of Washington);Stephanie Monks (Biostatistics, Univ. of Washington);Jim Mullins (Microbiology, Univ. of Washington) Ge-nomics is Solving Problems in Infectious Diseases; May-nard Olson (Univ. of Washington Genome Center) Rese-quencing Segments of the Human Genome: Experimentaland Statistical Considerations; Steve Self (or other repre-sentative from the Bioinformatics Group of the FHCRC);Elizabeth Thompson (Statistics, Univ. of Washington)Inferring Gene Locations from Genetic Data on Pedigrees;Martin Tompa (Computer Science and Engineering,Univ. of Washington) An Exact Algorithm to Identify Mo-tifs in Orthologous Sequences from Multiple Species; andEllen Wijsman (Division of Medical Genetics, School ofMedicine, Univ. of Washington).For more information please see: depts.washington.edu/statgen/Statgen/workshop.shtml.PIMS Postdoctoral Fellows for 2001/02The following PIMS postdoctoral fellows were selectedfor the year 2001/2002. The members of the reviewpanel were Gordon Slade (chair, UBC), Pauline van denDriessche (University of Victoria), Richard Lockhart(SFU), Robert Moody (University of Alberta), NickPippenger (UBC) and Rex Westbrook (University ofCalgary).Yuqing Wang: mathematical biology. Supervised byRobert Miura (Math, UBC) and Yue-Xian Li (Math,UBC).Luis Lehner: general relativity, numerical relativ-ity and quantum gravity. Supervised by Bill Unruh(Physics, UBC) and Matt Choptuik (Physics, UBC).Antal Jarai: mathematical physics (percolation the-ory). Supervised by Gordon Slade (Math, UBC).Kazuyuki Furuuchi: theoretical physics (string the-ory). Supervised by Gordon Semenoff (Physics,UBC).Joachim Stadel: numerical astrophysics. Super-vised by Julio Navarro (Physics, UVic) and Arif Babul(Physics, UVic).Inhyeop Yi: dynamical systems and operator algebras.Supervised by Ian Putnam (Math, University of Victo-ria).Nils Bruin: number theory and arithmetic algebraicgeometry. Supervised by Peter Borwein (Math, SFU),David Boyd (Math, UBC), Imen Chen (Math, SFU),Rajiv Gupta (Math, UBC) and Nike Vastal (Math,UBC).William Galway: computational number theory. Su-pervised by Jonathan Borwein (Math, SFU), Peter Bor-wein (Math, SFU), Imin Chen (Math, SFU), StephenChoi (Math, SFU) and Petr Lisonek (Math, SFU).Sumati Surya: quantum gravity. Supervised byKristin Schleich (Physics, UBC), Don Page (Physics,University of Alberta) and E. Woolgar (Math, UA).Matthias Neufang: functional analysis, harmonicanalysis and operator algebras. Supervised by VolkerRunde (Math, University of Alberta).Wen Chen: signal and image processing. Supervisedby Bin Han (Math, University of Alberta) and Rong-Qing Jia (Math, University of Alberta).Roman Vershynin: geometric functional analysis. Su-pervised by Nicole Tomczak-Jaegermann (Math, Uni-versity of Alberta).Christina Cobbold: mathematical biology. Super-vised by Mark Lewis (Math and Biological Sciences,University of Alberta).Luigi Santocanale: computer science and categorytheory. Supervised by Robin Cockett (Computer Sci-ence, University of Calgary).Peter Hoyer: algorithmics, data structures, complex-ity theory and quantum computing. Supervised byRichard Cleve (Computer Science, University of Cal-gary).Jorgen Rasmussen: conformal field theory and Kac-Moody algebras. Supervised by Mark Walton (Physics,University of Lethbridge).Paci£c Institute for the Mathematical Sciences Summer 200121Education ActivitiesMathCounts Vancouver IslandCompetitionContributed by David Leeming,UVic PIMS Education CoordinatorMathCounts Vancouver Island is a regional compe-tition, which is part of MathCounts British Columbia.Sponsored locally by the Association of Professional En-gineers and Geoscientists of BC (APEGBC) and PIMS, itprovides a combination of math coaching and a competi-tive programme for students in grades eight and nine.The 2001 competition was held on Friday, Febru-ary 9 at Lambrick Park Secondary School in Victo-ria. Teams of four students competed in various rounds todetermine the team and individual winners. There weresix grade eight and seven grade nine teams in this year’scompetition. The competition concluded with the excitingCountdown Round. This year, the top grade eight