FIELDSNOTES. Barbara Lee Keyfitz: Director elect. The National Program on Complex Data Structures (NPCDS)

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1 FIELDSNOTES MAY 2004 I VOLUME 4:3 FIELDS INSTITUTE Research in Mathematical Science FIELDS Barbara Lee Keyfitz: Director elect BARBARA LEE KEYFITZ HAS BEEN appointed as the new Director of the Fields Institute. She will begin her term on July 1, 2004, succeeding Kenneth R. Davidson who will return full-time to the University of Waterloo. Dr. Keyfitz is the John and Rebecca Moores Professor of Mathematics at the University of Houston. She was born in Ottawa during the time her father, renowned demographer Nathan Keyfitz, was at what is now known as Statistics Canada. After graduating from the University of Toronto, she received a PhD in 1970 at the Courant Institute of NYU under Peter Lax, and served on the faculties of Columbia, Princeton and Arizona State before being appointed at Houston in She has also held visiting positions at many institutions in the U.S., including Berkeley, Brown, and Duke, as well as in France and China. Keyfitz has made profound and original contributions to applied mathematics, particularly in the study of nonlinear partial differential equations and of fluid flow and transonic shock waves. She has served on the editorial boards of many journals, and has been very active in many different capacities in the American Mathematical Society, NSF and NSERC most recently as a member of the College of Reviewers for the Canada Research Chairs Program. She served as a vice-president of SIAM during and is currently Chair of its Activity Group on Analysis of PDE. She was appointed a Fellow of the American Association for the Advancement of Science in 1992, and is chair elect of their mathematics section. She was recently awarded the Canadian Mathematical Society s Krieger-Nelson Prize, and is incoming President of the Association for Women in Mathematics. Keyfitz is no stranger to the Fields Institute. She along with husband Marty Golubitsky, were visiting members during Barbara Lee Keyfitz the first year of the Institute s existence, in the winter/spring of She served as a member of the Scientific Advisory Panel in , and was most recently a plenary speaker in the workshop on bifurcation theory and spatio-temporal pattern formation held at the Institute last December. We have been exceptionally fortunate in attracting Dr. Keyfitz to the Directorship at the Institute. We know that she will maintain and enhance the role of the Institute in the years to come, and we bid her a most hearty welcome! Bradd Hart (McMaster) The National Program on Complex Data Structures (NPCDS) NPCDS IS A JOINT INITIATIVE between Canada s Statistical Science community and the nation s three Mathematical Sciences Institutes. Activity began in earnest shortly after funding was released by NSERC in April of This included workshops at le Centre de Recherches Mathématiques (CRM) and the Fields Institute, a successful MITACS application, appointments to research positions at Statistics Canada and the Toronto Rehabilitation Institute, a successful call for proposals and planned activity for the annual meeting of the Statistical Society of Canada (SSC) and at the Pacific Institute for the Mathematical Sciences (PIMS). In addition, NPCDS has sought opportunities at the Banff International Research Station (BIRS), has organized an SSC sponsored session at the Joint Statistical Meetings this year and has strengthened ties with the Statistical and Applied Mathematical Sciences Institute (SAMSI) in the United States. continued on page 4

2 A Monstrous Tale: The Work of John McKay THE 2003 CRM-FIELDS PRIZE was shared by Edwin Perkins of UBC and John McKay of Concordia University. Perkins spoke about his work in November 2003 (see the January 2004 Fields Notes). McKay delivered his lecture on March 8, McKay s observations over the course of more than two decades led to discoveries that climaxed in the Fields Medal of Richard Borcherds. In his talk at the Fields Institute, McKay recounted some of those observations and the myriad mathematical connections that they opened up. These connections seem to show no sign of abating and the talk presented several new themes. McKay begins with the j-function. Define the complex function E = (σ 3 (1)q + σ 3 (2)q ), where σ 3 (n) is the sum of the cubes of the positive divisors of n and q = exp 2πiz. The discriminant function = q(1-q) 24 (1-q 2 ) was studied by Ramanujan and leads to the j-function defined by j = E 3 /. Expanding j as a function of q, we find j(z) = q q +... This is a modular function in the sense that it is invariant under action by the modular group SL 2 (Z). That is, if a,b,c and d are integers such that ad bc =1, then j(az + b / cz + d) = j(z). All of this was known classically. But McKay was the first to notice the relevance of the equation in the title of his talk: = Here is a coefficient from the above expansion of j, while is the smallest non-trivial degree of a character of the monster group, the largest sporadic finite simple group. The order of the monster is , a number larger than 8 x The fact that there might be some relationship between the monster and modular functions first arose in an observation of Ogg. He pointed out that the prime divisors of the order of the monster group are exactly the same primes p for which the normalizer of the discrete group Γ 0 (p) in SL 2 (Z) gives a genus zero quotient of the upper half plane. However, no one had thought that there might be a relationship between the Fourier coefficients of the j-function and its analogues, and the character theory of the monster. Shortly after McKay made this simple but profound observation, he looked at the character table of the group E 8 and found another relationship between the degrees of the John McKay representation here and the Fourier coefficients of a cube root of the j-function. Based on some of McKay s observations, Conway and Norton formulated a general conjecture that became known as the Moonshine conjecture, possibly because it was so bizarre. It related character degrees of exotic finite simple groups to Fourier coefficients of certain modular functions. Why such a relationship should even exist was completely unknown until the work of Borcherds who introduced several new concepts including that of vertex algebras. Using the theory of these algebras, he was able to prove the Moonshine conjecture. But far from being the end of the story, it seems that many new connections and conjectures have been opened up. In his talk, McKay touched upon such diverse topics as quantum logic, replicable functions, dispersionless flow and Witten s conjectured 3-manifold in topological quantum field theory and how each of these is connected in some way to moonshine. John McKay presents his ideas with a characteristic modesty. Nevertheless, he has served as a catalyst for the development of some of the very important ideas of modern mathematics. Besides receiving the CRM-Fields prize, he was recently elected to the Royal Society of Canada in recognition of his many contributions. V. Kumar Murty (Toronto) 2 FIELDSNOTES FIELDS INSTITUTE Research in Mathematical Science

