C CENTRE R DERECHERCHES M MATHÉMATIQUES

AnnualReport 2011 2012

C CENTRE R DERECHERCHES M MATHÉMATIQUES

AnnualReport 2011 2012 Centre de recherches mathématiques Université de Montréal C.P. 6128, succ. Centre-ville Montréal, QC H3C 3J7 Canada [email protected]

Also available on the CRM website http://crm.math.ca/docs/docRap_an.shtml.

© Centre de recherches mathématiques Université de Montréal, 2014 ISBN 978-2-921120-50-0 Contents

Presenting the Annual Report 2011–2012 1

Thematic Program 3 Thematic Programs of the Year 2011–2012: “Quantum Information” and “Geometric Analysis andSpec- tral Theory” ...... 4 Aisenstadt Chairholders in 2011–2012 : John Preskill, Renato Renner, László Erdős, Elon Lindenstrauss, and Richard M. Schoen ...... 5 Activities of the Thematic Semesters ...... 9 Past Thematic Programs ...... 21

General Program 23 CRM activities ...... 24 Colloquium Series ...... 36

Multidisciplinary and Industrial Program 39 Activities of the Multidisciplinary and Industrial Program ...... 40

CRM Prizes 45 CRM–Fields–PIMS Prize 2012 Awarded to Stevo Todorcevic ...... 46 André-Aisenstadt Prize 2012 Awarded to Marco Gualtieri and Young-Heon Kim ...... 47 The CAP–CRM Prize 2012 Awarded to Luc Vinet ...... 48 The CRM–SSC Prize 2012 Awarded to Changbao Wu ...... 49

The CRM Outreach Program 50 The language of life : When mathematics speaks to biology — Gerda de Vries ...... 51 From Aristotle to the Pentium — Moshe Y. Vardi ...... 52 Major trends in world fisheries and their effects on ecosystems — Daniel Pauly ...... 53

CRM Partnerships 54 CRM Partners ...... 55 Joint Initiatives ...... 58

Mathematical Education 59 Institut des sciences mathématiques (ISM) ...... 60 Other Joint Initiatives ...... 63

Research Laboratories 64 Applied Mathematics ...... 65 CICMA – Centre Interuniversitaire en Calcul Mathématique Algébrique ...... 69 CIRGET – Centre Interuniversitaire de Recherches en Géométrie Et Topologie ...... 71 GIREF – Groupe Interdisciplinaire de Recherche en Éléments Finis ...... 73 LaCIM – Laboratoire de Combinatoire et d’Informatique Mathématique ...... 75 Mathematical Analysis ...... 77 Mathematical Physics ...... 79 PhysNum ...... 83 Statistics ...... 85

Publications 91 Recent Titles ...... 92 Previous Titles ...... 92

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Scientific Personnel 97 CRM Members in 2011–2012 ...... 98 Postdoctoral Fellows ...... 100 Visitors ...... 100

List of Students Having Graduated in 2011–2012 103 Ph.D. Students ...... 104 M.Sc. Students ...... 105

Governance and Scientific Guidance 109 Board of Directors ...... 110 Committee of Directors of Laboratories ...... 110 International Scientific Advisory Committee ...... 111

CRM Administrative and Support Staff 115 The Director’s Office ...... 116 Administration ...... 116 Scientific Activities ...... 116 Computer Services ...... 116 Publications ...... 116 Communications ...... 116

Mandate of the CRM 117

iv Presenting the Annual Report 2011–2012 Centre de recherches mathématiqes

It is a pleasure to present the CRM annual report Aisenstadt Prize 2012), Luc Vinet from the Université for 2011-2012. Our two themes for the year, Quan- de Montréal (CAP–CRM Prize 2012), and Changbao tum Information on one hand and Geometric Anal- Wu from the University of Waterloo (CRM–SSC Prize ysis and Spectral Theory on the other, are among 2012). the most important research areas in the mathemat- ical sciences. As is now the tradition at the CRM, For several years now the CRM has had international the Centre welcomed world-renowned experts in both agreements, in particular with the ALGANT consor- themes, including the Aisenstadt Chairholders: John tium of the European Union and the Tata Institute of Preskill, Renato Renner, László Erdős, Elon Linden- Fundamental Research in India. The year 2011 was a strauss, and Richard M. Schoen. Apart from the lec- milestone in the development of international relations tures by these Chairholders, the thematic semester on at the CRM, since the CNRS (the institution responsible Quantum Information featured one summer school, for research in France) established an Unité Mixte In- two conferences, and four workshops, while the the- ternationale (UMI) at the CRM. This UMI, one of only matic semester on Geometric Analysis and Spectral 30 UMIs (in all subjects) around the world, is led by Theory featured six workshops. In 2011-2012 theCRM Laurent Habsieger (CNRS) and the CRM director. It also had a substantial general program, since it or- supports visits of French mathematicians to the CRM ganized or supported 14 events (schools, conferences, and vice versa, thus ensuring the creation or strength- or workshops), in particular two very important sum- ening of links between the two countries. mer schools (the Summer School on Non-Equilibrium The activities of the CRM are supported by the Gov- Statistical Mechanics and the Séminaire de Mathé- ernment of Canada through NSERC, the Government matiques Supérieures on Metric Measure Spaces) and of Québec through FRQNT, the Government of the the International Workshop on the Perspectives on United States through the National Science Foundation High-Dimensional Data Analysis II. The multidisci- (NSF), the Mprime network, and its partner univer- plinary and industrial program of the CRM in 2011- sities: the Université de Montréal, McGill University, 2012 included a conference on statistics (Statistics 2011 the Université du Québec à Montréal, Concordia Uni- Canada), a workshop on the climate problem, and versity, the Université Laval, the Université de Sher- the Fourth Montréal Industrial Problem Solving Work- brooke, and the University of Ottawa. On behalf of the shop. CRM I extend my warmest thanks to all of these insti- The CRM is also proud of the outstanding researchers tutions, which have helped the CRM attain the status who were awarded its four prizes this year: Stevo of a world-class research centre in the mathematical Todorčević from the University of Toronto (CRM– sciences. Fields–PIMS Prize 2012), Marco Gualtieri from the Uni- versity of Toronto and Young-Heon Kim from the Uni- François Lalonde, Director versity of British Columbia (both awarded the André- Centre de recherches mathématiques (CRM)

2 Thematic Program Centre de recherches mathématiqes

Thematic Programs of the Year 2011–2012 “Quantum Information” and “Geometric Analysis and Spectral Theory” Quantum Information capsule summaries of the talks can follow the links provided below. Quantum information science is an interdisciplinary The scientific committee of the semester included the field lying at the boundary of mathematics, computer following researchers: Alexandre Blais (Sherbrooke), science and physics. The main goal of the field is toun- Gilles Brassard (Montréal), Claude Crépeau (McGill), derstand the fundamental nature of information in a Guillaume Duclos-Cianci (Sherbrooke), Christopher quantum mechanical world while simultaneously try- Fuchs (Perimeter Inst.), Patrick Hayden (McGill), Aram ing to exploit that understanding for technological Harrow (Washington), Peter Høyer (Calgary), Olivier gain. Montréal has been an important centre for quan- Landon-Cardinal (Sherbrooke), Michel Pioro-Ladrière tum information research from the beginning; twenty- (Sherbrooke), David Poulin (Sherbrooke), Bertrand five years ago, Gilles Brassard, a local researcher, in- Reulet (Sherbrooke), Louis Salvail (Montréal), and vented the first protocol for exchanging secret keys ex- Alain Tapp (Montréal). ploiting quantum mechanics. About fifteen years ago, Brassard, Claude Crépeau and collaborators discov- Geometric Analysis and Spectral Theory ered the famous quantum teleportation protocol fol- lowing a workshop here in Montréal. The 2012 Spring Semester focused on various topics in The Fall 2011 thematic semester on quantum informa- geometric analysis, spectral theory, partial differential tion was notable not just for the variety and success equations, and mathematical physics, including: geo- of its activities, but also for its judicious application of metric PDE, spectral geometry, probabilistic methods creative chronology. Fall 2011 officially began in June in geometry and analysis, quantum many-body sys- with the 11th Canadian Summer School on Quantum tems, and geometry and dynamics of fluids. The goal Information and ended when Montréal hosted the 2012 of the semester was to highlight some remarkable re- edition of the prestigious Quantum Information Con- cent developments and to foster collaboration between ference in December 2011. In between, there was a researchers working in these diverse and yet interre- student-only conference designed to provide young re- lated areas of mathematics. The semester featured six searchers with a supportive environment in which to workshops, respectively on convexity and asymptotic present their research, in addition to four workshops geometric analysis, geometric PDE, the geometry and exploring quantum information from the point of view dynamics of fluid, quantum many-body systems, the of computer science, many-body physics, communica- geometry of eigenvalues and eigenfunctions, and man- tion theory, and the foundations of quantum mechan- ifolds of metrics and probabilistic methods in geometry ics. Renato Renner of ETH Zürich and John Preskill and analysis. of Caltech together spent about five weeks in Québec The scientific committee of the semester included as the two Aisenstadt chairs, delivering seven brilliant the following researchers: Galia Dafni (Concordia), and well-attended distinguished lectures. Pengfei Guan (McGill), Dmitry Jakobson (McGill), Vo- The semester also benefited from the heroically in- jkan Jakšić (McGill), Niky Kamran (McGill), Sergei dustrious participation of Charles Bennett, Aram Har- Kuksin (École Polytechnique), Iosif Polterovich (Mont- row and Steve Flammia, the three schismatic popes réal), Stephen Preston (CU-Boulder), Robert Seiringer of the Quantum Pontiff blog (http://dabacon.org/ (McGill), Alexander Shnirelman (Concordia), Alina pontiff). Together, they produced live transcripts for Stancu (Concordia), John Toth (McGill), and Steve several of the thematic semester’s workshops and con- Zelditch (Northwestern). ferences. Readers interested in browsing the bloggers’