teamwas Cedar Hill Junior Secondary (Green) Team andthe top grade nine team was Lambrick Park Secondary(IBS) Team. The top grade eight individual was JeremyLi Foa Wing of Cedar Hill and the top grade nine indi-vidual was Kailyn Young of Lambrick Park. The gradenine team from Mt. Klitsa Junior Secondary Schoolin Port Alberni travelled the furthest to take part in theregional competition. David Leeming, UVic PIMS Ed-ucation Coordinator, was the Site Coordinator and LeoNeufeld of Camosun College (retired) was the Head Judge.The event was co-hosted by James Bernldez and Jan Buer-mans of APEGBC along with the support of many volun-teers from APEGBC, Camosun College and the Universityof Victoria.Math Mania at Sir James DouglasElementary SchoolContributed by David Leeming,UVic PIMS Education CoordinatorMaking bubbles withDr. Denny Hewgill.Another very successful MathMania Event was held at SirJames Douglas Elemen-tary School in Victoria onFebruary 28, 2001. Math Ma-nia provides interactive dis-plays, games and art alongwith hands-on activities in-cluding soap-bubbles, mathe-matical puzzles and paradoxesall showing kids and parentsfun ways to learn math andcomputer science concepts.This event, sponsored byPIMS, was attended by overtwo hundred students, parentsand teachers. Our outstand-ing volunteers included Dr. Pauline van den Driessche, Janand Paul Nienaber, Dr. Julie Zhou, Dr. Denny Hewgill andMerilyn Hewgill, Kelly Choo, Irina Gavrilova, Dr. FlorinDiacu, Elies Hoepner, Jeff Campbell, Charlie Burton,Elena Prieto, Shaun Pack, James Andersen, Peter An-derson, Geoff Schmidt, Dr. David Leeming, Mike Crowleand Dr. Rod Edwards. Enthusiastic family members andfriends of the faculty, graduate students and undergradu-ate students of the University of Victoria contributed tomaking this event a success.Students at Sir James Douglas Elementary School enjoy MathMania.Victoria’s Fourth Annual FAME Builds onSuccessContributed by David Leeming,UVic PIMS Education CoordinatorFor the fourth consecutive year, students in the GreaterVictoria School District participated in FAME, the For-ever Annual Mathematics Exhibition. It was held atS. J. Willis School on April 21, 2001. This year, therewere over eighty entries at three levels: Elementary (upto grade 7), Junior (grades 8-9) and Senior (grades 10-12). The event was organized by Wendy Swonnell, BettyDoherty, Betty McAskill and Tanis Carlow and was spon-sored, in part, by the Pacific Institute for the Mathemati-cal Sciences.The exhibits presented at FAME are judged for cre-ativity, skill, dramatic value and mathematical thought.For the first time this year, every entrant was given anaward — the categories being Distinction, First Class andRunner Up. A School trophy is presented at each level (El-ementary, Junior and Senior) based on the best aggregatescore of the top three projects. With more schools partic-ipating in FAME each year, this annual event will con-tinue to attract outstanding mathematical exhibits fromstudents in a wide range of grades.Vol. 5, Issue 2 Paci£c Institute for the Mathematical Sciences22Changing the Culture 2001The Fourth Annual Changing the Culture Confer-ence was held at SFU, Harbour Centre on May 11. Thisannual conference, sponsored by PIMS, brings togethermathematicians, mathematics educators and school teach-ers from all levels to work together towards narrowing thegap between mathematicians and teachers of mathematics.The theme was Writing, Speaking and Thinking Mathe-matics. The conference explored connections between nu-meracy and literacy, mathematics and language, mathe-matics and literature, and how we can use language toteach mathematics. There were two plenary talks:Mathematics and Literature: Cross Fertilization by BrettStevens, PIMS/IBM PDF, SFU.Breaking the Cycle of Ignorance by John Mighton, NSERCpostdoctoral fellow at the Fields Institute for Research inMathematical Sciences.John Mighton is the founder and coordinator of JUMP,Junior Undiscovered Mathematical Prodigies, an educa-tional no-cost outreach program for students who are do-ing badly in mathematics in school. This program hasbeen very successful and is rapidly