3 Donald A. Dawson Awarded CRM-Fields Prize for 2004 DONALD DAWSON OF CARLETON and McGill Universities is this year s recipient of the CRM-Fields Prize. Don is without doubt one of the best and most widely known Canadian mathematicians, and for good reason. His research, centered around the areas of measure-valued stochastic processes and infinite-dimensional branching processes, contains many truly seminal contributions. He has been a key figure in establishing the high profile of the Canadian probability community among the world s mathematicians. He has as well had a very positive and nontrivial influence on the broader Canadian mathematical scene, holding at one time or another some of its most important positions Chair of the NSERC statistics GSC, coeditor of the Canadian Journal of Mathematics, and Director of the Fields Institute. He is currently the President of the Bernoulli Society for Mathematical Statistics and Probability. Don received a BSc from McGill in 1958 and a PhD from MIT in His contributions have been recognized in almost every possible way, including Fellow of the Royal Society of Canada, the International Statistical Institute, and the Institute of Mathematical Statistics; Gold Medal of the Statistical Society of Canada; Jeffery-Williams Lecturer of the CMS; and invited lecturer at the 1994 ICM in Zürich. Don is the acknowledged world leader in measure-valued branching processes, and has been recognized through Dawson- Watanabe superprocesses becoming a standard phrase in probability theory. His notes on Measure-valued Markov Processes are the standard reference in the field. He also played a pivotal role in the birth of the field of stochastic partial differential equations. He has contributed basic results to statistical physics and mathematical biology. In fact his breadth of knowledge is remarkable, covering such diverse subjects as queuing systems, spin glass models, mathematical finance, dynamical systems, population genetics, statistical inference, Dirichlet forms, interacting particle systems, large deviations, signal processing, communications networks, epidemiology, computer science. His influence on Canadian mathematics has also been remarkable. Possibly the most far-reaching was his role as Director of the Fields Institute during the period This was a pivotal moment for the three Canadian mathematics institutes. In the case of the Fields Institute, it was a period when it considerably broadened its focus, reaching out to all of the mathematical sciences while at the same time developing a much stronger interaction with business and industry. This dynamic was the temper of the times, but it conformed exactly to Dawson s approach. Notably he was one of the principal architects of the very successful MITACS proposal put forward by the three institutes. The financial mathematics program at Fields also became a much broader enterprise under his leadership. Don played a strong role in enhancing the power and impact of the three institutes, as reflected in the critical 1997 NSERC Reallocation Exercise. It was a tumultuous time and Don provided constructive and moderating leadership throughout the whole period. Another of his lasting contributions was his role as editor (with Vlastimil Dlab) of the Canadian Journal of Mathematics during During this time the CMS, with their help, significantly restructured its publications operations and turned the Journal and the Bulletin into the profitable enterprises that they are today. Don has collaborated successfully with many coauthors in many different areas. His influence in probability will continue on throughout Canada Donald A. Dawson (and in fact, the United States as well) through his 24 PhD students (including professors at 13 Canadian universities) and 29 postdoctoral fellows. The Centre de recherches mathématiques (CRM) of l Université de Montréal, and the Fields Institute jointly established the CRM Fields Prize in 1994 with the goal of recognizing exceptional work in the mathematical sciences. Recipients are chosen by the Advisory Committee of the CRM together with the Scientific Advisory Panel of the Fields Institute. The main selection criterion is outstanding contribution to the advancement of research. Previous recipients are H.S.M. (Donald) Coxeter, George A. Elliot, James Arthur, Robert V. Moody, Stephen A. Cook, Israel Michael Sigal, William T. Tutte, John B. Friedlander, John McKay, and Edwin Perkins. Carl Riehm (Fields) FIELDS INSTITUTE Research in Mathematical Science FIELDSNOTES 3

4 The National Program on Complex Data Structures (NPCDS) continued from front cover Autumn 2003 saw Jim Berger, the Director of SAMSI, warmly accept an invitation to join the NPCDS Board of Directors which also includes the directors of the three Canadian institutes, Jim Ramsay from the SSC, and NPCDS director Jamie Stafford. Jim's position on the Board represents a potent way to advise and influence NPCDS activity to the mutual benefit of our programs. While NPCDS operates on a much smaller budget than SAMSI, the programs share many objectives and principles apparent in their respective descriptions. In addition, NPCDS has much to offer in terms of expertise, opportunities and an inclusive philosophy financial support from SAMSI and the event is now a joint effort where the potential for thematic program at SAMSI in this area will be discussed. NPCDS uses its resources to seed activity that has the potential to lead to National interdisciplinary projects. A two-stage mechanism is used that involves inaugural workshops and, if successful, subsequent two-year projects. Within this context, NPCDS currently supports one project in the analysis of Complex Survey Data for population health and social science, and another potential project in Statistical Genomics. Statistical Methods for Complex Survey Data: Survey data are now being collected and analyzed by many government, health and social science organizations with subsequent analysis being used to identify determinants of supervised jointly by researchers at these institutions and by professors at Universities throughout Canada. The team has successfully sought further support from MITACS and held an inaugural workshop hosted and supported by the CRM in April Statistical Genomics: As reported in the January 2004 Fields Notes, the Fields Institute hosted NPCDS s First Canadian Workshop on Statistical Genomics, for three days in early September One of the goals of the workshop was to expose relevant and important challenges that remain unsolved in the statistics of high-throughput genomic data, such as data obtained from DNA microarray, protein mass-spectrometry or SNPchip experiments. See the above mentioned issue for further details. The main organizers of the workshop...a pivotal event in a national effort through the NPCDS to build interdisciplinary research capacity with a strong statistical component. in its activities. In areas where our program activity overlaps there is potential for collaboration. To this end efforts began almost immediately with the success of a joint NPCDS/SAMSI proposal for a 2005 workshop at BIRS. The workshop will be a pivotal event in a national effort through the NPCDS to build interdisciplinary research capacity with a strong statistical component. A central networking component of the workshop will be to enhance ongoing cooperative efforts with SAMSI within NPCDS projects, and to identify further areas of overlap. This will include discussion of ongoing planning of thematic programs at SAMSI. Indeed this type of activity has already taken place in one scientific area. Derek Bingham's July 2004 workshop on the Design and Analysis of Computer Experiments for Complex Systems has received generous health and to influence public policy. Surveys have increasingly complex structures in both longitudinal and cross-sectional forms, and new statistical methods are needed to make the best use of these data. Canada is a world leader in sample survey methodology and many of Canada s top researchers in this area are on this team. These researchers have partnered with Statistics Canada and their affiliated Research Data Centers across the nation, the Toronto Rehabilitation Institute, UNESCO and WestStat. They carry out research in the general areas of modelling of survey data, missing data in the survey response file, and variance estimation under complex survey designs. One of team s activities is the placement of ongoing Ph.D. and postdoctoral students in collaborative research positions at Statistics Canada and at the Toronto Rehabilitation Institute. The students are are determined not to miss a historic opportunity for our field and are now engaged in organizing the Canadian Consortium in Statistical Genomics as an NPCDS project. In addition pilot projects are being launched in the Design and Analysis of Computer Experiments for Complex Systems, and in Data Mining Design and Analysis of Computer Experiments for Complex Systems: The rapid growth in computing power has made the computational simulation of complex systems feasible and helped avoid physical experimentation. Consequently, the design and analysis of computer experiments has become an integral part in the exploration of scientific and industrial processes as well as creating new and important challenges. The NPCDS is pleased to host an 4 FIELDSNOTES FIELDS INSTITUTE Research in Mathematical Science