4 Thematic Program

Aisenstadt Chairholders in 2011–2012 John Preskill, Renato Renner, László Erdős, Elon Lindenstrauss, and Richard M. Schoen John Preskill and Renato Renner were the Aisenstadt for two parties to expand a very short secret into an chairholders for the semester on quantum informa- arbitrarily long one, which can then be used as cryp- tion. László Erdős, Elon Linderstrauss, and Richard M. tographic fuel for secure encryption and many other Schoen were the Aisenstadt chairholders for the tasks. Information-theoretically secure key distribu- semester on geometric analysis and spectral theory. tion is impossible without invoking the laws of quan- tum mechanics, but in the 1980s Bennett and Bras- John Preskill sard showed how to exploit quantum mechanics to make it work. Real-world complications like noise and by Patrick Hayden (McGill University) loss confound their protocol and analysis, however. John Preskill is the Richard P. Feynman Professor of Université de Montréal Ph.D. student Dominic My- Theoretical Physics at Caltech and began his career ers found a way around those problems, but his argu- working at the intersection of particle physics and ment was uncommonly difficult to follow and, hence, cosmology. Early on, he observed that incorporating underappreciated. Preskill and Shor found a concep- grand unified theories of elementary particles into cos- tually simple proof by relating the security of real- mology predicts the widespread production of super- life key distribution protocols to the success of cur- heavy magnetic monopoles, which is in sharp conflict rently science-fictional entanglement distillation pro- with observation. Resolving the conflict ultimately led tocols. In cryptography, vulnerabilities stem just as of- to the theory of the inflationary universe. ten from subtle implicit assumptions as from failures of abstract reasoning, so the transparent simplicity of Inspired by Peter Shor’s landmark factoring paper in the Shor–Preskill proof greatly amplified its impact. the mid-1990s, Preskill became interested in whether quantum computers could ever be stabilized against In addition to being a leading researcher, Preskill has imperfections and environmental noise. With his stu- been a prolific mentor to young scientists. He has su- dent Daniel Gottesman and others, Preskill made the pervised more than 40 Ph.D. students over the years, profound discovery that once the noise is pushed be- an impressive fraction of whom are now leading re- low a certain threshold value, quantum computations searchers themselves. His lecture notes on quantum can be scaled up indefinitely. Contrary to expectation, computation form one of the standard references on longer and larger computations do not require appre- the subject. In 2000 he founded the Institute for Quan- ciably more precise apparatus. In the absence of the tum Information (IQI) at Caltech, which for many threshold theorem, quantum computation would have years was the undisputed theoretical hub of the sub- been a theoretical curiosity without any prospect of ject. (Today it is just the disputed hub.) Many of ever becoming an engineering reality. With the the- Canada’s leading young researchers in quantum infor- orem in hand (if not always understood), armies of mation spent time as postdoctoral fellows at the IQI, in- experimentalists are now trying to build viable quan- cluding Andrew Childs (Waterloo), Debbie Leung (Wa- tum computers. Over the past fifteen years, Preskill terloo), Ashwin Nayak (Waterloo), David Poulin (Sher- has relentlessly pursued improvements to the theory brooke), and Robert Raussendorf (UBC). (I was lucky to of quantum fault-tolerance. By simplifying the reason- spend three years there myself.) ing, improving the underlying computational building As the Aisenstadt chair, Preskill delivered a series of blocks, and introducing more realistic models of the four lectures: a public lecture, physics colloquia at noise, he, as much as anyone, has helped close the gap McGill and Sherbrooke, as well as a research talk in between what experimentalists can achieve and the the Codes, Geometry and Random Structures work- noise thresholds required for fault tolerance. shop. The public lecture, entitled “Putting weirdness to In another celebrated result, Preskill joined forces with work: quantum information science,” gave a high-level Peter Shor to give a proof of the security of quan- introduction to quantum algorithms, key distribution tum key distribution. The goal in key distribution is and fault-tolerance, ending with a report on the cur- rent experimental state of the art. The physics collo-

5 Centre de recherches mathématiqes quia were devoted to “Battling decoherence: the fault- quantum cryptography and statistical physics. Recip- tolerant quantum computer.” In each, Preskill man- ient of medals for the best diploma and Ph.D. theses aged to explain the crucial ideas behind quantum fault- at ETH Zürich, as well as a dissertation prize from the tolerance in just under an hour. Starting with an ex- Association for Computing Machinery, his alma mater planation of how quantum error correcting codes can quickly hired him as an assistant professor in their In- be used to correct continuous families of errors, he stitute for Theoretical Physics in 2007. then showed how to compute with encoded qubits, ul- The ideas and techniques introduced in Renner’s Ph.D. timately building to the recursive error-suppression of thesis have spread like wildfire through the commu- full fault-tolerant quantum computation. To analyze nity of quantum information researchers. Shannon’s the recursive construction, he used a particularly ver- entropy plays a central role in information theory satile and robust version of the threshold argument and the von Neumann entropy an analogous role in that he found with Gottesman and Aliferis in 2005. quantum information theory. When studying optimal The talk ended with a quick introduction to topolog- compression rates or communication capacities, how- ical quantum computation, in which the inherent sta- ever, the Shannon and von Neumann entropies pro- bility of the topological degrees of freedom thought to vide the right answers only when the systems being be present in certain exotic materials could eliminate studied have a great deal of independence in their con- (or at least mitigate) the need for active quantum error stituents. When communicating over channels with in- correction. ternal memory states or trying to analyze the eaves- Preskill’s contribution to the Codes, Geometry and dropping strategies of a malicious adversary, the stan- Random Structures workshop was a remarkable hybrid dard entropies prove to be clumsy and often inade- of nonlinear quantum electronics and quantum error quate tools. In his thesis, Renner introduced the quan- correction to which he gave the title “Protected gates tum min-entropy and developed a formalism for an- for superconducting qubits.” Over the past few years, alyzing it. This new entropy reduces to the von Neu- experiments building qubits out of the macroscopic mann entropy in the appropriate limit of many iden- degrees of freedom of superconducting circuits have tical and independent quantum states, but is univer- made tremendous strides. The decoherence time of sally applicable. The thesis then proceeded to give a such qubits, for example, has been extended by several new proof of the security of quantum key distribution orders of magnitude. Preskill’s objective was to find a sufficiently general to encompass most of the known way to engineer superconducting qubits that would be protocols. More importantly, the proof yielded quanti- intrinsically fault-tolerant, just as excitations in ma- tative bounds on the security of the protocols for finite terials with topological order are thought to be. Re- length keys; previous arguments were only valid in the markably, he, Peter Brooks, and Alexei Kitaev showed limit of infinite key lengths. that there is a quantum error correcting code lurking Since completing his thesis, Renner has been astonish- 0 inside the previously proposed superconducting “ – ingly productive, having written over 90 articles at last π ” qubit. More importantly, logic gates can be fault- count, including an amazing 21 last year, during which tolerantly applied to the encoded qubits using noth- he was also graciously fulfilling his duties as Aisen- ing more exotic than a tunable Josephson coupling be- stadt chair. That work has now comprehensively refor- tween an LC oscillator and the qubits in question. This mulated quantum information theory in the universal work arguably increases from two to three the number min-entropy formalism. One benefit of the formalism of known paradigms for achieving fault-tolerant quan- is that the theory applies without modification to real tum computation. More importantly, it hints that there physical systems, in which the independence assump- are probably others awaiting invention. tions justifying the use of the von Neumann entropy are often violated. In a beautiful recent Nature paper, Renato Renner Renner and his collaborators showed that the condi- by Patrick Hayden (McGill University) tional min-entropy is proportional to the amount of work required to erase the contents of one quantum Despite having only received his Ph.D. in 2005, Renato memory register without modifying another. Provid- Renner has already had a tremendous impact on quan- ing an interesting twist on the second law of thermo- tum information theory and its applications to both dynamics, the fact that the conditional min-entropy

6 Thematic Program is negative for some entangled quantum states means by contradiction, making use of an experiment in- that erasing information can sometimes produce work spired by previously proposed quantum key distribu- rather than consuming it. tion protocols. For his talk in the Quantum Computer Renner gave a series of three Aisenstadt lectures: a Science workshop, Renner spoke about “Free random- public lecture and two scientific talks, one each in ness amplification,” another project with Roger Col- the Quantum Computer Science and Quantum Many- beck. The mathematical concept of free randomness is Body Physics workshops. The public lecture addressed actually a way of formalizing, through the use of ran- the question: “What does quantum cryptography tell dom variables located in spacetime, the words “cho- us about quantum physics?” Renner started by observ- sen freely” used in the theorem above. In his lecture, ing that Aisenstadt, like himself, had obtained a doc- he showed how a weak source of free randomness torate in Zürich and then somewhat later become in- could be processed and upgraded into a form suffi- volved with the CRM. While Renner’s supervisor was ciently good to be used in the theorem or in crypto- the very eminent cryptographer Ueli Maurer, Aisen- graphic applications. Crucially, the argument doesn’t stadt worked for none other than Albert Einstein. Since assume the validity of quantum mechanics, just the Renner’s talk would be devoted to consequences of impossibility of signalling faster than light. Finally, cryptography for the completeness of quantum me- changing gears somewhat, Renner devoted his final chanics, the latter a subject of great concern to the lecture, in the Quantum Information in Many-Body great man himself, it seemed an auspicious beginning. Physics workshop, to “An information-theoretic view on thermalization.” The talk sketched some of the im- John Bell’s great discovery in the 1960s was that quan- plications of our rapidly advancing understanding of tum mechanics made predictions incompatible with lo- quantum information for thermodynamics, including cal realism, the paired assumptions that signals can’t the remarkable discovery mentioned earlier in this ar- propagate faster than light and that objects have well- ticle that work can sometimes be extracted when eras- defined states prior to being measured. Experiments ing parts of entangled quantum states. have since confirmed Bell’s predictions, requiring that either locality or realism be false. These developments László Erdős were generally thought to refute Einstein’s view that a more complete theory of physics would ultimately In the week of March 19, Professor László Erdős was replace quantum mechanics. However, while Bell’s re- visiting the CRM as Aisenstadt chair. L. Erdős is Chair sult ruled out a wholesale replacement of quantum me- of Applied Mathematics and Numerics at the Ludwig- chanics by a local realistic theory, it isn’t widely appre- Maximilians-Universität München, Germany. He has ciated that the possibility of a more complete theory of made substantial contributions to the analysis of large physics remained open. In his talk, Renner presented quantum systems, in particular concerning the deriva- joint work with Roger Colbeck (Perimeter) that finally tion of effective kinetic equations in certain scaling lays that possibility to rest. Half the challenge was for- limits. His recent research has led to spectacular new mulating a clear mathematical question, but they ulti- results in the theory of random matrices, which was mately proved a more formal version of the following the topic of his Aisenstadt lectures. statement: L. Erdős gave three lectures during his visit. The first Theorem. Assume that measurement statistics are cor- one, which was suitable for a general audience, was rectly predicted by quantum theory and that measure- entitled “Universality of spectral statistics of random ment settings can be chosen freely. Then there cannot ex- matrices.” It contained a description of the recent proof ist any extended theory that provides additional infor- of the celebrated Wigner–Gaudin–Mehta–Dyson con- mation about the outcomes of quantum measurements. jecture, which was obtained by L. Erdős in collabora- Not surprisingly, the formalization of “providing ad- tion with Benjamin Schlein, Horng-Tzer Yau and Jun ditional information” involves Renner’s beloved quan- Yin. This conjecture asserts that the local eigenvalue tum conditional entropies. The proof of the theorem statistics of a random matrix with independent entries was both ingenious and elementary, allowing him to depend only on the symmetry class of the random ma- present it in its entirety during the public lecture. The trix and is independent of the detailed structure of the connection to cryptography is that the argument was matrix ensemble. In particular, it is the same as for the Gaussian ensembles, where the eigenvalue distribution