gaining momentum inToronto. John talked about his experiences with JUMPand how to make math accessible for kids whom the stan-dard methods have not reached. John is also a Governor’sGeneral award winning playwright. Robert LePage’s lat-est film, Possible Worlds, was adapted from one of hisplays, and he was a math consultant and actor in GoodWill Hunting. He is also a professional mathematician atthe Fields Institute.Each participant was able to attend two of the follow-ing workshops:1. JUMP: Junior Undiscovered Mathematical Prodigiesprogram. Leader: John Mighton2. Contextualizing Mathematics. Leader: Brett Stevensand Karen Meagher3. Connecting Early Numeracy and Literacy. Leaders:Cynthia Nicol and Heather KelleherFor further information, see the webpagewww.pims.math.ca/education/2001/ctc. Both ple-nary lectures are available via streaming video from thiswebpage.Mathematics Projects in the Greater Vancouver Regional Science FairContributed by Natasˇa Sirotic´.The 2001 Greater Vancouver Regional Science Fair(GVRSF) took place at UBC, April 5–7. It held 26projects within the Mathematical/Computer Sciences ex-hibit category. Within this category, there were 2 com-puter science projects while all others were mathematical.In terms of the grade-level distribution, there were 10junior projects (grades 7, 8), 10 intermediate (grades 9,10), and 6 senior (grades 11, 12). Projects came from thefollowing schools: University-Hill Secondary, Point GreyMini School, Britannia Secondary School, York House,Collingwood School, Sir William Osler Elementary School,Windermere Secondary, and Vancouver Technical.This is the third time that PIMS provided assistanceand expertise to promote mathematics projects develop-ment within the GVRSF by informing and involving math-ematics teachers, giving presentations and workshops togroups of students, helping and providing assistance tostudents that have undertaken mathematics projects, andby judging and awarding the projects. The special awardjudges for PIMS were David Boyd, Klaus Hoechsmann,Leah Keshet, and Sandy Rutherford.Although participation did not increase (there were 26math projects last year as well) we have witnessed a signifi-cant increase in the quality of projects. Two of the projectsmade it into the Canada Wide Science Fair in Kingston,Ontario,and won multiple awards even at this very toplevel. These projects were “Trees A Math Lesson fromNature” by Christine Pop from Sir William Osler Ele-mentary and “Calculating Equilateral Triangles within anEquilateral Triangular Grid” by Mahmoud Bazarganfrom U-Hill Secondary.Mahmoud Bazargan’s project set out to determine howmany triangles there are inside a general equilateral trian-gular grid without having to count them. He split theproblem into considering those triangles that face upward-sand those that face downwards, and then by analyzingthe pattern for the various triangle sizes within the gridhe found a general formula.Christine Pop’s project was remarkably outstanding,and so in her words it is outlined:“The purpose of my project is to find out if I can geo-metrically model natural objects and describe their shapesand motions using mathematical concepts.There are two options I can work with: classical Eu-clidean geometry or new fractal geometry. Since Euclideangeometry deals strictly with the zero-dimensional point,the one-dimensional line, the two-dimensional plane, andthe three-dimensional solid, the crinkly motions of naturecannot be defined in a satisfactory waywithin such rigidlimits. Fractal geometry, though, deals with looking atobjects of non-integer dimensions that are seen as dynam-ical systems, systems that form a result using iteration.Therefore, fractal geometry will serve best for my pur-pose, because nature itself does not contain any perfectlystraight lines or flat planes. Nature is a fractal that canbe modelled by fractal geometry, thus supporting my hy-pothesis, that I will be able to describe natural objectswith math.The natural object I decided to use is the tree. I canPaci£c Institute for the Mathematical Sciences Summer 200123geometrically compose this using the properties of frac-tals