5 inaugural workshop that aims to address three main problems in this area: screening experiments, function fitting in high dimensions and integration of physical and computer experiments. The workshop will receive partial support from the Los Alamos National Lab and novel aspects include a reading list distributed in advance with which participants are expected to be intimately familiar. The workshop will be held at PIMS or BIRS in A formal announcement is forthcoming. Data Mining: Canada's Mathematical Sciences Institutes continue their supportive role in NPCDS and in one instance the Fields Institute has been instrumental in fostering a relationship between NPCDS and a potential industrial partner. NPCDS scientists are organizing a joint workshop in Data Mining, with the firm Generation Five generously providing partial support. The goal of this workshop is to bring together researchers and practitioners interested in data mining problems, identify emerging research areas in the field, and form new research partnerships between researchers, students, and industrial partners. The workshop will attempt to cover some important aspects of statistical learning theory as applied to data mining, namely predictive modeling, clustering, and the rare target problem. The latter is a special case of predictive modeling and clustering, and is an example of a new problem specific to data mining. Information about the program may be found on the Fields website. Jamie Stafford (Toronto) Workshop on Bifurcation Theory and Spatio-Temporal Pattern Formation, In Honour of Bill Langford IN DECEMBER 2003, THE FIELDS INSTITUTE hosted a workshop on Bifurcation Theory and Spatio-Temporal Pattern Formation in Partial Differential Equations (PDE). The workshop was a sixtieth birthday celebration for William Langford, one of the pioneering researchers in the field of bifurcation theory in Canada. In addition to a distinguished teaching career at McGill and at the University of Guelph, where he was Chair of the Mathematics and Statistics Department from 1990 to 1996, Bill served as Deputy Director of the Fields Institute from 1996 to Nonlinear phenomena and the formation of spatio-temporal patterns play an increasingly important role in current research on partial differential equations. Progress in the past quarter-century in the development of equivariant bifurcation theory and the theory of mode interactions and deterministic chaos has made possible a better understanding of spatio-temporal patterns in a wide variety of physical and biological contexts. The workshop fit in well with the current thematic program on PDE, and it complemented the Workshop on Patterns in Physics. Recent progress in equivariant bifurcation theory for Hamiltonian systems and in particular the Hamiltonian-Hopf bifurcation was also addressed in the workshop, thus providing a segue to the winter-spring component of the PDE program. The workshop attracted leading researchers from Canada and abroad, as well as many graduate students, providing a stimulating venue for scientific exchanges of ideas. At a banquet Friday evening, Bill was recognized for his fundamental contributions and leadership in bifurcation theory and pattern formation and for his service to the Canadian mathematical community. In addition to workshop participants, many of Langord s past graduate students now established researchers in the field of Bifurcation Theory and colleagues from the University of Guelph attended the banquet. The current Chair of the Department of Mathematics and Statistics at the University of Guelph, Brian Allen, and the chair who hired Langford at Guelph, William Smith, both spoke warmly about Bill s career, his achievements, and his numerous contributions, and presented him with a beautiful poster displaying his mathematical genealogy. The workshop was financially sponsored by the Fields Institute with additional support by the U.S. National Science Foundation and the Guelph Department of Mathematics and Statistics. The organizers of the workshop were Anna T. Lawniczak (Guelph), Victor G. LeBlanc (Ottawa), Wayne Nagata (UBC), and N. Sri Namachchivaya (Illinois, Urbana-Champaign). They wish to acknowledge the superb organizational support provided by the Fields Institute and in particular by Alison Conway and Jonathan Kassian. Anna T. Lawniczak (Guelph) The Fields Institute for Research in Mathematical Sciences publishes FIELDSNOTES three times a year (September, January, and May). Director: Kenneth R. Davidson Deputy Director: Thomas S. Salisbury Managing Editor: Maryam Ali Distribution Co-ordinator: Laura Gass Scientific Editor: Carl Riehm Sri Namichchivaya, Wayne Nagata, Bill Langford, Victor LeBlanc and Anna Lawniczak FIELDS INSTITUTE Research in Mathematical Science FIELDSNOTES 5

6 Weekend Workshops on Arithmetic and Geometry of Algebraic Varieties THE WEEKEND WORKSHOPS ON CALABI-YAU varieties and mirror symmetry at the Fields Instite were very successful. In , we broadened the subjects to Arithmetic and Geometry of Algebraic Varieties (in particular, higher dimensional varieties) with special emphasis on Calabi-Yau varieties and mirror symmetry. These weekend workshops organized by myself and James Lewis (Alberta) have been getting to be known in the community. Besides local Canadian regular participants, a number of participants came from various parts of the United States. Due to high interest, we organized three workshops in the academic year (October 4-5 and November 8-9, 2003; March 27-28, 2004). The three workshops were a huge success. Postdoctoral fellows and graduate students were especially encouraged to take part in the activities. All participants and also several colleagues who could not be present at this year's workshops have already asked for schedules for the workshops in the coming year. We are planning the first workshop in the academic year in October. For a listing of speakers and titles see the Fields website. Noriko Yui (Queen's) Workshop on Nonlinear Wave Equations DURING THE WEEK OF MARCH 15-19, the Fields Institute hosted a workshop on nonlinear wave equations, as a component of the Thematic Program Year on Partial Differential Equations. This meeting was organized by Claude Bardos (Université de Paris 7), Jim Colliander (Toronto), Walter Craig (McMaster), Nick Ercolani (Arizona), and Catherine Sulem (Toronto). This was one of a pair of workshops on related material, the second being the workshop on kinetic theory, which was held one week later. The design of holding major workshops as pairs, in closely aligned weeks was to allow mathematicians who are working in both areas to attend as one extended event. Included in this time frame was the short-course on the theory of collisionless plasmas, which took place in the intervening week. The focus of the week on nonlinear wave equations included nonlinear microlocal analysis of evolution equations, results and ideas from Hamiltonian PDE, existence theory for the initial value problem (both local and global in time, and in optimal function spaces), and applications of this theory to a number of physically relevant partial differential Walter Craig, Claude Bardos, Nick Ercolani, Catherine Sulem and Jim Colliander equations. The setting of this work ranged from Einstein's equations of general relativity, to the nonlinear equations of fluid dynamics, to the nonlinear Schroedinger equations of plasma physics, including nonlinear optics and multi-particle quantum mechanics. Participants came from South America, numerous European countries, as well as Canada and the US. The number of postdoctoral speakers and graduate student participants was notably very high. There are numerous nonlinear evolution equations that have been derived in a context relevant to mathematical physics, for which it is a challenging mathematical problem to analyze the properties of the solution map for time evolution of the system. The theme of this workshop was on recent results on precise properties of solutions of the initial value problem, involving new techniques of harmonic and microlocal analysis for this purpose. Principal questions include the well-posedness of the nonlinear equations, and in which function spaces, the precise regularity of solutions, and the phenomenon of the formation of singularities as compared with the possibility of globally defined evolution in time. One of the main themes was the close analogy between microlocal techniques for linear PDE and the analysis of nonlinear kinetic equations. In fact the timing of the meeting to be close to both the workshop on kinetic theory and the short-course on collisionless plasmas was useful in this context. The schedule of 25 talks kept the schedule full but not too busy, and left the participants time to work and to discuss mathematics together with each other. I personally found the talks very informative, the nature of the audience very receptive, and all in all it was a very positive event in the active life of our program year. Walter Craig (McMaster) 6 FIELDSNOTES FIELDS INSTITUTE Research in Mathematical Science