7 Centre de recherches mathématiqes can be calculated explicitly. L. Erdős presented a nice if the manifold has negative sectional curvature (which overview of the history of this subject, and explained implies that the classical dynamics is uniformly hyper- the key steps involved in their proof. bolic, hence “chaotic”), the eigenfunctions of the Lapla- His subsequent talk (“The local version of Wigner’s cian should become equidistributed in the semiclassi- semicircle law and Dyson’s Brownian motion”) con- cal limit. tained some of the details of the proof. In particular, In the first lecture (titled “Entropy and Quantum L. Erdős explained the notion of Dyson Brownian mo- Unique Ergodicity”), Professor Lindenstrauss gave an tion and how it can be used in combination with a lo- overview of ergodic flows, the Kolmogorov–Sinai en- cal version of Wigner’s semicircle law to prove uni- tropy of ergodic measures, the Ledrappier–Young en- versality for arbitrary Wigner matrices. Finally, in the tropy formula, and the Bowen–Margulis theorem on third talk by L. Erdős (“Quantum diffusion and random equidistribution of periodic orbits. He then reviewed band matrices”), the problem of localization vs. diffu- Shnirelman’s Quantum Ergodicity theorem and the sion for random band matrices was discussed. Random Quantum Unique Ergodicity conjecture, and he dis- band matrices can be viewed as intermediate between cussed recent results due to Anantharaman, Nonnen- completely random matrices and random Schrödinger macher, and Koch that hold for general negatively operators, where the randomness is only in the diag- curved surfaces. onal. There is a precise conjecture on the critical band The second and third lectures were devoted toQuan- width separating the regimes of localization and delo- tum Unique Ergodicity on finite area arithmetic hyper- calization, respectively, and L. Erdős and his collabora- bolic surfaces. Such surfaces possess a lot of symmetry, tors have recently made substantial progress towards provided by the Hecke operators. Joint eigenfunctions a proof of this conjecture. of the Laplacian and those operators are called Hecke– Maass automorphic forms. They play an important role Elon Lindenstrauss in modern analytic number theory. One can use Hecke Professor Elon Lindenstrauss from Hebrew University operators to get much more information about Hecke– of Jerusalem delivered a series of three Aisenstadt lec- Maass forms than about general eigenfunctions. Lin- tures from June 4 to June 7, 2012, during the Workshop denstrauss surveyed recent results about these eigen- on Geometry of Eigenvalues and Eigenfunctions. Pro- functions (and the closely related class of holomor- fessor Lindenstrauss is a world leader in Ergodic The- phic forms) using both number theoretic and dynam- ory and Dynamical Systems. His contributions include ical techniques developed by himself (some of them the proof of the Arithmetic Quantum Unique Ergod- together with Bourgain), Silberman and Venkatesh, icity conjecture of Rudnick and Sarnak, work on the Holowinsky and Soundararajan. Littlewood conjecture, and study of distributions ofpe- Professor Lindenstrauss also presented his recent joint riodic torus orbits in some arithmetic spaces. He was work with S. Brooks, which relates the study of eigen- awarded the Fields Medal in 2010. Professor Linden- functions and quasi modes on arithmetic surfaces to strauss has received numerous other prizes, including the study of eigenfunctions of the discrete Laplacian the Clay Fellowship, the 2003 Salem Prize, the 2004 Eu- on finite graphs. ropean Mathematical Society Prize, the 2008 Michael Bruno Memorial Award, and the 2009 Erdős and Fer- Richard M. Schoen mat Prizes. Professor Richard Schoen delivered a series of three In the lectures, Professor Lindenstrauss discussed his Aisenstadt lectures from February 27 to March 2, 2012. proof of the Quantum Unique Ergodicity conjecture Professor Schoen is Anne T. and Robert M. Bass Pro- and related work, which concerns asymptotic distribu- fessor of Mathematics at Stanford University. He is tion of eigenfunctions of the Laplacian on a Rieman- a world leader in the field of geometric analysis. His nian manifold in the semiclassical limit. Asymptotic many outstanding research achievements include the behaviour of eigenfunctions is one example of the re- proof of the positive mass conjecture in General Rela- lationship between classical dynamics of systems and tivity (with Shing-Tung Yau), the solution of the Yam- their quantum behaviour. The Quantum Unique Er- abe problem, and the proof of the differentiable sphere godicity Conjecture of Rudnick and Sarnak states that theorem (with Simon Brendle). He has been awarded

8 Thematic Program the Bôcher Memorial Prize, the MacArthur Fellowship, of the timelike character of the total energy momen- and the Guggenheim Fellowship. He is a member of tum vector using the marginally outer trapped surface the National Academy of Sciences and the American (MOTS) equation. They also improved the density the- Academy of Arts and Sciences. orems for initial data sets satisfying the dominant en- The three lectures by Professor Schoen focused on ergy condition. some recent developments in geometric analysis. His Aisenstadt Chair first lecture was on “The geometry of positive curva- ture.”He started with a beautiful survey of Riemannian The Aisenstadt chair was endowed by Montréal phi- manifolds of positive curvature, summarizing what is lanthropist Dr. André Aisenstadt. Under its auspices, known and what is conjectured. He then presented the one or more distinguished mathematicians are invited recent breakthrough on the quarter pinching theorem, each year for a period of at least one week, ide- which was proved by S. Brendle and himself. This land- ally one or two months. During their stay the lec- mark result was achieved through a powerful analy- turers present a series of lectures on a specialized sis of the Ricci flow, one of the most important tech- topic. They are also invited to prepare a monograph niques in geometric analysis, together with geodesic (see the chapter on publications in the present re- and minimal surface techniques. This result provides port for a list of these monographs). At the request of deep insight into the geometry of manifolds with pos- Dr. Aisenstadt, the first lecture given by an Aisenstadt itive curvature and represents another major advance chairholder should be accessible to a wide audience. in mathematics after Perelman’s proof of the Poincaré Previous holders of the Aisenstadt chair are: Marc conjecture. Kac, Eduardo Zarantonello, Robert Hermann, Marcos In the second lecture, Professor Schoen described his Moshinsky, Sybren de Groot, Donald Knuth, Jacques- recent work with A. Fraser concerning an extremal Louis Lions, R. Tyrrell Rockafellar, Yuval Ne’eman, problem for the first Steklov eigenvalue on surfaces Gian-Carlo Rota, Laurent Schwartz, Gérard Debreu, with boundary. This question is closely related to the Philip Holmes, Ronald Graham, Robert Langlands, investigation of extremal metrics for the first eigen- Yuri Manin, Jerrold Marsden, Dan Voiculescu, James value of the Laplacian on compact closed surfaces. Arthur, Eugene B. Dynkin, David P. Ruelle, Robert In both Laplace and Steklov cases, extremal eigen- Bryant, Blaine Lawson, Yves Meyer, Ioannis Karatzas, value problems are linked to the study of minimal sur- László Babai, Efim I. Zelmanov, Peter Hall, Sir David faces. For closed surfaces these are minimal surfaces Cox, Frans Oort, Joel S. Feldman, Roman Jackiw, in spheres, while for surfaces with boundary one ob- Duong H. Phong, Michael S. Waterman, Arthur T. tains minimal surfaces in a ball satisfying some natural Winfree, Edward Frenkel, Laurent Lafforgue, George boundary condition. A detailed description was given Lusztig, László Lovász, Endre Szemerédi, Peter Sarnak, for extremal surfaces for the first Steklov eigenvalue in Shing-Tung Yau, Thomas Yizhao Hou, Andrew J. Ma- the genus zero case. jda, Manjul Bhargava, K. Soundararajan, Terence Tao, The final lecture was concerned with a new meancur- Noga Alon, Paul Seymour, Richard Stanley, John J. vature proof of the space-time positive mass theo- Tyson, John Rinzel, Gerhard Huisken, Jean-Christophe rem. The original Schoen–Yau mean curvature proof Yoccoz, Wendelin Werner, Andrei Okounkov, Svante of the general positive mass theorem gave the posi- Janson, Craig Tracy, Stéphane Mallat, Claude Le Bris, tivity of energy. In a recent joint work with M. Eich- Akshay Venkatesh, Yuri Gurevich, Angus Macintyre, mair, L. Huang, and D. Lee, a direct proof was given Alexander Razborov, James Robins.

Activities of the Thematic Semesters

11th Canadian Summer School on Main Organizer: David Poulin (Sherbrooke) Quantum Information Co-organizers: June 6–15, 2011, Jouvence Alexandre Blais (Sherbrooke), Michel Pioro-Ladrière Sponsored by the CRM, the Université de Sherbrooke, (Sherbrooke), Bertrand Reulet (Sherbrooke) EPIQ, CIFAR, INTRIQ, Mitacs, the Perimeter Institute for Theoretical Physics, and QuantumWorks

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Speakers: nal exam on the students’ focus and work ethic. The Patrice Bertet (CEA/Saclay), Gilles Brassard (Mont- next edition of the school will take place in Waterloo réal), Carlton M. Caves (Albuquerque), Andrew Childs in the summer of 2012. (Waterloo), Daniel Gottesman (Perimeter Inst.), Kurt Jacobs (UMass Boston), Michele Mosca (Waterloo), 8th Canadian Student Conference on Jason Petta (Princeton), Robert Raussendorf (UBC), Quantum Information Renato Renner (ETH Zürich), Norbert Schuch (Cal- June 16–17, 2011, Jouvence tech), Graeme Smith (IBM Res.) Sponsored by the CRM, the Université de Sherbrooke, Number of participants: 112 EPIQ, CIFAR, INTRIQ, Mitacs, the Perimeter Institute Over the past decade, the Canadian Summer School for Theoretical Physics, and QuantumWorks on Quantum Information has developed into a vener- Organizers: able institution as the go-to summer destination for Guillaume Duclos-Cianci (Sherbrooke), Olivier Lan- young people interested in pursuing research in the don-Cardinal (Sherbrooke) area. The School has rotated through Calgary, Mont- Speakers: réal, Toronto, Waterloo, and Vancouver over the years, Khulud Almutairi (Calgary), Félix Beaudoin (Sher- so bringing it back to the Montréal area was the perfect brooke), Ran Hee Choi (Calgary), Julien Camirand- way to kick off the thematic semester. This 11th edition Lemyre (Sherbrooke), Sergey Filippov (MIPT), Kent was organized by Université de Sherbrooke professors Fisher (Waterloo), Jan Florjanczyk (McGill), Jose David Poulin, Alexandre Blais, Michel Pioro-Ladrière, Raul Gonzalez Alonso (Southern California), Paweł and Bertrand Reulet. More than 90 students attended, Mazurek (Gdańsk), Leonardo A. Pachon (Toronto), representing 37 universities in 21 countries. Those in- Kyungdeock Park (Waterloo), Sarah Plosker (Guelph), ternational students were treated not just to challeng- Anna Przysiężna (Gdańsk), Cyril Stark (ETH Zürich), ing courses, but to a quintessentially Canadian lake- Xiaoya Judy Wang (McGill), Marco Zaopo (Pavia), side setting at the idyllic Centre de villégiature Jou- Lucy Liuxuan Zhang (Toronto) vence in Québec’s Parc national du Mont-Orford. The quiet setting allowed the students, ranging from the The student conference was held in Jouvence immedi- M.Sc. to the postdoctoral level, to focus on their intense ately after the summer school, making it convenient program of twelve mini-courses, offered by as many to participate in both. The conference has also become world-renowned researchers. The wide-ranging list of something of a tradition, organized and attended ex- topics (given below) introduced the students to the in- clusively by students, free from the intimidating inter- terdisciplinary scope of quantum information science. ference of their graduate supervisors. This year, the or- ganizers were Université de Sherbrooke Ph.D. students • Patrice Bertet, Superconducting qubits Guillaume Duclos-Cianci and Olivier Landon-Cardi- • Gilles Brassard, Communication complexity nal. The conference fulfills a real need since traditional • Carlton M. Caves, High precision measurements conferences usually provide very few opportunities for • Andrew Childs, Quantum algorithms exposure to junior researchers. At the student confer- • Daniel Gottesman, Quantum error correction ence, every participant had the opportunity to present • Kurt Jacobs, Decoherence his or her work as either a talk or a poster. Speakers • Michele Mosca, Quantum algorithms were strongly encouraged to make their presentations • Jason Petta, Spin qubits in quantum dots accessible. In the end, 70 students participated, from • Robert Raussendorf, Topological fault-tolerance countries as diverse as Colombia, Korea, India, Italy, • Renato Renner, Quantum cryptography Switzerland, Poland, Russia, and the United States. • Norbert Schuch, Quantum many-body physics • Graeme Smith, Quantum channels and capacities Workshop on The organizers also took the innovative step of making Quantum Computer Science the summer school a formal graduate-level course at October 4–7, 2011, CRM the Université de Sherbrooke. Students received three credits for successful completion of the school, which Organizers: for the first time included a challenging final exam as- Peter Høyer (Calgary), Alain Tapp (Montréal) sembled from questions supplied by the lecturers. The organizers noted the positive effects of the looming fi-