to show that a tree grows under the different laws offractal geometry. These properties are self-similarity andreduction or factor-scaling, which are both implied in theiterated process that creates a fractal. I can use theseguidelines to create my tree structure. The main reasonfor choosing the tree is that it is a beautiful creation thatcan be represented from various perspectives ranging froma scribbled stick figure by a kindergarten child to a paint-ing by a famous artist.As a context for my research and findings, I composeda list of simple tree structures made up of mathematicalconcepts: the decimal tree, the H-fractal (tree), the binarytree, and the Pythagoras Tree. Spirals and geometric se-quences are also an important part of my project becausethe Pythagoras Tree expresses these concepts.Focusing only on the Pythagoras Tree, I tried to findout under which law it grew. The basic construction ofthis fractal consists of the association of three squares that,joined together, use the Pythagorean theorem, a2+b2 = c2.Using a, b, and c as the sides of the first right triangle andangle α and β (or pi/2−α) of that triangle, the operationwould have to repeat indefinitely to show the transforma-tions of the left and right rotations.As part of my project, I determined, a general rule, thegeometric sequence that takes place in the spirals of thePythagoras Tree. The common ratio, also identified as thereduction factor, helped me calculate the sum of the termsof the geometric sequence, which is in fact the total lengthof the spiral formed by each branch of the Tree.Modifying angle α of the right triangle introduced afirst degree of liberty, which led to interesting ‘compos-ite trees’, altered versions of the original Pythagoras Tree.Using an obtuse isosceles triangle and an equilateral one,a tree that looks like broccoli and periodic tiling, respec-tively, is formed. Connected to changing the angle, I alsomodelled a visual representation of the Tree when α was 90degrees and 360 degrees, in both cases keeping the originalmeasurements for the squares.Introducing a different orientation of the triangle gavean even higher degree of liberty because the tree couldbe changed so that it looked more like a fir tree than amaple one. This new degree of freedom implies random-ness and overlapping. I saw how the trees’ growing law wasinfluenced, calculated the length of the similarity trans-formations, and looked for patterns in the way that the‘branches’ overlapped.As stated in my hypothesis, through fractal geome-try, I can successfully model the shape and movement ofnatural objects. Paradoxically, complex fractal graphicsare derived from simple mathematical equations. The se-cret to making fractals is to explore to infinite depths.By choosing the tree structure to exploit my research andbasing it on fractal geometry, I could record the imagesof its movements in space. They are pictures of the waythings fold and unfold, feeding back into each other andinto themselves.Fractal geometry is still a young field in math. In myproject, I looked only at the primary formulas without go-ing too much in depth. Like fractals, I am still young,but even at this stage, I realize that not only do fractalshave interesting aspects and patterns, but that they willprove to be a new way of looking at the world around us.Fractals, for sure, will enhance our appreciation of math’saustere beauty.”Westwood Students Enjoy Mathematics UnpluggedContributed by Pam Hagen.Christian Price (centre) with his siblings Jordanand Christina.Westwood Elementary School students recently took part in their annualmath conference, Mathematics Unplugged. PIMS has supported thisevent since its beginning and this was the fifth Math Unplugged. Theschool is in Port Coquitlam, British Columbia, and has approximately250 students.The event is styled just like an adult conference with a keynotespeaker followed by workshops for the students to attend during theday. The keynote speaker has a difficult job to do as he/she needs tobe able to hold the attention of students from K – G5 for at least 30minutes and make it fun and interesting. This year every