7 The Point of Point Processes THE POINT OF POINT PROCESSES WORKSHOP was a Fields Institute/University of Ottawa Workshop held in Ottawa from February 23-25, There were a total of 36 participants, including 17 graduate students, 4 non-academic researchers, and 15 university professors. While many arrived in Ottawa from all over the globe, including Israel, Poland, Germany and Mexico, the students came primarily from Ontario universities. Most participants arrived in time to take advantage of the final weekend of Winterlude prior to the workshop. The primary focus of the workshop was the probabilistic foundation of point processes and the resulting broad range of applications in areas such as statistics, finance, neuroscience and the environment. The workshop began with a six hour minicourse on the two main approaches to point processes, namely random measures and martingale methods. All participants were provided with complete lecture notes, prepared and largely presented by Rafal Kulik. Dr. Kulik, originally from Wroclaw University in Poland, is a postdoctoral fellow at the University of Ottawa. All the participants gratefully acknowledged the very high quality of his notes and lectures. The organizers are pleased that Kulik will be remaining in Ottawa for a second year under a postdoctoral fellowship funded in part by the Fields Institute. The invited speakers included world-renowned experts in the field. The topics ranged from theory to practice. On the theoretical end, Ely Merzbach spoke on a multidimensional generalization of the renewal property, and Riszard Szekli talked about stochastic orders. Bruce Smith and Bruno Remillard presented well-developed applications of point processes to sea level data and credit risk assessment, respectively. John Braun presented an exploratory data analysis of forest fire ignitions in Ontario. A physicist, André Longtin, highlighted the strong potential for the application of point process methods in the analysis of neural spike trains. In addition, there were a number of contributed talks by graduate students on their current research. All participants commented on the benefits of a broad exposure to an important subject in an intimate environment that provided ample opportunity for interaction and discussion. Gail Ivanoff and André Dabrowski (Ottawa) Lila Kari s RCI/Fields Lecture: How does Nature compute?...and FOR THAT MATTER, DOES NATURE COMPUTE? Only recently (since Turing, Post, and Church) could one be sure what one meant by whether computing was going on. Only in the last ten years (since Leonard Adleman's experimental demonstration) could one hope to use natural computational tools to answer human questions. Today it is clear that the questions are sensible. Natural DNA carries information in the form of sequences composed in a small alphabet as does a Turing machine. Processing the sequences is done by a small repertory of operations not the same as one might dream up for purposes of a theoretical analysis or an electronic implementation, but still quite the same sort of operation as we're used to discussing. The question of the range of transformations realizable by this information-processing is just such a question as theoretical computer scientists study. The DNA is out there, computing away; we can prove things about the capacity of the process; it is not clear yet whether we will be able call on DNA to do OUR computing for us, the way we now call on silicon chips. Lila Kari is one of the leaders of this new field of DNA computing. She is associate professor of computer science at the University of Western Ontario and holder of a Canada Research Chair in Biocomputing there. On Sunday February 29 she spoke on How does Nature compute? under the joint sponsorship of the Fields Institute and the Royal Canadian Institute for the Advancement of Science. No large-scale working DNA computer exists yet only theorems and small-scale demonstrations. One of the striking positive results presented was Kari's theorem with L.F. Landweber that the operations known to be available to a ciliate in chopping and resplicing its DNA for its own purposes give the computing power of a universal Turing machine. One of the striking negative results, due to L. Adleman, J. Kari, D. Reishus, and the speaker, says that checking the concatenation rules of an alphabet of tiles to be assembled on a plane lattice, to see whether arbitrarily long chains may result, is a check which can not be done by any algorithm! The grail of biological computing remains before us. The DNA computer would start with huge advantages: greatly denser information storage, and much greater parallelism available, for instance. Though such a system might not be perfectly reliable, still we can say a great deal about what it might be capable of. In response to a listener's question, Prof. Kari reminded us that Nature's computing is not reliable either, but its unexpected outputs are sometimes very useful to evolution. One wonders what comes next in human use of the method. Chandler Davis (Toronto) FIELDS INSTITUTE Research in Mathematical Science FIELDSNOTES 7

8 Seventh Workshop on Quantum Information Processing WITH THE REALIZATION THAT THE properties of information are very closely linked with the physical medium that carries it, the notion of what constitutes information has undergone a radical change over the past few decades. Could it be that information stored in, say, physical states of the atom inherits the quantum mechanical behaviour observed in matter at that length scale? Does this fundamentally change our view of communication and computation? If so, how? These questions have led to a growing body of work in the mathematics (and physics!) of quantum information, work that has overthrown our earlier understanding of feasibility and computational complexity in information processing. The QIP workshops have become the premiere annual conference on the computer science aspects of quantum information processing. This year, the Perimeter Institute for Theoretical Physics and the Institute for Quantum Computing (based at University of Waterloo) proudly hosted QIP 2004, the Seventh Workshop on Quantum Information Processing, in Waterloo, Canada. The four and a half day workshop went from January 15 until January 19, 2004 at the Centre for International Governance Innovation, in Waterloo. The event was additionally supported through generous contributions from several sponsors including CIAR, the Fields Institute, MITACS, ORDCF, NSERC, RIM, CIGI, the Guelph-Waterloo Physics Institute, St. Jerome s University, and the University of Waterloo. The scientific events were conducted in the impressive setting of the old Seagram Museum, the new home of the Centre for International Governance Innovation (CIGI). QIP 2004 brought together a record number of researchers about 190 including 75 students and 40 postdocs. Twenty-four invited speakers gave fulllength talks that spanned a broad selection of topics from algorithms, complexity theory, communication and information theory, cryptography, and their connections to the foundations of quantum mechanics. Three sessions of the workshop were devoted to short contributed talks on the most recent advances. The speakers included a large number of young researchers, with a fair number of graduate students and postdoctoral fellows. Around 55 participants presented posters on their current work. It was evident from the talks that the area of quantum information and computation has come of age. Links were drawn between Bell inequality violations and complexity theory, specifically, the breakdown of classical multiple prover interactive proof systems (R. Cleve). On the other hand, complexity theory was brought to bear on the cost of simulating correlations arising from quantum communication (I. Kerenidis), and on the characterisation of quantum states that are presumably hard to engineer (S. Aaronson, R. Raz). G. Brassard speculated on a natural formulation of quantum mechanics based on information theoretic principles. A couple of talks were devoted to the influence quantum computation has had on classical theoretical computer science L. Valiant spoke about a linear algebraic approach to showing separation of classical complexity classes, and O. Regev about efficient classical proofs for lattice problems. A milestone was set with a new quantum walk based algorithmic technique for the design of algorithms (A. Ambainis). D. Aharonov described how realistic adiabatic quantum processes could be used to efficiently implement any quantum algorithm. Several excellent talks focused on new...the notion of what constitutes information has undergone a radical change over the past few decades. methods in the analysis of cryptographic protocols (U. Maurer, K. Tamaki) and their applications to problems in information theory (A. Winter). L. Schulman showed combinatorial limits on the efficacy of heat-bath cooling of NMR quantum computers. The contributed talks also shone, and showed even more variety. A. Harrow introduced the notion of coherent classical communication, S. Laplante recast lower bounds for quantum algorithms in terms of Kolmogorov complexity, D.Poulin discussed the computational power of a single quantum bit, and B. Sanders described results on experimental quantum secret sharing. 8 FIELDSNOTES FIELDS INSTITUTE Research in Mathematical Science