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Speakers: co-authors introduced to prove no-go theorems in the Aleksandr Arkhipov (MIT), Gilles Brassard (Mont- area of position-based cryptography. Pumping wa- réal), Harry Buhrman (CWI & Amsterdam), Andrew ter through a network of pipes hung from his torso, Childs (Waterloo), Matthias Christandl (ETH Zürich), Harry calculated the value of a function by determin- Richard Cleve (Waterloo), Andrew Drucker (MIT), ing which of his feet got more heavily splashed by the Daniel Gottesman (Perimeter Inst.), Peter Høyer, Marc apparatus. Kaplan (Montréal), Elham Kashefi (Edinburgh), So- phie Laplante (Paris-Sud), Debby Leung (Waterloo), Workshop on Michele Mosca (Waterloo), Ashwin Nayak (Waterloo), Quantum Information in Quantum David Poulin (Sherbrooke), Oded Regev (ÉNS), Ben Re- Many-Body Physics ichardt (Waterloo), Renato Renner (ETH Zürich), Wim October 18–21, 2011, CRM van Dam (UC Santa Barabara), John Watrous (Water- loo) Organizer: David Poulin (Sherbrooke) Number of participants: 45 Speakers: The promise of a quantum computer is not that itwill Héctor Bombin (Perimeter Inst.), Sergey Bravyi run more quickly than a traditional computer. Indeed, (IBM Res.), Courtney Brell (Sydney), Winton Brown it is quite likely that the individual logic gates of any (Sherbrooke), Olivier Buerschaper (Perimeter Inst.), real quantum computer will be slower than the gates in Philippe Corboz (ETH Zürich), Andrew Darmawan their classical counterparts. Instead, quantum comput- (Sydney), Guillaume Duclos-Cianci (Sherbrooke), ers have the potential to reduce the scaling of running Jutho Haegeman (Gent), Alioscia Hamma (Perime- time with problem size. Most famously, Peter Shor dis- ter Inst.), Stephen Inglis (Waterloo), Ann Kallin (Wa- covered in the 1990s that a quantum computer could terloo), Roger Melko (Waterloo), Spiros Michalakis factor integers in an amount of time polynomial in the (Caltech), Anne E. B. Nielsen (MPI Quantenoptik), number of digits of the integer, even though there is Tobias Osborne (Hannover), Renato Renner (ETH no known algorithm for traditional “classical” com- Zürich), Norbert Schuch (Caltech), David Sénéchal puters capable of doing so. Quantum computer sci- (Sherbrooke), Barbara Terhal (RWTH Aachen), André- ence includes the design of quantum algorithms and Marie Tremblay (Sherbrooke), Matthias Troyer (ETH the related classification of problems according to the Zürich), Maarten van den Nest (MPI Quantenoptik), quantum mechanical resources required to solve them, Frank Verstraete (Wien), Guifre Vidal (Perimeter Inst.), known as quantum complexity theory. Tzu-Chieh Wei (Stony Brook), Johannes Wilms (Wien) Number of participants: 42 The workshop, organized by Alain Tapp and Peter Many recent developments in the theory of quantum Høyer, brought together 45 researchers interested in information have led to important insights and ap- various aspects of quantum computer science, broadly plications in condensed matter physics. For instance, interpreted. Participants presented new algorithms, the theory of entanglement has shed new light on such as Matthias Christandl’s quasipolynomial time al- the density matrix renormalization and the real space gorithm for testing quantum separability, and refined renormalization numerical methods, culminating in a our understanding of quantum complexity classes, deeper understanding of the strengths of the methods as in Andrew Ducker’s study of quantum computa- and applications to a wider class of problems including tion with non-standard sources of “advice.” The talks critical systems and systems in more than one spatial made surprising connections to physics as well. Daniel dimension. Similarly, the theory of quantum error cor- Gottesman explained why finding the ground state en- rection has led to new theoretical models of interacting ergy of even translationally invariant one-dimensional particles that exhibit topological order, an exotic phase systems can be computationally intractable while Alex of matter in which excitations can have non-Abelian Arkipov explained how optical experiments in the near statistics. Moreover, the study of information propa- future should be capable of performing calculations gation in a system of interacting particles was used to thought to be intractable for traditional computers. prove the existence of an entanglement entropy area Harry Buhrman supplied one of the highlights of the law in the ground state of systems with local interac- workshop when he gave an experimental demonstra- tions. The problem of finding ground states of asys- tion of “garden hose complexity,” an idea he and his tem composed of interacting particles was proven to be

11 Centre de recherches mathématiqes complete for the complexity class QMA, the quantum One of the primary concerns of quantum information analogue of NP. These are just a few examples illus- theory is the design of codes for achieving commu- trating the connections between quantum information nication in noisy environments, often while simulta- and condensed matter physics. neously achieving cryptographic objectives. The prob- The workshop, organized by David Poulin, brought to- abilistic method is often used to prove the existence gether experts from both domains to discuss the lat- of good codes and may even play a role in more ex- est results and new directions. A major emphasis was plicit and efficient constructions. At the same time, the study of numerical techniques for the simulation many basic quantum-information-theoretic tasks have of many-body quantum systems on today’s “classi- natural geometric interpretations that link them to a cal” computers. More traditional techniques like quan- range of other application areas such as compressed tum Monte Carlo and mean field approximation were sensing and approximation algorithms through shared compared to new quantum information-inspired algo- underlying mathematics. This workshop, organized by rithms like multiscale entanglement renormalization Patrick Hayden and Aram Harrow, provided a forum and matrix product states. Another theme was the un- for participants to present the latest developments in derstanding of the nature of topological order. Sergey the theory of quantum communication while high- Bravyi of IBM Research described an exotic three-di- lighting the range of mathematical techniques used in mensional lattice system that would store quantum the area, including representation theory, asymptotic mechanical information robustly in topological de- geometric analysis, random matrix theory, and opera- grees of freedom without the need for additional er- tor theory. ror correction, a first step towards building a “quan- One of the most exciting talks of the workshop also tum hard drive.” Meanwhile, Spiros Michalakis of Cal- happened to be the first, by Fernando Brandão. Ran- tech explained his proof that topological order en- dom unitary transformations play a role in quantum sures that an energy gap between the ground and ex- information theory analogous to that of random func- cited states is robust against weak perturbations for so- tions in traditional information theory. Brandão ex- called frustration-free Hamiltonians. plained how to prove that composing small random Steve Flammia of the Quantum Pontiff blog produced unitary gates generates approximate polynomial uni- k an amazingly detailed transcript of the workshop’s tary designs, which are the analogs of -wise inde- pendent random variables. The talk blended elements talks at http://tinyurl.com/7ags843. from condensed matter theory, Markov chains, and Workshop on computer science. Later the same day, Marius Junge Quantum Information: explained how Shannon’s information theory can be Codes, Geometry and Random Structures naturally re-expressed using the language of Banach October 24–26, 2011, CRM spaces. The translation then lifts to the quantum, con- verting basic questions about quantum information Organizers: theory into analogous problems in the theory of op- Patrick Hayden (McGill), Aram Harrow (Washington) erator spaces. For some questions, notably about how Speakers: badly communication above a channel’s maximum ca- Robin Blume-Kohout (Los Alamos Natl. Lab.), Fer- pacity must fail, this translation is quite fruitful. Partic- nando Brandão (UF Minas Gerais), Matthias Christandl ipants also reported remarkable progress on the design (ETH Zürich), Frédéric Dupuis (ETH Zürich), Omar of practical error correcting codes for communicat- Fawzi (McGill), Marius Junge (UI Urbana-Champaign), ing over quantum media. Jean-Pierre Tillich explained Yi-Kai Liu (NIST), Ashley Montanaro (Cambridge), how to build quantum turbo codes that are excellent John Preskill (Caltech), Joseph M. Renes (ETH Zürich), at reducing if not completely eliminating errors, while Mary-Beth Ruskai (Tufts), Pranab K. Sen (Tata Inst.), Joseph Renes and Mark Wilde presented their respec- Graeme Smith (IBM Res.), Jean-Pierre Tillich (INRIA tive approaches to quantum polar coding. A highlight Rocquencourt), Michael Walter (ETH Zürich), Mark of the workshop was an hour-long moderated discus- Wilde (McGill), Jürg Wullschleger (Montréal), Deping sion. While the participants objected somewhat to the Ye (Memorial) organizers’ semi-facetious invitation to identify the ar- Number of participants: 36 eas of quantum information research that had proved

12 Thematic Program to be dead ends, the resulting spirited conversation know much more now about the “Fuchs–Brassard con- confirmed that the field as a whole is vibrant andfull jecture”: that the possibility of tamper-evident secret of interesting research problems. key distribution, combined with the impossibility of Simultaneously wearing his organizer’s cap and his bit commitment, might go a long way toward charac- pope’s mitre, Aram Harrow managed to produce a lu- terising quantum theory. But to an even greater ex- cid summary of the talks for the Quantum Pontiff blog tent the workshop showcased, and furthered, exciting work that is very recent or still in progress, under- at http://tinyurl.com/897qxsu. lining the continued vibrancy of this line of research. Workshop on A major theme that emerged was the desire to inte- Quantum Foundations in the Light of grate information-based and axiomatic approaches to Quantum Information III quantum theory with spacetime physics, a project that December 6–9, 2011, CRM is less advanced than the informational and axiomatic understanding of quantum-information-style “Alice ’n Organizers: Bob” quantum theory, but clearly a focus of current ac- Gilles Brassard (Montréal), Christopher Fuchs (Perime- tivity. Some of the formal presentations are described ter Inst.) below, but a crucial component of the workshop’s suc- Speakers: cess was the ample time for informal interaction, dur- D. Marcus Appleby (Perimeter Inst.), Somshubhro ing which a lot of serious mathematics and physics was Bandyopadhyay (Bose Inst.), Howard Barnum (New done and new collaborations were initiated, many in- Mexico), Caslav Brukner (Wien), Jeffrey Bub (Mary- volving student and postdoc participants. land), Giulio Chiribella (Perimeter Inst.), Man-Duen Sharpening a seminal 2000 result of Lucien Hardy, Choi (Toronto), Giacomo Mauro D’Ariano (Pavia), Markus Müller, working with Lluis Masanes, showed Lucien Hardy (Perimeter Inst.), Jan-Åke Larsson that finite-dimensional quantum theory is character- (Linköping), Markus P. Müller (Perimeter Inst.), Paolo ized, among finite-dimensional convex theories allow- Perinotti (Pavia), John A. Smolin (IBM Res.), Robert ing all measurements consistent with the state space, Spekkens (Perimeter Inst.), Michael D. Westmoreland by requiring: (1) that states of composite systems are (Denison) determined by the statistics and correlations of mea- Number of participants: 37 surements on their parts (“local tomography”); (2) that This was the third CRM workshop with this title, the continuously reversible dynamics can take any ex- first having been held in 2000, and the second (which tremal (“pure”) state to any other; and (3) that each sys- was also a Commune) in 2002. All were organized with tem or subsystem for which the largest set of perfectly great flair by Gilles Brassard and Christopher Fuchs. A distinguishable states has a given size (the system’s main goal was “to explain quantum-mechanical phe- “information capacity”) is isomorphic to every other nomena as inevitable consequences of information- system with that information capacity. With Cozmin theoretic considerations, and to derive as much of Ududec, he showed that if reversible dynamics can take quantum mechanics as possible from this perspec- any pair of perfectly distinguishable states to any other tive.” This project has proved intellectually compelling, such pair, then the system has a self-dual unnormal- spawning a resurgence of interest in the axiomatic ex- ized state space, a very strong condition, satisfied by ploration of mathematically represented physical the- quantum theory and physically interesting because of ories, fed by an infusion of fresh ideas involving com- its connections to time-reversal symmetry and other posite systems, information processing, and proba- important properties. bilistic inference, and using mathematical tools such The Pavia group of Chiribella, D’Ariano, and Perinotti as category theory (physical processes as morphisms) reviewed their derivation of quantum theory from as- and ordered linear spaces (for representing states and sumptions including local tomography and the exis- measurements by compendia of probabilities). tence, for every mixed state of a system A, of a “purifi- To an extent, QFLQI III celebrated and reviewed the cation”: a state on a composite of A with another sys- enormous advances that have been made since the tem, having the original state as its marginal A state, early CRM workshops, in no small part catalyzed by unique up to reversible transformations on the addi- them. For example, while the story is not finished, we tional system, showing that given their assumptions