student wenthome with a tangram set, and a copy of the Tangram story.The goal of this event is to try to lay an enjoyable and fun foundationfor further mathematical awareness and engagement, which can last alifetime.Klaus Hoechsmann, PIMS Education Coordinator, helped plan the conference and visited the school on the day. Hishelp was very much appreciated.The conference was a success with the students who participated in it. One student replied when told it was time togo out to recess, “Oh, do we have to go out to recess, Math Unplugged is so much more fun!” Christian Price who is inG3 particularly enjoyed the event. He is shown, with his older brother and younger sister, holding the thank you picturehe made for the PIMS office. He used his tangram set on the picture.Vol. 5, Issue 2 Paci£c Institute for the Mathematical Sciences24PIMS ELMACON 2001Contributed by Krisztina Va´sa´rhelyiThe third annual PIMS Elementary Grades MathContest (ELMACON) took place on May 26th at UBC.This contest is organised by PIMS under the guidance ofDr. Cary Chien of David Thompson Secondary School incollaboration with the BCAMT and volunteers from LowerMainland schools of all levels. It is open to students ingrades 5 to 7 and it is designed to complement the popu-lar MathCounts competition for higher grades.A total of 223 students attended the contest this year,a substantial increase from last year, with 73, 80 and 70students in grades 5, 6 and 7, respectively. This year weimplemented an improved online registration procedure al-lowing students to sign up for the contest as well as todownload their admission tickets.The format of the contest followed the formula of pre-vious years. Students competed in three divisions in thesprint, target and countdown rounds. The sprint and tar-get rounds consisted of two sets of written questions whichwere evaluated immediately while contestants enjoyed re-freshments and listened to a lively presentation of problem-solving strategies.In the countdown round, the top ten students in eachdivision— determined by combined scores from Sprint andTarget rounds (with correct answers in the latter count-ing double)—participated in individual competitions. Thetenth ranking student competed against the ninth, thewinner then faced the eighth, and so on. A projector dis-played one question at a time, and the contestants wererequired to ring a buzzer—within a certain time limit—as soon as they had an answer. A correct answer, scoreda point; otherwise the opponent had the rest of the timelimit to come up with the solution. This was repeated sev-eral times to determine which of the two could advance.Eventually an overall winner was found.Each contestant received a score between 0 and 49based on the written competition alone. The score was cal-culated by adding their Sprint Round score (0–25) to dou-ble their Target Round score (0–24). The average scoresfor grades 5, 6 and 7 were 19, 20 and 20.5, respectivelyand a score of 27, 25 and 27 for these grades was enoughto place a contestant in the top 25%.The lists below show the top 10 winners in each grade.The top ten finishers received a commemorative T-shirtand medal, together with a stylish binder donated by theBC Association of Mathematics Teachers. The top threealso received a trophy, and an electronic calculator.Grade 5: 1. Jimmy He, 2. Sherwin Kwan, 3. AramEbtekar, 4. David Lam, 5. Bryan Huang, 6. Simon T.H.Tseng, 7. Christin Chan, 8. Sara Hyunjung Kim, 9. AlanTung, 10. Tiffany Le Gentil.Grade 6: 1. Steven Karp, 2. Arthur Yip, 3. Arthurda Silva, 4. Jason Ng, 5. Connor Joseph Wagner, 6. Ser-ena Ip, 7. David Di, 8. Rickey Tam, 9. Nestor Choi, 10.Sviatoslav Moldavanov.Grade 7: 1. Sam Wang, 2. William Wanki Kim, 3. Di-ane Wu, 4. Steven Hermann, 5. Yoshiaki Sono, 6. HowardYan, 7. Carter (Wan Jae) Lee, 8. Fanhao Meng, 9. JeffreyNguyen, 10. Isaac TangOverall, the contest was a success. About 50 on-sitevolunteers from the UBC Science Ambassadors Program,various schools throughout BC as well as some parentshelped the organising committee stage the event. NineEL531VB scientific calculators which were awarded to thetop three students in each grade, were