9 The high point of the social events was undoubtedly the conference banquet on Sunday, Jan 18, at Waterloo Inn. A superb meal was followed by an inspiring talk by Mike Lazaridis, co-ceo, Research in Motion (RIM), and the visionary behind the Perimeter Institute (also a major benefactor of the Institute for Quantum Information). Lazaridis shared his passion for fundamental physics, and spoke at length on how it has resulted in significant technological advances. He stressed the importance of a scientifically aware society and government, and the role of researchers in achieving this. The evening was capped by a highly entertaining, semi-serious talk by Charles Bennett, IBM Research, Yorktown Heights, a pioneer in quantum information processing. Bennett regaled the audience with amusing snippets from the scientific talks at the workshop. Then, inspired by the exhibits at the old the Seagram museum (the conference venue), he went on to the physics of distillation and its parallels in entanglement purification in quantum information theory. The meeting was from all accounts very successful, thanks in no small part due to the months of preparation by Daniel Gottesman (Perimeter) and Michele Mosca (U. Waterloo & Perimeter), with whom I co-chaired the event, and Wendy Reibel (IQC) who most efficiently lead the local organization and meticulously ensured that everything went like clockwork. Thanks also to Fields, and all our sponsors, for the support and help that made it all possible! For more details on QIP 2004, please visit the conference website Ashwin Nayak (Waterloo and Perimeter) Young Mathematicians Conference: Partial Differential Equations and Dynamical Systems A SATELLITE OF THE THEMATIC PROGRAM on Partial Differential Equations at the Fields Institute, the two day conference provided an opportunity for promising young Canadian mathematicians to present their work in a very friendly and active atmosphere, to meet each other, and to interact with more senior mathematicians. There were twelve 30 minute talks delivered by junior scientists. There was also a poster session presented by the lively joint effort of nine invited junior scientists. The participants were also asked to give a five minute oral summary, during the regular seminar time, of the results described in the posters (for a complete list of speaker names and titles see the Fields website). Two 45 minute talks were delivered by senior scientists. N. Kamran (McGill) spoke on solutions of the wave equation problems in the context of general relativity and in particular on his results on wave propagation with a Kerr black hole background Lorentzian metric. A. Nachman (Toronto) presented an overview of inverse problems in partial differential equations. The success of the conference was the result of a team effort. The organizers, Stefanella Boatto (McMaster), Walter Craig (McMaster) and Catherine Sulem (Toronto) would like to extend their particular thanks to the chairs of the sessions, Robert McCann (Toronto), Matheus Grasselli (McMaster), Bill Langford (Guelph), Dmitry Pelinovsky (McMaster,) and Jianhong Wu (York). They participated actively by promoting and taking part in the mathematical discussions. The Fields Institute provided an excellent venue for presentations, discussions, and collaborative activities. We extend our thanks in particular to the Institute staff, Alexa Brand and Alison Conway. The conference was supported by the Fields Institute, the NSERC Leadership Support Initiative, and the Canada Research Chairs Program. Stefanella Boatto (McMaster) Paul Tupper and Stefanella Boatto FIELDS INSTITUTE Research in Mathematical Science FIELDSNOTES 9

10 JUMP Spring 2004 Update John Mighton with a student JUNIOR UNDISCOVERED MATH PRODIGIES (JUMP) is a volunteer-based tutoring organization founded in 1998 by mathematician John Mighton. The program started in John's apartment with 7 tutors and 15 students and now has over 300 volunteers and 2000 students in 17 schools. The main objective of JUMP is to provide underprivileged elementary school children with free tutoring in mathematics. This year, however, in response to an explosive growth of interest in the program among educators and parents, we also began to make our methods and materials available to a wider public. Over the course of the year, we produced workbooks for students and training materials for teachers (for grades 3 to 6), and we held talks and training sessions for hundreds of teachers, administrators, parents, and volunteer tutors at the Fields Institute, and at schools, universities and community centers across Canada. JUMP s administrative office is located at the Fields Institute. When students start JUMP, they are immediately taught to perform operations with fractions at a level several years beyond their grade level in order to capture the attention of the weakest students, boost their confidence, and build the basic mathematical skills those students need to progress to more advance conceptual work. Teachers and tutors in the program are trained to guide their pupils in small steps that even the most delayed student can grasp. We have found that when children become convinced that they can master advanced operations, they invariably show remarkable changes in confidence, memory, attention and general conceptual ability. One of our students has made such remarkable progress that his doctor has asked John to talk to a panel on child development at Sick Kids Hospital. After students complete the JUMP fractions unit (with a mark of 80% or higher), they cover the regular curriculum at their grade level. Through a series of carefully designed exercises and toy models and problems, they are taught to how to discover and explain concepts by themselves. Students in JUMP are also introduced to beautiful mathematical ideas and applications that they normally wouldn't encounter until high school or university (but that involve only elementary math). We are presently developing units that show how mathematics appears in biology, chemistry, magic tricks, secret codes, strategy games, art, and computer science, as well as units on logic, topology, and graph theory. Perhaps the most exciting development in JUMP this year is the growth of our partnerships with dedicated educators. A number of teachers and administrators in Canada and the States have started pilot projects, which demonstrate that schools can easily implement JUMP in classrooms or after-school, without stretching their resources. With the publication of John Mighton's The Myth of Ability in May of 2003, we have received hundreds of phone calls and s from people across Canada, the United States, and from as far away as Australia, New Zealand, Greece and South Africa. Many have asked how they could start their own program locally. Through the help of a grant by the J.W. McConnell Family Foundation, JUMP is planning to provide partner organizations, such as schools and community groups, with JUMP's expertise, materials and ongoing support. We hope to reach many more children through these partnerships than by trying to manage every project directly. For more information, please visit the JUMP website at: John Mighton (JUMP) The kids are so excited about what they've learned they beg to go to math class every day, including "fun" Fridays and are inviting their classroom teachers to watch them perform feats of math in our afterschool program! Lynn Sobolov Kaleidoscope Project Director, Morgantown, WV We at Xit'olacw have introduced JUMP for our Math programme and what is happening is nothing short of a miracle. This programme will be incredible in developing math students and teachers in our First Nation Schools. Liz Barrett Teacher, Xit'olacw Community School, Mount Currie, BC JUMP math is so brilliantly organized that it allows students to see and incorporate patterns. They are now seeing patterns in reading, writing and other subjects. Students who were in Grade 3, 4 and 5 and who had never achieved higher than a D in math are now achieving between 80 and 90 percent. Liga Miklasevics Principal, Toronto District School Board 10 FIELDSNOTES FIELDS INSTITUTE Research in Mathematical Science