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There is One Church of the Larger Convex State Space tada Kobayashi (NII), Debbie Leung (Waterloo), Re- and It is the Church of the Larger Hilbert Space. (Quan- nato Renner (ETH Zürich), Christian Schaffner (Am- tum information theorists have practiced the CLHS’s sterdam), Norbert Schuch (Caltech), Peter Shor (MIT), rite of purification daily since ancient times.) But most Graeme Smith (IBM Res.), Thomas Vidick (UC Berke- of their presentations aimed to meld this operational ley), John Watrous (Waterloo), Stephanie Wehner (NU approach with spacetime physics, with D’Ariano de- Singapore) riving discrete Dirac-like equations on a lattice of Steering Committee: qubits in an approach somewhat reminiscent of the Ignacio Cirac (MPI Quantenoptik), Eddie Farhi (MIT), work of Feynman and Jacobson, but aimed at interpret- Aram Harrow (Washington), Patrick Hayden (McGill), ing mass and propagation speed informationally, and Louis Salvail (Montréal; Chair), Barbara M. Terhal Chiribella and Perinotti investigating probabilistic the- (RWTH Aachen), Andreas Winter (Bristol; CQT), An- ories where the causal structure is not fixed ahead of drew Yao (Tsinghua) time. Rob Spekkens also emphasized the need to for- Local Organizers: mulate quantum theory in a causally neutral way, as a Kassem Kalach (Montréal), Marc Kaplan (Montréal), theory of Bayesian inference. Howard Barnum talked Magalie Lascar (Montréal), Louis Salvail (Chair), about the possibility of abandoning local tomography, Benno Salwey (Montréal), Dave Touchette (Montréal) and thereby being able to make composites of systems Plenary Speakers: whose cones of measurements are homogeneous and Itai Arad (Hebrew), Aleksandrs Belovs (Latvia), Sergey self-dual, as well as some information-processing no- Bravyi (IBM Res.), Eric Chitambar (Toronto), Markus tions (purification, and Schrödinger’s notion of “steer- Greiner (Harvard), Jeongwan Haah (Caltech), Sandu ing” an ensemble) that imply homogeneity. Michael Popescu (Bristol), Jérémie Roland (ULB) Westmoreland discussed the fascinating quantum-like Other Speakers: mathematical phenomena that arise when one tries to Salman Beigi (IPM), Fernando Brandão (UF Minas do something like quantum theory with Z2 instead of Gerais), Gilles Brassard (Montréal), Jop Briet (CWI), the complex numbers as the scalars. After some wise Josh Cadney (Bristol), André Chailloux (UC Berkeley), remarks on the nature of language and its relevance Matthias Christandl (ETH Zürich), Richard E. Cleve to physics, Marcus Appleby reviewed work on a beau- (Waterloo), Toby Cubitt (Complutense), Nilanjana tifully simple question of pure mathematics that has Datta (Cambridge), Runyao Duan (UT Sydney), Guil- seen an enormous amount of interest and effort in laume Duclos-Cianci (Sherbrooke), Rodrigo Gallego quantum information and foundations: Does there ex- (ICFO), Sevag Gharibian (Waterloo), Esther Hänggi ist, in n-dimensional complex space with a sesquilinear (NU Singapore; CQT), Robert Koenig (IBM Res.), An- inner product, an equiangular set of n2 lines? We leave drew Landahl (Sandia Natl. Labs.), Olivier Landon- this as an exercise for the reader. Cardinal (Sherbrooke), François Le Gall (Tokyo), Troy Lee (CQT), Spyridon Michalakis (Caltech), Rajat Mit- 15th Conference on tal (Waterloo), Abel Molina (Waterloo), Ashwin Nayak Quantum Information Processing — (Waterloo), Joseph M. Renes (ETH Zürich), Miklos QIP 2012 Santha (Paris Diderot; CNRS), Or Sattath (Hebrew), December 12–16, 2011, UQAM Norbert Schuch (Caltech), Martin Schwarz (Wien), Sponsored by the CRM, INTRIQ, the Institute for Rolando Somma (Los Alamos Natl. Lab.), Florian Speel- Quantum Computing, Sandia National Laboratories, man (CWI), Mark Wilde (McGill), Xiaodi Wu (Michi- the National Science Foundation (NSF), the Université gan), Jon Yard (Los Alamos Natl. Lab.) de Montréal, ID Quantique (IDQ), Tourisme Montréal, Number of participants: 257 and the Perimeter Institute for Theoretical Physics The final event of the semester was also the largest. Quantum Information Processing (QIP) 2012, which Program Committee: took place at UQAM’s Cœur des Sciences, had 257 Dorit Aharonov (Hebrew; chair), Michael Ben-Or (He- registered participants from around the world. QIP is brew), Fernando Brandão (UF Minas Gerais), Sergey the leading conference on quantum algorithms, com- Bravyi (IBM Res.), Ronald de Wolf (CWI), David munication, and complexity. Each year, a small hand- DiVincenzo (Jülich; RWTH Aachen), Matt Hastings ful of researchers who have made outstanding break- (UC Santa Barabara), Sandy Irani (UC Irvine), Hiro- throughs are invited to speak at QIP. The remaining

14 Thematic Program speaking slots are filled through a competitive selec- Organizers: tion process. Since there are no proceedings, partic- Monika Ludwig (NYU-Poly; TU Wien), Vitali Milman ipants are free to submit work being published else- (Tel Aviv), Alina Stancu (Concordia) where, ensuring that nearly all of the year’s best re- Speakers: sults get presented at QIP. Before 2012, the most re- Judit Abardia (Frankfurt am Main), Semyon Alesker cent incarnations of the conference took place in Sin- (Tel Aviv), David Alonso Gutiérrez (Alberta), Andreas gapore, Zürich, New Mexico, and New Delhi. Further Bernig (Frankfurt am Main), Andrea Colesanti (Firen- excavation of its history, however, reveals that the year ze), Dmitry Faifman (Tel Aviv), Joseph Fu (Georgia), 2000 incarnation of QIP was also hosted by the CRM in Maria Hernandez Cifre (Murcia), Dan Klain (UMass Montréal. This was the first time QIP had ever returned Lowell), Alexander Koldobsky (Missouri), Alexander to the same city. That the quantum information com- Litvak (Alberta), Mohammad Najafi Ivaki (Concordia), munity was so enthusiastic about returning to Mont- Grigoris Paouris (Texas A&M), Peter Pivavorov (Texas réal is in no small part due to the exceptional support A&M), Liran Rotem (Tel Aviv), Dmitry Ryabogin (Kent the CRM has provided over the years! State), Eugenia Saorín Gómez (Magdeburg), Matthias The conference’s eight plenary speakers were ami- Schulte (Case Western Reserve), Carsten Schütt (Kiel), crocosm of the field as a whole, providing echoes of Alexander Segal (Tel Aviv), Thomas Wannerer (ETH the highlights of the semester’s workshops. Sergey Zürich), Elisabeth Werner (Case Western Reserve), Jie Bravyi and Jeongwan Haah spoke about three-dimen- Xiao (Memorial), Vlad Yaskin (Alberta), Deping Ye sional topological quantum memories and their sta- (Memorial), Artem Zvavitch (Kent State) bility against thermal noise. Itai Arad explained how Number of participants: 43 to prove an area law for one-dimensional frustration- This workshop included talks that were as diverse as free quantum systems that is exponentially stronger the field itself, a result of the rapid developments seen than those previously known. Aleksandrs Belovs ex- in the area in recent years. Moreover, almost a third plained new characterizations of quantum query com- of the speakers were very young researchers: gradu- plexity, while Jérémie Roland presented a powerful ate students or postdocs within 3 years of their thesis new quantum algorithmic tool called quantum rejec- completion, giving a measure of renewed interest and tion sampling. Meanwhile, Eric Chitambar disposed of intense current activity in new and classical challenges a longstanding problem in quantum information the- of the field. ory by showing that the set of local operations with One of the directions emphasized in this meeting was classical communication (LOCC) is not closed. Sandu the complexity of duality. The classical duality for con- Popescu treated the audience to a beautiful discussion vex bodies is reflected in the space of convex functions in the foundations of thermodynamics about how to as two other types of dualities whose properties are construct the smallest possible thermal machines. Fi- just being understood. New results were the subject of nally Markus Greiner brought everyone back to reality talks by Liran Rotem and Alexander Segal. One should by describing his experiments on lattices of ultracold note that duality of convex bodies is also at the core of atoms, which would have sounded like science fiction Mahler’s conjecture, an old outstanding problem in the not very long ago. field, on which progress was reported by Artem Zvav- The Quantum Pontiff bloggers, of course, covered itch and Grigoris Paouris, each in a different context. the whole conference. Their report can be found at The topics of area measures and their connection to http://dabacon.org/pontiff/?p=5865. QIP 2013 PDEs, affine differential geometry, and Hermitian inte- will take place at Tsinghua University in Beijing. gral geometry were touched upon by Mohammad Na- jafi Ivaki and Thomas Wannerer (respectively). Further Workshop on connections to quantum information theory (Elisabeth Convexity and Asymptotic Geometric Werner), containment problems (Dan Klain), and geo- Analysis metric, isoperimetric-type, inequalities (David Alonso April 16–20, 2012, CRM Gutiérrez) were also presented. Partly funded by the National Science Foundation Another direction of research emphasized at the meet- (NSF) ing was probabilistic in nature. One of the 2011 E. W. R Steacie Memorial Fellowship’s recipients,