donated by Sharp.The New Issue of Pi in the SkyThe June 2001 issue of Pi in the Sky includes We’veGot Your Number by Ted Lewis, Have You Used Ille-gal Drugs Lately? or How to Ask Sensitive Questionsby Carl Schwarz, and Constructing Fractals in Ge-ometer’s SketchPad by Michael Lamoureux. Thesearticles explain how visa card companies, for exam-ple, determine whether or not you have entered avalid number, the ideas behind randomized responsesurveys, and how to build fractals using Geometer’sSketchPad software. The magazine also features ar-ticles about the history of algebraic equations, theFields Medal and famous physicists who started outas mathematicians. There is also the usual excitingand challenging collection of mathematical exercisesincluding problems about the principle of mathemat-ical induction.This time students from Old Scona AcademicHigh School in Edmonton are featured on the cover.Paci£c Institute for the Mathematical Sciences Summer 200125The Women and Mathematics Poster CampaignContributed by Krisztina Va´sa´rhelyiThe February poster featuring Hypatia of Alexandria. Ada Lovelace, namesake of the computer language Ada.In February 2001, PIMS launched a new contest serieswith the title of Women and Mathematics. A posteris displayed on the PIMS website each month featuring afamous woman who contributed significantly to the math-ematical sciences. The posters are accompanied by a quizconsisting of four questions about the life and work of thefeatured mathematician.The concept of the present campaign is similar to theprevious one but with a few key differences. This year,mathematical problem-solving is still a component of thecontest, but it is not the only focus. The posters them-selves depict images of the women featured but in mostcases, the goal is also to use visual communication to con-vey something about the mathematical contributions ofthe featured individual. An intriguing quote is also a re-peating component of the posters, which do not revealthe identity of the person involved but are designed in-stead to attract viewers to the website and explore further.The contest website typically includes four questions eachmonth. Each question is introduced by some backgroundinformation to set the context. Links to biographical re-sources are given on the webpage where the answers tothe three biographical questions can be found. The fourthquestion always involves mathematical problem-solving. Itis chosen to complement the biographical information andit is in some way related to the mathematician’s area ofspecialisation.This year the posters are not displayed on the busesbut instead they are distributed to schools in BC, Albertaand in Washington State. The theme is highly appropriatefor high school students, especially girls, who stand beforemajor decisions regarding a course of study to follow atuniversity. The feeling that mathematics is dry and bor-ing or too difficult is still highly prevalent among this agegroup. The main objective of the “Women and Mathe-matics” campaign is to show that women who engaged inthe study and application of mathematics often lived fas-cinating lives. Thus these women may serve as role modelsfor young people who are inclined to judge mathematicaloccupations and mathematicians in a negative light.The stories of the colourful and often dramaticlives of the women featured in this contest provideApril featuring Olga Taussky-Todd.plenty of ma-terial for chal-lenging negativeconcepts aboutmathematicians.The first contestof the series inFebruary told thetale of Hypa-tia of Alexan-dria. Hypa-tia, who livedaround 400 AD,was the daugh-ter of Theon, amathematicianand philosopherhimself. She waslegendary in herown time for herintellect, integrityof character, andgreat physicalbeauty. Her lifeended tragically when she was murdered by a mob fearfulof the concept of critical and independent thought whichshe symbolised.Everyone is familiar with the famous poet Lord Byronbut perhaps not many are aware that his daughter, AdaLovelace, was a talented mathematician also. Ada was avibrant character who died young at 36, just like herVol. 