11 Seminar Series on Quantitative Finance NOW IN ITS TENTH YEAR, the monthly quantitative finance seminar has successfully established itself as the principal occasion at which academics and practitioners in the Toronto area gather regularly to discuss financial mathematics. Participants come from mathematics or economics departments, business schools, financial service or software firms, banks, regulatory agencies, and a host of other places besides. The audience is large and lively, on occasion leaving standing room only. The organizing committee consists of Phelim Boyle (Waterloo), Michel Crouhy (CIBC), Ron Dembo (Algorithmics), John Hull (Toronto), Tom Hurd (McMaster), Alexander Levin (TD), Moshe Milevsky (York), and Tom Salisbury (Fields). The seminar is sponsored by the Fields Institute and by MITACS, and meets the last Wednesday of each month, with two evening talks separated by a reception and informal discussion. The October seminar was sponsored by PhiMAC, the financial mathematics laboratory of McMaster University. It saw a pair of interesting talks on the general topic of volatility modelling, one by Nour Meddahi (Economics, Université de Montréal) and the other by Yacine Aït Sahalia, the director of Princeton s Bendheim Center for Finance. In November, the seminar heard from Elizier Prisman (Schulich School of Business), and Ulrich Haussmann (Mathematics, UBC), on some effects of noise on model imputation and portfolio optimization respectively. In January, Ivar Ekeland (PIMS director) presented a Hilbertian term structure model, while Agnes Tourin (McMaster) described some numerical methods for HJB equations. February saw a packed house, with John Hull (Rotman School of Management) speaking on credit risk, and Philip Protter (ORIE, Cornell) analyzing a model incorporating liquidity effects. René Carmona (ORFE, Princeton) and Heath Windcliff (TD securities) gave the March seminar, both Phillip Protter and John Hull talking about aspects of American type options with multiple exercise features. The April seminar (upcoming as of this writing) will be held in conjunction with the 3rd annual IFID conference on personal risk management, and the year s seminar series will conclude in May. The past year also saw one former speaker, Robert Engle, win a Nobel prize for his work. With the high standards of past years seminars more than maintained by this year s speakers, can another such Nobel be far away? Tom Salisbury (Fields) Noted JIM ARTHUR ELECTED PRESIDENT OF THE AMS Jim has served on the Scientific Advisory Panel, won the CRM-Fields prize, and was an organizer of the Automorphic Forms program in LISA JEFFREY WINS NSERC 2004 STEACIE FELLOWSHIP Lisa was an organizer of the Symplectic Geometry program in 2001 and will co-organize the String Theory program next year. BARBARA KEYFITZ RECEIVES CMS 2004 KRIEGER-NELSON PRIZE Barbara has served on the Scientific Advisory Panel and will be the next director of the Institute (see front cover). The Midwest Several Complex Variables Meeting THIS MEETING HAS BEEN HELD once or twice a year, more or less regularly, since the late 1970s. It is always well attended by members of the active complex analysis and geometry community in the US Midwest and neighbouring provinces and states, from graduate students to senior researchers. This year, Dan Coman and Evgeny Poletsky of Syracuse University and Finnur Larusson of the University of Western Ontario organized two Midwest meetings, one in Syracuse on October 10 12, 2003, partly supported by NSF, and another in London on April 2 4, 2004, partly supported by Fields. The meeting in London was held in conjunction with the UWO Distinguished Lecture Series in Mathematics, now in its eighth year. This year's speaker was Professor Yum-Tong Siu of Harvard University. He kicked off a long weekend of mathematics with his first talk on analytic methods in algebraic geometry on Thursday afternoon April 1. His second and third talks were embedded in the Midwest meeting, which began the next morning. There were 49 participants, mostly from Canada and the United States, but also from France, Mexico, Slovenia, and Spain. Almost a third were graduate students. Most of the available funds were reserved for travel support for them and other junior researchers. The 18 talks, four of them by graduate students, reflected the broad scope of modern complex analysis and geometry. They involved such diverse areas as algebraic geometry, differential geometry, dynamical systems, partial differential equations, and pluripotential theory. For more information about the meeting visit the Fields website. Finnur Larusson (UWO) FIELDS INSTITUTE Research in Mathematical Science FIELDSNOTES 11

12 Philip Siller: Deputy Chair of the Fields Board of Directors and Polymath A POLYMATH IS A PERSON OF MUCH OR VARIED LEARNING, A GREAT SCHOLAR, according to the Oxford dictionary. This definition aptly describes Philip Siller of the Fields Board of Directors: mathematician, lawyer, teacher at the Munk Centre for International Studies at the University of Toronto, baseball enthusiast, crossword puzzle competitor, Talmudic student, and eager filmgoer. Philip has been steeped in mathematics all his life. His father, Harry Siller, whom he describes as a chess player and intellectual, had a PhD in mathematics from NYU specializing in real and complex analysis. Following his MSc in mathematical physics under Richard Courant, Harry Siller worked in Washington during the 1930s and 1940s in code breaking and operations research. After growing up in New York City, Philip completed his PhD in mathematics at the University of Minnesota under Erwin Engeler (now at ETH in Zürich) on Models and Filtermaps. As jobs in mathematics were scarce in the early 1970s, he decided to study law and enrolled at University of Toronto s Faculty of Law on the grounds that it was a small, good, law school in an urban setting and Toronto was a nice place to live. He and Rob Prichard, former President of U of T, formed a study group in law school and have been in touch ever since. Siller is the president of Hexagram & Co., a private venture management firm. Its clients are successful owner-managed companies that are, however, faced with problems of growth and expansion. Owners may lack experience in doing business on a large scale, or may need to solve problems including finance, international expansion, systematic information, contracts, or alliances. As Hexagram concerns itself with management modelling, the sector is irrelevant. Client companies range from electronics manufacturing to environmental services, real estate, retail, and telecommunications. Mathematics has had an impact on my work, says Siller. One learns to read very carefully, to notice what s been said and what omitted. I have to be attuned to recognize the logical structure of a situation, to notice resemblances in what are apparently differing circumstances. Mathematics is inclined towards elegant solutions rather than inelegant ones. Elegant solutions work better in the real world too they are less costly and less complicated. There is less risk in more elegance. For eight years, jointly with U of T Professor Janice Gross Stein, Director of the Munk Centre for International Studies, he has taught a seminar course on the Theory of Negotiation, which involves the cognitive science of risk and the nature of negotiations in differing institutional contexts. Stein and Siller have just introduced a new course on Accountability and Responsibility in Public Administration, attended in the main by law students and political science students. He remarked on the changes in mores in public administration during the past generation or two that make such a course a hot topic. Siller s other interests include crossword puzzle competitions. He goes every April to the New York Times competition in Stamford, Connecticut, a three-day event organized by Will Shortz. Then there is baseball he has written on statistical analysis in the game. When asked about baseball greats, he names Lefty Grove as the best pitcher before the Second World War, and Warren Spahn and Roger Clemens for the post-war period. Among non-pitchers, he picked Babe Ruth, Ted Williams, Willie Mays, and Barry Bonds. During the decade he has sat on the Fields Board of Directors, Philip Siller has contributed greatly to the Fields Institute. He was involved in the early applications for the first NSERC grant, was active with the site selection committee in 1993, and represented the Institute on the joint U of T Fields committee during the design and construction of the Fields building at 222 College Street. More recently, he served on the Director Search Committee (2003) and played an active role in the design by Scott Thornley + Company of the new Fields logo. When asked about how the management consultant in him sees the Fields, he replied, It is a small organization trying to do what it does well, and to mature without blowing up! Over the years each director has been just right for the circumstances, and each in turn has transformed the Institute in his own way. For his part, through his connection to the Fields, Siller continues his life-long association with mathematics. Philip Siller Elaine Riehm (Fields) 12 FIELDSNOTES FIELDS INSTITUTE Research in Mathematical Science