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Alexander Litvak, delivered a lecture on estimates on Weinkove, Natasa Sesum, Junfang Li, McKenzie Wang, norms of random matrices with applications in convex Tom Illmanen and Maria Buzano. The increasingly im- geometry, computational geometry, and compressive portant role played by torsion in non-Kähler Hermi- sensing theory. Different other probabilistic aspects tian geometry and the emergence of the Chern–Ricci were addressed by Carsten Schutt and Peter Pivovarov. flow as a new model for flows on complex surfaces, The latter presented novel distributional inequalities the recent advances in the study of singularity for- for the volume of random convex sets. mation for the mean curvature flow of surfaces using Finally, in an exciting direction, the theory of valuation new ideas from geometric measure theory, ancient so- now opens a new road to algebraic integral geometry lutions to the Yamabe flow and the explicit construc- (Andreas Bernig), while classical problems of extend- tion of Ricci flows on manifolds with large isometry ing continuously valuations from subspaces of convex groups were highlighted throughout these lectures. compact sets to the whole space are seeing solutions • Extremal Kähler and other special metrics: These (Semyon Alesker). formed the substance of the lectures by Vesti Apos- Overall, the atmosphere was very enthusiastic, filled tolov, Jixiang Fu, Valentino Tosatti, Ailana Fraser and with discussions, and many of the talks were attended Spiro Karigiannis. Recent developments on the explicit by local people outside the field. The special CRM–ISM construction of extremal Kähler metrics on toric orb- colloquium of the two-time ICM speaker, Vitali Mil- ifolds, Hermitian Yang–Mills metrics on stable vector man, was integrated within the workshop’s program bundles, collapsing of Calabi–Yau manifolds, extremal and added to the visibility of the meeting. eigenvalue problems for surfaces with boundary, and G2 structures were at the heart of this set of lectures. Workshop on • PDE problems in connection with the Monge–Ampère Geometric PDE equation, the Yamabe problem, and General Relativity: April 23–27, 2012, CRM These were dealt with in the lectures by Bo Guan, Joel Spruck, Steve Zelditch, Mu Tao Wang, Lei Ni, Mar- Organizers: cus Khuri, Ahmed Zeriahi, and Gantumur Tsogtgerel. Pengfei Guan (McGill), Niky Kamran (McGill), Alina Many important advances and new perspectives were Stancu (Concordia) covered in the lectures. Again, torsion in Hermitian ge- Speakers: ometry occupied a prominent place in the talks con- Vestislav Apostolov (UQAM), Maria Buzano (Oxford), cerned with the Monge–Ampère equation, as well as Ailana Fraser (UBC), Jixiang Fu (Fudan), Bo Guan the analysis of the initial value problem in connec- (Ohio State), Tom Ilmanen (ETH Zürich), Spiro Kari- tion to the geodesic equation on the set of Kähler met- giannis (Waterloo), Marcus Khuri (Stony Brook), Jun- rics. From the General Relativity perspective, the cen- fang Li (Alabama at Birmingham), Qun Li (Wright tral role was played by the initial value problem with State), Lei Ni (UC San Diego), Natasa Sesum (Pennsyl- various geometric assumptions on the initial data sets, vania), Joel Spruck (Johns Hopkins), Valentino Tosatti as well as the important problem of defining of quasi- (Columbia), Cristina Trombetti (Federico II), Gantu- local mass and momentum for isolated systems. mur Tsogtgerel (McGill), McKenzie Y. Wang (McMas- The workshop was very successful in bringing together ter), Mu-Tao Wang (Columbia), Ben Weinkove (UC San some of the strongest researchers active today in ge- Diego), Steve Zelditch (Northwestern), Ahmed Zeriahi ometric analysis. Many fruitful scientific discussions (Paul Sabatier) and exchanges took place during the workshop, dur- Number of participants: 36 ing and between the lectures, making this a memorable The goal of this workshop was to bring together re- scientific event. searchers working in geometry and PDEs, with the objective of reviewing important recent results in the Workshop on field and highlighting new research trends. The lec- Geometry and Dynamics of Fluid tures were anchored around several subthemes of cur- May 21–25, 2012, CRM rent interest. • Geometric flows in Riemannian and Hermitian geom- etry: These topics were covered in the lectures byBen

16 Thematic Program

Organizers: some integrable 1D equations, Vizman described dual Sergei Kuksin (École Polytechnique), Stephen Preston pair structures for generalized Camassa–Holm equa- (CU-Boulder), Alexander Shnirelman (Concordia) tions, and Zeitlin discussed finite-dimensional Lie al- Speakers: gebra structures to approximate fluid and geostrophic Emanuele Caglioti (La Sapienza), Dongho Chae equations. (Chung-Ang), Alexey Cheskidov (UI Chicago), Diego (iii) Diego Cordoba, Walter Craig, Susan Friedlander, Córdoba (ICMAT), Walter Craig (McMaster), Sergey Boris Khesin, Filippo Santambrogio, Vlad Vicol, and Denissov (Wisconsin–Madison), David Ebin (Stony Xinwei Yu all spoke about various one- and two-di- Brook), Susan Friedlander (Southern California), mensional PDEs that share structures with the 3D Eu- François Gay-Balmaz (ÉNS), John D. Gibbon (Impe- ler or Navier–Stokes equations. Friedlander and Vi- rial Coll.), Boris Khesin (Toronto), Anna Mazzucato col spoke about different aspects of active-scalar equa- (Penn State), Gerard Misiolek (Notre Dame), Clément tions such as the surface-quasi-geostrophic equation. Mouhot (Cambridge), Tudor Ratiu (EPFL), Filippo San- Yu spoke about some generalizations of the two-di- tambrogio (Paris-Sud), Roman Shvydkoy (UI Chicago), mensional magnetohydrodynamic equations. Craig Vladimir Sverak (Minnesota), Feride Tiglay (Fields), and Khesin spoke about vortex filament and vortex Vladimir Tseitline (ÉNS), Vlad Vicol (Chicago), Cor- membrane equations, which model fluids for which nelia Vizman (Vest din Timişoara), Xinwei Yu (Alberta) vorticity is concentrated on singular sets. Cordoba Number of participants: 33 spoke on free-boundary problems describing inter- The workshop featured 25 speakers, who gave 40- faces between two ideal irrotational fluids. Santambro- minute talks on various topics related to fluid mechan- gio described a crowd-flow model that relates to opti- ics. The goal of the workshop was to get experts in mal transport and generalized flows of fluid. disparate areas of fluid mechanics interested in each other’s work, and our compressed format of short talks (iv) Alexey Cheskidov, John D. Gibbon, Roman Shvy- made it easy for people to attend many of them. dkoy, and Vladimir Sverak spoke about aspects of tur- bulence and blowup in the 3D Euler and Navier–Stokes The topics our speakers focused on broadly included equations. Cheskidov and Gibbon addressed intermit- (i) long-time behaviour of two-dimensional fluids, tency in the Navier–Stokes equations (i.e., large de- (ii) aspects of the diffeomorphism group geometry, viations from the mean in vorticity) and its possible (iii) one- and two-dimensional model systems for flu- relation to blowup. Shvydkoy discussed nonexistence ids, (iv) aspects of turbulence in three-dimensional flu- of self-similar blowup solutions of the Euler equation, ids, and (v) weak solutions of the Euler equations. while Sverak discussed self-similar solutions of the Navier–Stokes equation. (i) Emanuele Caglioti and Clément Mouhot spoke on various aspects of the long-time behaviour of solu- (v) Finally, Anna Mazzucato, Gerard Misiolek, and tions of the 2D Euler equation. Although global ex- Sergey Denisov spoke on aspects of weak solutions istence for sufficiently smooth solutions of 2D Eu- of Euler and Navier–Stokes equations. Mazzucato de- ler has been known for many years, there are still scribed results on the dissipation of enstrophy in poorly understood phenomena such as the seeming weak solutions of the 2D Euler equation with un- existence of attractors and the energy cascade. Cagli- bounded vorticity. Misiolek described the failure of oti explained aspects of attractors in a weak-damping well-posedness in the Hadamard sense for 2D Euler, limit, and Mouhot described a rigorous approach to constructing examples for which the dependence on Landau damping. initial conditions is continuous but not uniformly con- tinuous. Denisov gave sharp results on the dynamics (ii) David Ebin, Francois Gay-Balmaz, Feride Tiglay, of vortex patches that collapse into each other asymp- Cornelia Vizman, and Vladimir Zeitlin spoke on global totically, as well as estimates on the growth of Sobolev differential-geometric aspects of the Euler and related norms for smooth 2D Euler solutions. equations, which follow the Arnold approach to fluid mechanics via Riemannian geometry of the diffeomor- The workshop featured a lively mix of talks together phism group. Ebin described the geometry of quanto- with some social events such as a reception, a walk- morphism groups, Gay-Balmaz spoke on liquid crys- ing tour of Old Montréal, and a free banquet in order tal equations, Tiglay spoke about geometric aspects of to foster discussion and collaboration. The diversity of

17 Centre de recherches mathématiqes speakers (by age, gender, location, and field) was a pri- their interest in returning to the CRM in the near fu- mary goal of the organizers. Graduate students were ture for similar events. actively supported and encouraged to attend all events. The workshop started on Monday with a talk byEl- Attendees expressed great appreciation for the organi- liott Lieb, in which he explained entanglement in zation and the facilities of the CRM, and we believe we quantum systems and ways to quantify it using en- fostered several useful collaborations that will develop tropy inequalities. The second morning talk, by Heinz in the future. Siedentop, concerned a model of a graphene quan- tum dot, for which spectral properties were investi- Workshop on gated. Graphene was also the topic of the first after- Quantum Many-Body Systems noon talk by Vieri Mastropietro, who presented a proof May 28–June 1, 2012, CRM of universal conductivity using rigorous renormaliza- tion group techniques. The final talk on Monday was Organizers: given by Alessandro Giuliani, and discussed the scal- Vojkan Jakšić (McGill), Robert Seiringer (McGill) ing limit of correlation functions in nonintegrable Ising Speakers: models. Michael Aizenman (Princeton), Jan Derezinski (War- saw), Rupert L. Frank (Princeton), Alessandro Giu- Mathieu Lewin gave the first talk on Tuesday, in which liani (Roma Tre), Christian Hainzl (Tübingen), Victor he explained how to obtain the Pekar model for a Ivrii (Toronto), Israel Klich (Virginia), Edwin Lang- polaron as a macroscopic limit of a microscopic po- mann (KTH), Mathieu Lewin (Cergy-Pontoise), El- laron model. The Scott correction in different models of liott H. Lieb (Princeton), Vieri Mastropietro (Tor Verga- atoms and molecules was the topic of the second talk, ta), Bruno Nachtergaele (UC Davis), Heinz Siedentop given by Jan Philip Solovej. Rupert Frank’s talk in the (München), Israel Michael Sigal (Toronto), Robert Sims afternoon concerned ground state properties of mul- (Arizona), Jan Philip Solovej (Copenhagen), Daniel tipolaron systems, in particular the question of stabil- Ueltschi (Warwick), Simone Warzel (TU München), ity and binding. The last talk on Tuesday was given by Jakob Yngvason (Wien), Valentin Zagrebnov (Aix- Michael Sigal, in which he discussed Rayleigh scatter- Marseille) ing and the propagation speed of photons in phonons Number of participants: 30 in simple quantum field models. This workshop consisted of 20 one-hour lectures by the The effects of randomness on quantum systems were participating experts. The unifying theme of the work- the topic of the first three talks on Wednesday. The shop was the mathematical analysis of models in quan- session started with a talk by Michael Aizenman on tum mechanics describing a large number of mutu- phase transitions in quantum and classical spin sys- ally interacting particles. The topics covered concerned tems subject to random external fields. It was followed the renormalization group analysis of lattice models by Simone Warzel’s talk on the Bose–Hubbard model. in condensed matter physics, including graphene, the Jakob Yngvason gave the first talk in the afternoon, ex- interaction of matter with radiation, effects of impu- plaining the effects of random impurities on one-di- rities (i.e., randomness) on interacting particle sys- mensional Bose–Einstein condensates, described by tems, semiclassical analysis of atoms and molecules, the Lieb–Liniger model. The second afternoon talk was and the characterization of possible phases occurring given by Victor Ivrii, explaining the asymptotics of the in ground states in low-dimensional spin systems. ground state energy for heavy atoms and molecules. Four lectures were scheduled each day of the week, In the first talk on Thursday, Bruno Nachtergaele ex- two in the morning and two in the afternoon. This plained the classification of ground state phases in schedule left plenty of time for discussions among the gapped one-dimensional quantum systems. The sec- participants before and after the lectures. These discus- ond talk by Robert Sims contained results on dynam- sions have led to new ideas, interesting open problems, ical localization for the random XY spin chain. Israel and new research directions that will be pursued in Klich gave the first afternoon talk on Thursday, ex- the future. The excellent facilities and pleasant atmo- plaining entanglement in systems of matter coupled to sphere at the CRM have contributed to the success of radiation. Finally, Valentin Zagrebnov closed the ses- the workshop, and many participants have expressed