5, Issue 2 Paci£c Institute for the Mathematical Sciences26The May poster designed by Jeni Rae Duschak. Grace Hopper developed the computer language COBOL.father. Her vivid imagination allowed her to play with ab-stract concepts of “poetical science” in the context of fu-ture possibilities. Her collaboration with Charles Babbageresulted in what now many call the first computer pro-gram ever written. Ada Lovelace was the subject of theMarch contest. Olga Taussky-Todd, multitalented inher youth, and growing up to be a brilliant mathematician,was presented in April, followed by the dynamic GraceHopper, an officer of the Navy, the inventor of COBOL,who was featured in June.Her life might have been the subject of a storybook:Sophie Germain dressed up as a man to be admitted tothe E´cole Polytechnique where her mathematical geniuswas discovered, and she was the secret saviour of Gauss,whose life was threatened during Napoleon’s invasion. InMay, PIMS was treated to a special poster-presentation ofSophie Germain. Jeni Rae Duschak, a young Americanartist who studied mathematics and liberal arts, gener-ously donated her time to produce a beautiful poster forthe contest, featuring her illustration of Sophie Germainin an appealing animation-style. Jeni Rae has a websiteabout Sophie’s life which includes a biography that shetells as a story illustrated with her drawings. Our dis-covery of her site led to an enjoyable collaboration whichresulted in the special poster. The June contest websiteincludes a profile of Jeni Rae which describes her personalcampaign to raise young women’s awareness of the impor-tance of mathematics.The contest for July features Florence Nightingale,another remarkable personality. She rejected the privilegesof her class and the comforts and security of a conventionallifestyle. Following lengthy struggles with her family, sheset out to pursue her training in nursing and eventuallyled a team of 38 nurses to care for wounded soldiers of theCrimean war. A deeply spiritual person,Florence Nightingale was also a realist who had a greatappreciation and love of mathematics. It was her abilityto quantify and visually represent data on public healthand social issues which lead to groundbreaking changesand eventually earned her wide public recognition and re-spect, including the honour of being elected as a fellow ofthe Royal Statistical Society.As for Mathematics is Everywhere, the presentcontest attracts a varied audience, with a wide age-span, as well as an expanding geographic range. On thewhole, male and female participation is approximatelyequal. The February winner was Wayne Matthews,a 56 year old mathematics instructor at CamosunFlorence Nightingale was infuential inthe application of statistics.College in Vic-toria, BC. Heteaches pre-calculus and cal-culus and triesto communicatehis enjoyment ofmathematics tohis students. Helearnt about thecontest from Piin the Sky mag-azine, and sincehe enjoys stay-ing active andinformed, he de-cided to enter,and had fun do-ing so. Jan Han-nemann was thewinner in March.Jan is German,but he is cur-rently living inVancouver com-pleting his PhD in Computer Science at UBC. He is 27years old and he also enjoys snowboarding and music. HisDiploma from Germany is in Applied Systems Science.He has been following the contests on the website sincehe first saw the posters last year on Vancouver’s publicbuses.Please see Women page 28.Paci£c Institute for the Mathematical Sciences Summer 200127Women and MathematicsContinued from page 27.Wayne Chevier (29) from Langley, BC, won in April. Wayne is along-time fan of the PIMS contests and he was also one of the win-ners last year. He has a wide range of interests including computers,mathematics, sciences, linguistics, science fiction and fantasy, andmusic. He says that he enjoyed the present contest as he learnt quitea bit about the history of mathematics. The May winner, ChrisDieterle is a 15 years old grade 10 student from London Ontario.He is interested in physics, astronomy and (of course) mathematics,as well as music, baseball and long-distance running. He also enjoysreading, especially good mysteries, and good science fiction. He