13 McMaster Mathematics Building wins Governor-General s Architecture Award THE NEW HOME OF THE DEPARTMENT of Mathematics and Statistics at McMaster, the James Stewart Centre, was officially opened on Thursday October 30. The Centre is located in historic Hamilton Hall, one of the original buildings on the campus, built in The renovation was carried out by KPMB Architects, who also designed the Fields Institute. It was recently announced that the project was selected by the Royal Architectural Institute of Canada to receive a medal in the 2004 Governor General s Architecture competition. Architect Bruce Kuwabara described Hamilton Hall as Collegiate Gothic. The design adopted contrasts the old weathered exterior with a dramatic new interior. Thus while the Gothic stone exterior was maintained, the interior was radically transformed, interweaving classrooms, seminar rooms, faculty offices, three laboratories, and graduate study areas. Oversized corridors throughout the building are furnished with tables, benches, and blackboards to encourage group study and mathematical discussion. On the ground floor, the Math Café is equipped not only with an espresso machine but also with a series of blackboards, thus reflecting its dual role as a café and a student drop-in centre. The centre is named after Fields fellow James Stewart, long-time faculty member at McMaster and author of several well-known series of high school and undergraduate textbooks. Jim s generous donation to the building fund was crucial in getting the project approved by the University administration. He was personally involved, along with several faculty members, in guiding the architect to design the centre to enhance interactivity among all users of the building. And that hope has been realized -the corridors are filled with clusters of students working at problems, often with the help of faculty, and postdoctoral and graduate students. Carl Riehm (Fields) Thanks to our Sponsors MAJOR SPONSORS Government of Ontario Ministry of Training, Colleges, and Universities; Government of Canada Natural Sciences and Engineering Research Council (NSERC) CORPORATE SPONSORS Algorithmics, General Motors, Generation 5, the Individual Finance and Insurance Decisions (IFID) Centre, Sigma Analysis and Management, and TM Bioscience PRINCIPAL SPONSORING UNIVERSITIES Carleton University, McMaster University, University of Ottawa, University of Toronto, University of Waterloo, University of Western Ontario, and York University AFFILIATED UNIVERSITIES Iowa State University, University of Guelph, University of Manitoba, University of Maryland, University of Notre Dame, University of Saskatchewan, and Queen s University. The Fields Institute is grateful to all its sponsors for their support. OTHER EVENTS 2004 THROUGH APRIL SAW MORE FIELDS EVENTS than can be reported here in detail. These include thematic activities such as the Workshop on Kinetic Theory (March 29 - April 2, 2004 organized by D. Levermore, Th. Passot, C. Sulem, and P.-L. Sulem), a Colloquium in Geometric Analysis organized by W. Craig and P. Guan, as well as three short courses on Isoperimetric Inequalities for Eigenvalues of the Laplacian; Kinetic Theory; and Collisionless Plasmas. General scientific activity supported by Fields included George Elliot s weekend meeting on Operator Algebras held March 13-14, 2004; a workshop on Mathematical Oncology, organized by A. Oza and S. Sivaloganathan April 23-24, 2004; Ottawa-Carleton Discrete Mathematics Day, held April 24, 2004 at Carleton University; plus a number of ongoing seminar series. The institute's commercial and industrial mathematics (CIM) program saw its third annual IFID conference on Personal Risk Management, held April 28, 2004 on the topic of Asset Allocation and Mortality and organized by Moshe Milevsky. The institute helped inaugurate a new CIM project, the PRMIA Risk Management seminars, the first of which heard Erik Heitfield of the Washington Federal Reserve Board speak to a full house on March 17, 2004 on aspects of the Basel accord. The monthly Mathematics Education Forum continued its work, addressing topics such as on-line learning objects for mathematics education (November 29, 2003), how the double cohort fared (January 24, 2004), mathematics education of elementary school teachers (February 28, 2004), mathematics education issues at the college level (March 27, 2004), and facilitating research in mathematics education (April 24, 2004). Tom Salisbury (Fields) FIELDS INSTITUTE Research in Mathematical Science FIELDSNOTES 13

14 Call for Proposals, Nominations, and Applications For detailed information on making proposals or nominations, please see the website: General Scientific Activities Proposals for short scientific events in the mathematical sciences are welcome any time, with a lead time of at least one year recommended. Activities supported include workshops, conferences, seminars, and summer schools. If you are considering a proposal, we recommend that you contact the Director or Deputy Director Thematic Programs Deadlines for letters of intent and proposals for semester or year-long programs at the Fields Institute are March 15 and August 31 each year. Organizers are advised that a lead time of several years is required, and are encouraged to submit a letter of intent prior to preparing a complete proposal. They may consult the directorate about their projects in advance to help structure their proposal. Postdoctoral Opportunities Applications are invited for postdoctoral fellowship positions for the academic year. The thematic program on Renormalization and Universality in Mathematics and Mathematical Physics will take place at the Institute from August-December 2005, while the thematic program on Holomorphic Dynamics, Laminations, and Hyperbolic Geometry will run from January-June Qualified candidates who have recently completed a PhD in a related area of the mathematical sciences are encouraged to apply. The fellowships provide for a period of at least one year of engagement in research and participation in the activities of the Institute. They may be offered in conjunction with partner universities, through which a second year of support may be possible. One recipient will be awarded the Institute s prestigious Jerrold E. Marsden Postdoctoral Fellowship. Applicants seeking postdoctoral fellowships funded by other agencies (such as NSERC or international fellowships) are encouraged to request the Fields Institute as their proposed location of tenure, and should apply to the address below for a letter of invitation. The deadline for postdoctoral applications for the programs is December 10, 2004, although late applications may be considered. CRM-Fields Prize The Centre de recherches mathématiques (CRM) and the Fields Institute invite nominations for this joint prize in recognition of exceptional achievement in the mathematical sciences. The candidate s research should have been conducted primarily in Canada or in affiliation with a Canadian university. Previous recipients are H.S.M. Coxeter, George A. Elliott, James Arthur, Robert Moody, Stephen A. Cook, Israel Michael Sigal, William T. Tutte, John Friedlander, John McKay, Edwin Perkins and Donald A. Dawson. Nominations for the CRM-Fields Prize should reach the Institute by October 1, Please send applications, nominations, and proposals to: The Director, Fields Institute 222 College Street, Toronto, Ontario, M5T 3J1 Canada 14 FIELDSNOTES FIELDS INSTITUTE Research in Mathematical Science