18 Thematic Program sion with a talk on his results on a model of a leaky tral Geometry, Semiclassical Theory of Eigenfunctions photon cavity pumped by an atomic beam. and PDEs (CRM/Fields), and Spectral Theory and Au- Friday was the last day of the workshop, and it started tomorphic Forms in 2004. with a talk by Jan Derezinski on the joint energy- One of the main highlights of the meeting was a se- momentum spectrum of homogeneous Fermi gases. ries of Aisenstadt lectures on quantum unique ergod- The second talk, by Daniel Ueltschi, investigated the icity by Elon Lindenstrauss. Quantum ergodicity and nature of correlations in quantum Heisenberg models. properties of eigenfunctions in the semiclassical limit Luttinger-type models of correlated fermions in higher were among the central themes of the workshop. Re- dimensions were the topic of the first afternoon talk, lated topics were discussed in the talks by Suresh given by Edwin Langmann. The final talk of the work- Eswarathasan, Hans Christianson, Shimon Brooks, shop was given by Christian Hainzl, explaining the mi- Yiannis Petridis, and Yaiza Canzani. A survey talk by croscopic derivation of the Ginzburg–Landau model Victor Ivrii focused on the asymptotic distribution of from the microscopic Bardeen–Cooper–Schrieffer the- eigenvalues and remainder estimates in Weyl’s law. ory. Dan Mangoubi presented a new proof, not involving “hard analysis,” of the celebrated Donnelly–Fefferman Workshop on estimate on the growth of high-energy eigenfunctions. Geometry of Eigenvalues and In the talk on symbolic calculus of Fourier integral op- Eigenfunctions erators, Yuri Safarov developed an analytic machine June 4–8, 2012, CRM that could be used to study quantum ergodicity for branching billiards. Organizers: The talks by Alexandre Girouard, Vladimir Kozlov, Dmitry Jakobson (McGill), Iosif Polterovich (Montréal) Alexei Penskoi, Eveline Legendre, and Christopher Speakers: Judge were concerned with the properties of eigen- Ram Band (Bristol), Alex Barnett (Dartmouth Coll.), values of the Laplacian and other elliptic operators on Rafael D. Benguria (PUC), Shimon Brooks (Stony Riemannian manifolds and Euclidean domains. Many Brook), Almut Burchard (Toronto), Yaiza Canzani important subjects were discussed, including extremal (McGill), Hans Christianson (UNC—Chapel Hill), problems for eigenvalues on surfaces, estimates on the Suresh Eswarathasan (McGill), Alexandre Girouard eigenvalues of Dirichlet-to-Neumann operators, do- (Neuchâtel), Victor Guillemin (MIT), Victor Ivrii main dependence of Dirichlet eigenvalues, Kähler met- (Toronto), Christopher Judge (IU Bloomington), Achim rics with simple Laplace spectrum, and existence of Kempf (Waterloo), Vladimir Kozlov (Linköping), Eve- embedded eigenvalues in the continuous spectrum for line Legendre (Paul Sabatier), Elon Lindenstrauss (He- hyperbolic triangles. Almut Burchard presented some brew), Dan Mangoubi (Hebrew), Alexei V. Penskoi recent results on Steiner symmetrization of compact (Moscow SU; IU Moscow), Peter A. Perry (Kentucky), sets. Steiner symmetrization is a powerful technique in Yiannis Petridis (Univ. Coll. London), Grigori Rozen- geometric analysis that is used, in particular, to prove blioum (Chalmers UT), Yuri Safarov (King’s Coll. Lon- sharp isoperimetric inequalities for eigenvalues. don), Alexander Strohmaier (Loughborough), Steve Zelditch (Northwestern) Several talks, including the ones by Rafael Benguria, Number of participants: 49 Peter Perry, and Achim Kempf, emphasized the links The workshop brought together the leading re- between spectral theory and mathematical physics. searchers and young mathematicians working in vari- The talks by Ram Band and Grigori Rozenblioum fo- ous areas of geometric spectral theory. Many problems cused on the properties of eigenvalues and eigenfunc- in the field are motivated by questions originating in tions of the Laplace and Schrödinger operators on com- the study of real life phenomena: quantum-mechani- binatorial and quantum graphs. cal effects, vibration of membranes and plates, oscilla- Recent advances in computational spectral theory tions of fluids, etc. The conference continued a series of were presented by Alex Strohmaier and Alex Barnett. related meetings at the CRM, including workshops on In particular, a new efficient method for numerical Spectrum and Dynamics and Mathematical Aspects of computation of Dirichlet eigenvalues of planar do- Quantum Chaos in 2008, as well as workshops on Spec- mains was presented, as well as a fast algorithm for

19 Centre de recherches mathématiqes calculating eigenvalues and spectral zeta functions on mathematically defined and KPZ relations were proved Riemannian surfaces with explicitly controlled error using the DDK’s GFF approach. estimates. Monday afternoon talks were devoted to the geome- The workshop also featured a stimulating session try of the space of Riemannian metrics. Brian Clarke on open problems. A number of interesting ques- introduced the L2 (or Ebin) distance on the space of tions were proposed by Victor Ivrii, Rafael Benguria, Riemannian metrics, discussed the construction of its Alexandre Girouard, and Dmitry Jakobson. completion, and showed that the resulting metric space has nonpositive curvature. Sun surveyed the work on Workshop on the metric geometry of the space of Kähler metrics, and Manifolds of Metrics and Probabilistic its importance in the study of canonical metrics in Käh- Methods in Geometry and Analysis ler geometry, in particular of constant scalar curvature July 2–6, 2012, CRM metrics. Yanir Rubinstein gave a survey on different as- pects (PDEs, Hamiltonian dynamics, geometric flows, Organizers: convex geometry, geometric quantization, metric ge- Dmitry Jakobson (McGill), Semyon Klevtsov (ULB), ometry) of the geometry of the infinite-dimensional Steve Zelditch (Northwestern) space of Kähler metrics. Speakers: Bertrand Duplantier started his morning talk on Robert Adler (Technion), Robert Berman (Chalmers Wednesday July 4th, by congratulating the audience UT; Gothenburg), Nicolas Burq (Paris-Sud), Yaiza Can- on the discovery of the Higgs particle, announced on zani (McGill), Linan Chen (McGill), Brian Clarke that very day. After that François David talked ona (Stanford), François David (CEA/Saclay), Bertrand new (physical) derivation of the KPZ relation using Duplantier (CEA/Saclay), Frank Ferrari (ULB), Boris the replica trick. Liam McAllister reviewed recent ad- Hanin (Northwestern), Dmitry Jakobson, Semyon vances in the problem of counting metastable vacua Klevtsov, Nikolai G. Makarov (Caltech), Liam McAllis- in the string theory landscape, due to the creative ap- ter (Cornell), Liviu Nicolaescu (Notre Dame), Raphaël plication of random matrix model methods. Wednes- Ponge (Seoul NU), Yanir A. Rubinstein (Stanford), Scott day’s afternoon session was devoted to novel ap- Sheffield (MIT), Bernard Shiffman (Johns Hopkins), proaches to random metrics. Semyon Klevtsov talked Lior Silberman (UBC), Song Sun (Imperial Coll.), Igor on a novel definition of random metric on a Kähler Wigman (Cardiff), Steve Zelditch manifold, which arises as the scaling limit of random Number of participants: 31 matrix ensembles of Bergman metrics and its relation The workshop brought together mathematicians and to stability in Kähler geometry. In Robert Berman’s physicists working on questions related to random ge- talk Kähler–Einstein metrics “emerge” in the large N ometry in a broad sense. The organizers hope that this limit of certain random point processes, giving rise conference will spur rapid development in the new to a new notion of stability. Physical applications of area of rigorous approaches to random metrics, in- Aubin–Yau and Mabuchi action functionals in Käh- spired by the physics research in this subject within ler geometry, possibly leading to the extensions of the the last 30 years. Polyakov’s Liouville model of quantum gravity, were Morning sessions during the first two days of the explained by Frank Ferrari on Friday. The Tuesday talk workshop were devoted to lectures on 2d quantum by Scott Sheffield described Imaginary Liouville Quan- gravity and the physical definition of random metrics. tum Gravity and its implications. Frank Ferrari started on Monday with the introduction A possible extension of results obtained by Duplantier to the seminal 1981 work of Polyakov on Liouville 2d and Sheffield in dimension two to higher dimen- gravity. Further developments in Liouville gravity dur- sions was outlined on Friday. Raphaël Ponge gave an ing the 80’s and 90’s were reviewed in two lectures overview of Fefferman’s program and conformally in- by Francois David on Monday and Tuesday. Finally, variant differential operators (including the Yamabe Bertrand Duplantier gave an introductory lecture on and the Paneitz operators). He also presented a com- his ground-breaking 2008 work with Scott Sheffield, putation of the logarithmic singularities of the Green where a random two-dimensional volume form was functions of the conformal powers of the Laplacian. Linan Chen outlined a construction of random mea-

20 Thematic Program sures in dimension four (inspired by the construction Nicolas Burq gave a talk on probabilistic Sobolev em- of Duplantier and Sheffield in dimension two), and de- beddings, showing that, from a PDE point of view, scribed an approach to derive a KPZ-type relation for randomly chosen functions may behave much more spherical averages of those measures. nicely than what the deterministic theory would pre- Several talks at the conference were devoted to the dict. On Friday, Yaiza Canzani described recent re- properties of random functions, random sections of sults on the distribution of perturbations of propagated holomorphic line bundles, and related problems. On Schrödinger eigenfunctions, establishing asymptotics Tuesday, Bernard Shiffman discussed critical points of for their moments under certain admissibility condi- random sections of holomorphic line bundles. Boris tions (which involve the geometry of the space of met- Khanin discussed his recent results on correlations and rics on Riemannian manifolds). nearest neighbour spacings between zeros and critical Several talks at the conference were also devoted to points of random polynomials. Nikolai Makarov dis- the geometry of manifolds of metrics. In addition to cussed distribution of eigenvalues for random normal the talks describing the geometry of spaces of Käh- matrix ensembles, near the boundary and near some ler metrics, and the talk of Brian Clarke on the L2 singular points in the bulk. distance, Lior Silberman described how the CAT(0) On Thursday, Robert Adler discussed some results in property of the manifold of Riemannian metrics can be random algebraic topology, including the persistence used to show that random groups with strong fixed- homology of the sublevel sets of Gaussian processes point properties have no nontrivial smooth volume- over manifolds, and limit theorems for the Betti num- preserving actions on compact manifolds, via the asso- bers of random complexes built over random point pro- ciated action on the space of metrics. Finally, Dmitry cesses. Liviu Nicolaescu described his results on critical Jakobson described how one can define Gaussian mea- values of random functions on a given compact Rie- sures on manifolds of metrics with the fixed volume mann manifold, given as a random Fourier series in- form, and use them to compute the moment-generat- volving the eigenfunction of the Laplacian. Igor Wig- ing function for the Ebin distance to the reference met- man described his results on nodal length fluctuations ric. for random Gaussian Laplace eigenfunctions on the torus (“arithmetic random waves”).

Past Thematic Programs

The Centre de recherches mathématiques has organized thematic activities every year since 1993. From 1987 to 1992, the CRM organized various types of activities, including special semesters, concentration periods, and thematic activities. Here is a list of the main activities organized by the CRM since 1987.