alsoplans to make a telescope this summer. He found out about thePIMS website and the contest in the fall when he read a little writeup about it in the Kitchener Record, the local newspaper. He foundthe contest interesting and challenging at the same time and plans tocontinue to participate. Rebecca Oulton from Acadia Universityin Wolfville, Nova Scotia won in June. She is a 20 year old uni-versity student in her third year in Mathematics and Statistics withBusiness. She is currently working for the Mathematics and Statis-tics Department at Acadia for the summer. She also likes, walking,reading, playing sports, socialising with friends, and spending timewith her family. She discovered the contest by chance as she wasexploring the PIMS website while searching for interesting links toadd to her department’s site. In her own words: “I really enjoythese monthly contests and feel that it will increase the awarenessof not only mathematics but also the role of women in mathemat-ics. So naturally I have it bookmarked and am looking forward toparticipating again this month.”Nobel Prize winning theoretical physicist Maria Goeppert-Mayer.Physicist Maria Goeppert-Mayer features on the Augustposter. She received her doctorate in theoretical physics in 1930Germany under the tutelage of Max Born. When she moved to theUnited States with her husband she had to take an unpaid “volun-tary” teaching position, and did not hold a paying, full universityprofessorship until she was 53. In 1963, Maria Goeppert-Mayer wasawarded the Nobel Prize jointly with Hans Jensen for their work onthe shell model of nuclear structure. The award was for the discov-ery of the magic numbers and their explanation in terms of a nuclearshell model with strong spin-orbit coupling.PIMS Contact ListDirector: Dr. N. GhoussoubAdmin. Asst: Jacquie BurianPhone: (604) 822–9328, Fax: 822–0883Email: director@pims.math.caSFU-site Director: Dr. R. RussellAdmin. Asst: Fuyuko KitazawaPhone: (604) 268–6655, Fax: 268–6657Email: sfu@pims.math.caUA-site Director: Dr. B. MoodieAdmin. Asst: Shirley MitchellPhone: (780) 492–4308, Fax: 492–1361Email: ua@pims.math.caUBC-site Director: Dr. D. RolfsenAdmin. Asst: Leslie MacFaddenPhone: (604) 822–3922, Fax: 822–0883Email: ubc@pims.math.caUC-site Director: Dr. G. MargraveAdmin. Asst: Marian MilesPhone: (403) 220-3951, Fax: 282-5150Email: uc@pims.math.caUVic-site Director: Dr. F. DiacuPhone: (250) 472–4271, Fax: 721–8962Email: uvic@pims.math.caUW-site Director: Dr. T. ToroAdmin. Asst: Mary SheetzPhone: (206) 543–1173, Fax: 543–0397Email: uw@pims.math.caScientific Executive Officer: Dr. A. RutherfordPhone: (604) 822–1369, Fax: 822–0883Email: sandy@pims.math.caEducation Coordinator: Dr. K. HoechsmannPhone: (604) 822–3922, Fax: 822–0883Email: hoek@pims.math.caAsst. to the Director: Katrina SohPhone: (604) 822–6851, Fax: 822–0883Email: katrina@pims.math.caPIMS/MITACS Website Manager: Kelly ChooPhone: (250) 472–4927, Fax: 721–8962Email: chook@pims.math.caComputer Systems Manager: Shervin TeymouriPhone: (604) 822–0410, Fax 822-0883Email: shervin@pims.math.caComputer Systems Manager: Brent KearneyPhone: (604) 268-6654, Fax: 268-6657Email: brentk@pims.math.caCommunications Officer: Heather JenkinsPhone: (604) 822–0402, Fax: 822–0883Email: heather@pims.math.caPIMS-MITACS Admin. Asst., UBC: Clarina ChanPhone: (604) 822-0401, Fax: 822–0883Email: clarina@pims.math.caPIMS-MITACS Admin. Asst., UA: Lisa HarabaPhone: (780) 492-4835, Fax: 492–1361Email: lharaba@math.ualberta.caNewsletter Editors: A. Rutherford and H. JenkinsThis newsletter is available on the world wide webat www.pims.math.ca/publications.PIMS is supported by:• The Natural Sciences and EngineeringResearch Council of Canada• The Alberta Ministry of Innovationand Science• The British Columbia Information,Science and Technology Agency• Simon Fraser University, University ofAlberta, University of British Columbia,University of Calgary, University ofVictoria, University of Washington,University of Northern British Columbiaand University of Lethbridge.Vol. 5, Issue 2 Paci£c Institute for the Mathematical Sciences28

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