15 Fields Activities Chalk it up to Mathematics MAY TO SEPTEMBER 2004 Detailed information: Thematic Programs FIELDS PARTIAL DIFFERENTIAL EQUATIONS, MAY 3-5, 2004 Coxeter Lecture Series, Sergei Kuksin MAY 10-13, 2004 Distinguished Lecture Series, Jean Bourgain MAY 12 15, 2004 Short Course on Hamiltonian Partial Differential Equations MAY 17 21, 2004 Workshop on Integrable and Near-integrable Hamiltonian PDE (joint with CRM) MAY 24 28, 2004 Workshop on Hamiltonian Dynamical Systems (joint with CRM), at CRM JUNE 1 11, 2004 Workshop on Semi-classical Analysis (joint with CRM) June 1 5, at CRM; June 7 11, at Fields JUNE 14 18, 2004 Conference on Free Surface Water Waves GEOMETRY OF STRING THEORY, General Scientific Activities at Fields unless otherwise indicated MAY 5-9, 2004 Representation Theory of p-adic Groups, at University of Ottawa MAY 6-8, 2004 Mathematics of Computer Algebra and Analysis, at University of Waterloo MAY 8-18, 2004 Quantum Information Geometry and Quantum Computing May 7-17, at McMaster University; May 18, at Fields MAY 12 14, 2004 Shape Optimization and Applications, at University of Ottawa MAY 12 15, 2004 Large-Scale Nonlinear and Semi-definite Programming, at University of Waterloo MAY 12 16, 2004 The Coxeter Legacy: Reflections and Projections, at University of Toronto MAY 14 18, 2004 Geometry and Topology of Manifolds, at McMaster University MAY 17-18, Canadian Symposium on Abstract Harmonic Analysis, at University of Western Ontario MAY 18 19, 2004 Southern Ontario Statistical Graduate Student Seminar, at University of Waterloo MAY 19 23, Canadian Operator Theory and Operator Algebra Symposium, at University of Waterloo MAY 25-27, 2004 Model Theory Workshop JUNE 7 26, 2004 Summer School on Probability Models and Statistical Analyses for Ranking Data, at University of Ottawa JUNE 11-13, 2004 Mathematics of Learning Objects Symposium, at University of Western Ontario JUNE 17 19, 2004 Conference in Honour of D. Brownawell, at University of Waterloo JUNE 20 25, 2004 Canadian Number Theory Association VIII Meeting, at University of Toronto JUNE 21-25, 2004 Fourth Canadian Summer School on Quantum Information, at University of Waterloo JUNE 22, 2004 Public Lecture by Hendrik Lenstra JULY 16-20, 2004 Algebraic Topological Methods in Computer Science II, at University of Western Ontario JULY 19-23, 2004 Quantum Information and Quantum Control JULY 28-30, 2004 MOPTA 2004 McMaster Optimization Conference: Theory and Applications, at McMaster University AUG. 4-7, 2004 IMS, New Researchers Conference, at York University AUG. 5-6, 2004 Workshop on Missing Data Problems AUG. 6-7, 2004 New Directions in Probability Theory SEPT , 2004 Distinguished Lecture Series in Statistical Science, Sir David Cox FIELDS INSTITUTE Research in Mathematical Science FIELDSNOTES 15

16 From the Director: Farewell THIS IS MY LAST ARTICLE as director of the Institute, as I will be passing the torch to Barbara Keyfitz on July first. I am confident that I am leaving the Institute in good hands. I hope that everyone will continue to give her the same high level of support that I have received during my three years Kenneth Davidson in the job. Indeed, I cannot emphasize enough that the Institute is as strong as it is because of the enthusiastic support it received from the dozens of people involved in organizing activities every year. The Institute has welcomed two new sponsoring universities in this period, with Carleton joining just recently; we now have seven universities that have recognized the importance of the Institute and are willing to support it at this level. In return, we are now running many off-site activities a program which has been incredibly successful. Indeed, this has been the most dramatic change over the past few years, and I think that there has been a significant increase in the role of Fields at all of our sponsoring and affiliate universities. We continue to push the boundaries of the role of mathematics. While there are many important issues central to the domain of pure mathematics, the role of the mathematical sciences in science, engineering, business and industry is also increasing. The Fields Institute is here to foster both. Indeed this interaction with other disciplines is one place where Fields plays a crucial role. There is a great opportunity here to do even more in the future. One very positive development has been the increased involvement of statisticians in the institutes across Canada through the creation of the National Program on Complex Data Systems, which is reported elsewhere in this newsletter. The Fields Institute plays an important role as an intermediary that binds the mathematical community in Canada together. It is a meeting place where interested parties from different universities, and even different departments of the same university, can meet on neutral ground. This creates both a forum, and a focal point for action, that has helped to bring people together. It allows us as a community to move forward on certain issues of mutual interest without having to divide up the turf. The thematic program at Fields this year has been in partial differential equations. This program has been (and continues to be) one of the busiest ever. Thanks go out to Walter Craig, Catherine Sulem and Nick Ercolani who led the team, as well as to all those who organized workshops, taught grad courses and ran seminars or colloquia. Coming too late for this newsletter are the Coxeter lectures by Sergei Kuksin and the Distinguished Lecture Series by Fields medallist Jean Bourgain, which will likely have taken place by the time you read this. May and June are also packed with four weeks of workshops split between Fields and the CRM, who are running a related program, as well as a conference on water waves. So this program will end with a bang, not just fade away. Many other interesting events are coming up over the summer at Fields and on our sponsoring university campuses. Check the list of upcoming events. Recent visitors to the Institute will have noticed a piano tucked under the spiral staircase. This was Donald Coxeter's life-long instrument. He learned to play on it as a child, composed music using it, and later moved it from England to Canada. We are extremely pleased that it has been donated to the Institute by his daughter, Susan Thomas. The Rud Ibach Sohn baby grand, which is about 150 years old, has been repaired and tuned back into good shape. There will be a concert in May during the Coxeter symposium in which the piano will feature along with voice and a string quartet. Four of the musicians are mathematicians, and the program will include one of Coxeter's own compositions. Let me finish by extending my thanks to the wonderful staff at the Institute. Anyone who has run an event here can appreciate the efficient, friendly and effective support that they receive from our program staff. This support is one of the most obvious and tangible benefits we offer to our organizers. In addition, behind the scenes, we have a dedicated and skilled staff running the office, maintaining our finances and backing up our computers. The Institute cannot function without them. So thanks again. I am returning to my old haunts at the University of Waterloo, but I am not turning my back on the Institute. I look forward to continued involvement, and I expect to continue to run into the many friends and acquaintances that I have made during this interesting period as director. Kenneth Davidson (Fields) FIELDS INSTITUTE Research in Mathematical Science 222 COLLEGE STREET, 2ND FLOOR TORONTO, ONTARIO, CANADA M5T 3J1 Tel Fax FIELDS Creative: Scott Thornley + Company st-c.com

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