January–June 2011 Statistics June–December 2007 Applied Dynamical Systems July–December 2010 Geometric, Combinatorial January–June 2007 Recent Advances in and Computational Group Theory Combinatorics January–April 2010 Number Theory as June–December 2006 Combinatorial Optimization Experimental and Applied Science 2005–2006 Analysis in Number Theory August–December 2009 Mathematical Problems in 2004–2005 The Mathematics of Stochastic and Imaging Science Multiscale Modelling 2008–2009 Joint CRM-PIMS Program: Challenges 2003–2004 Geometric and Spectral Analysis and Perspectives in Probability 2002–2003 Mathematics in Computer Science 2008–2009 Probabilistic Methods in Mathematical 2001–2002 Groups and Geometry Physics 2000–2001 Mathematical Methods in Biology and January–June 2008 Dynamical Systems and Medicine Evolution Equations 1999–2000 Mathematical Physics

21 Centre de recherches mathématiqes

1998–1999 Number Theory and Arithmetic 1991–1992 Automorphic Forms in Number Theory Geometry 1991 Operator Algebras (special semester) 1997–1998 Statistics 1990 Nonlinear PDEs and Applications 1996–1997 Combinatorics and Group Theory (concentration period) 1995–1996 Applied and Numerical Analysis 1988 Shimura Varieties (special semester) 1994–1995 Geometry and Topology 1987 Quantum Field Theory (special semester) 1993–1994 Dynamical Systems and Applications 1987–1988 Fractals: Theory and Application 1992 Probability and Stochastic Control 1987 Structural Rigidity (special semester) (special semester)

22 General Program Centre de recherches mathématiqes

he CRM’s general program funds a wide variety of scientific events, both on the premises of the CRMand T elsewhere in Canada. Whether it be for specialized workshops attended by a small number of researchers or large meetings attended by hundreds of participants, the general program promotes research in the mathematical sciences at all levels. The program is quite flexible, allowing projects to be considered as theyarise. The reports are presented in the language in which they were submitted.

CRM activities

Workshop on geometry and analysis, such as the geometry of differ- Moving Frames in Geometry ential equations and conservation laws, geometric sub- June 13–17, 2011, CRM manifold flows, and classification problems in differ- ential and algebraic geometry. Each topic began with a Organizers: one-hour general overview of the subject given by one Niky Kamran (McGill), Abraham Smith (McGill), Fran- of the primary speakers. It was followed by more tra- cis Valiquette (McGill) ditional contributed research talks of 30 to 45 minutes. Keynote Speakers: The breadth of the list of topics covered in this talkwas Robert Bryant (UC Berkeley), Andreas Cap (Wien), quite remarkable. The discussion sessions scheduled in Jeanne N. Clelland (CU-Boulder), Mark Fels (Utah the workshop were particularly stimulating and fruit- State), Peter Olver (Minnesota), Keti Tenenblat (Brasí- ful and helped to chart the course for future develop- lia) ments in this very active field of geometry. Other Speakers: Stephen Anco (Brock), Andrea Dziubek (SUNY IT), CRM Special Lecture Daniel Fox (CC Philadelphia), Tania Goncalves (Kent), “What is the Shape of Inner Space?” by Thomas Ivey (Coll. Charleston), Nabil Kahouadji Shing-Tung Yau (McGill), Irina Kogan (North Carolina State), Gloria June 20, 2011, CRM Mari Beffa (Wisconsin–Madison), Thomas Mettler (UC Berkeley), Robert Milson (Dalhousie), Peter J. Olver In this public lecture, Professor Yau spoke about how (Minnesota), Juha Pohjanpelto (Oregon State), Colleen mathematics and physics can come together to the Robles (Texas A&M), Konrad Schöbel (Jena), Ekate- benefit of both fields, particularly in the case of Calabi– rina Shemyakova (Western Ontario), Roman Smirnov Yau spaces and string theory–our leading attempt to (Dalhousie), Chuu-Lian Terng (UC Irvine), Dennis The explain the universe to date. He discussed his personal (Texas A&M), Robert Thompson (Minnesota), Peter introduction to geometry, as well as a bit of the history John Vassiliou (Canberra), Igor Zelenko (Texas A&M) of geometry. Thus Professor Yau gave his audience a Number of participants: 49 sense of how mathematicians think and approach the Brought to maturity by Elie Cartan, the method of world and conveyed the realization that mathematics moving frames has been in the mathematical land- does not have to be a wholly abstract discipline, dis- scape for more than a century. From the Frenet– connected from everyday phenomena, but is instead Serret frame to Cartan’s “repère mobile” and beyond, crucial to our understanding of the physical world. moving- frame techniques have proven indispensable Professor Yau’s work has impacted both mathemat- in the study of symmetries, invariants, and other in- ics and physics. Calabi–Yau manifolds are among the trinsic properties of geometrical objects. Explicit appli- “standard toolkit” for string theorists today. He has cations of moving-frame techniques range from classi- made fundamental contributions at the interface be- cal differential geometry to integrable systems, and on tween geometry and theoretical physics. His proof toward control theory and computer vision. of the positive energy theorem in general relativity The objective of this workshop was to discuss recent demonstrated sixty years after its discovery that Ein- applications and theoretical advances of these tech- stein’s theory is consistent and stable. His proof of the niques. Several particular topics were covered deal- Calabi conjecture allowed physicists using Calabi–Yau ing with contemporary applications of both Cartan’s compactification to show that string theory is a viable equivalence method and equivariant moving frames in candidate for a unified theory of nature. Shing-Tung

24 General Program

Yau is Professor of Mathematics at Harvard University. gram consisted of 24 invited presentations and 14 con- His fundamental contributions to research have been tributed talks. The lectures, given by some of the lead- recognized by the Fields Medal, the Crafoord Prize, the ers in their respective fields, covered a large range National Medal of Science, and the Wolf Prize. He is of topics: Geometric Function Theory; Approximation also a member of the National Academy of Sciences of Theory; Operator Theory; Function Spaces; Classical, the United States. Abstract, and Probabilistic Potential Theory; Pluripo- tential Theory; Harmonic Analysis; Orthogonal Poly- Complex Analysis and Potential Theory nomials; Complex Dynamics; and other topics. The A Conference in Honour of Paul M. conference proceedings, containing more than 20 ref- Gauthier and Kohur GowriSankaran ereed articles, were published in the CRM Proceedings June 20–23, 2011, CRM & Lecture Notes Series. The proceedings are a mixture Sponsored by the Mathematical Analysis Laboratory, of original research and expository articles. the Canada Research Chair in Spectral Theory and The conference was honouring the important contri- Complex Analysis, the Département de mathéma- butions to mathematics and the mathematical commu- tiques et statistique of the Université de Montréal, nity of two influential analysts from Montréal: Pro- and the Department of Mathematics and Statistics of fessor K. N. GowriSankaran (McGill University) and McGill University Professor Paul M. Gauthier (Université de Montréal). Organizers: Each of them has had a long and distinguished career André Boivin (Western Ontario), Javad Mashreghi (La- in Montréal, extending over four decades. The confer- val) ence brought together specialists, young researchers, Speakers: and graduate students in both Complex Analysis and Hiroaki Aikawa (Hokkaido), Victor Anandam Potential Theory; it fostered exchanges of ideas and (Madras), Nadya Askaripour (Calgary), Dominique techniques and cooperation to find new research per- Bakry (Paul Sabatier), Lucian Beznea (Simion Sto- spectives. ilow), Maritza Branker (Niagara), Alexander Brud- nyi (Calgary), Debraj Chakrabarti (Tata Inst.), Fausto Summer School on Di Biase (G. D’Annunzio), David Drasin (Purdue), Non-Equilibrium Statistical Mechanics Driss Drissi (Kuwait), Peter L. Duren (Michigan), July 1–29, 2011, CRM Roman Dwilewicz (Missouri UST), Konstantin Fe- Sponsored by the Agence Nationale de la Recherche dorovskiy (Moscow STU), Alastair Fletcher (War- (ANR), the CNRS, the CRM, NSERC, McGill Univer- wick), Richard Fournier (Dawson; Montréal), Stephen sity, and the Université de Cergy-Pontoise Gardiner (UC Dublin), Wolfhard Hansen (Bielefeld), Organizers: Tsubasa Itoh (Hokkaido), Sebti Kerbal (Sultan Qa- Laurent Bruneau (Université de Cergy-Pontoise), Vo- boos), Dmitry Khavinson (South Florida), Nikolai G. jkan Jakšić (McGill University), Roberto Livi (Univer- Makarov (Caltech), Jane McDougall (Colorado Coll.), sità degli Studi di Firenze), Claude-Alain Pillet (Uni- Yoshihiro Mizuta (Hiroshima), Jürgen Müller (Trier), versité du Sud Toulon-Var), Robert Seiringer (McGill Vassili Nestoridis (Athens), Ivan Netuka (Charles), University) Markus Niess (KU Eichstätt-Ingolstadt), Anthony G. O. Number of participants: 59 O’Farrell (NU Ireland), Petr Paramonov (Moscow SU), The summer school on Non-Equilibrium Statistical Me- Thomas J. Ransford (Laval), Murali Rao (Florida), chanics took place at the CRM in July 2011 and Dominic Rochon (UQTR), Azimbay Sadullaev (NU was the second part of the joint CRM–Université de Uzbekistan), Nageswari Shanmugalingam (Cincin- Cergy-Pontoise semester on Frontiers in Mathematical nati), David Singman (George Mason), Manfred Stoll Physics. The first part of the joint semester washeld (South Carolina), Nikolai Tarkhanov (Potsdam), Jie at the Université de Cergy-Pontoise in the month of Xiao (Memorial), Eduardo Santillan Zeron (Cinvestav), May. The May program included two eighteen-hour Ruhan Zhao (Coll. Brockport, SUNY) mini-courses titled Dynamics and statistics on lattices Number of participants: 49 and networks and Non-equilibrium quantum statisti- This four–day international conference gathered more cal mechanics, given, respectively, by Roberto Livi and than 50 mathematicians from 15 countries and its pro- Vojkan Jakšić; a one-day seminar (Dynamics in spa-

25 Centre de recherches mathématiqes tially extended systems) held on May 6 (the speak- Y. Ogata (Tokyo), A. Panati (Toulon), Y. Pautrat (Paris- ers were H. Chaté, CEA/Saclay; J. Kurchan, ESPCI Dauphine), D. Ruelle (IHÉS), A. Shirikyan (Cergy- ParisTech; A. Pikovsky, Potsdam; A. Politi, Firenze); Pontoise), D. Taj (Toulon), L. Thomas (Virginia), and a two-day workshop (Frontiers in Mathemati- M. Westrich (Aarhus), J. Yngvason (Wien), and V. Za- cal Physics) held on May 26–27 (the speakers were grebnov (Méditerranée). M. Aizenman, Princeton; S. De Bièvre, Lille 1; V. Jakšić, A selection of articles based on the courses will be McGill; A. Joye, Joseph Fourier; A. Klein, UC Irvine; published in a special issue of the Journal of Math- F. Klopp, Paris 13; C.-A. Pillet, Toulon; R. Seiringer, ematical Physics devoted to the summer school. We McGill; and S. Warzel, TU München). These activi- are also happy to acknowledge, with special thanks ties were followed by an intense four-week program to B. Nachtergaele, the financial contribution of the held in Montréal in July, and described below. The American Institute of Physics/Journal of Mathematical joint semester was initiated and enthusiastically sup- Physics toward the organization of the summer school. ported by F. Germinet, vice-president of the Université The summer school and the entire joint semester de Cergy-Pontoise. The organizers were L. Bruneau, were a considerable success. In spite of the inten- V. Jakšić, R. Livi, C.-A. Pillet, and R. Seiringer. sity of the program, there was plenty of time for dis- The July program included a fifteen-hour course by cussions and forging of new scientific collaborations. J. Derezinski (Warsaw) titled A mathematical intro- A very friendly and relaxed atmosphere was com- duction to quantum electrodynamics, and twelve three- bined with one of the most pleasant springs/summers hour mini-courses listed below. Paris/Montréal had in a long time. • L. Bruneau (Cergy-Pontoise) Repeated Interaction Quantum Systems. I. SMS 2011 Summer School • B. Derrida (ÉNS) Density and current fluctuations in Metric Measure Spaces: Geometric and non-equilibrium diffusive systems. Analytic Aspects • G.-M. Graf (ETH Zürich) Adiabatic evolution and de- June 27–July 8, 2011, Université de Montréal phasing. Sponsored by the CRM, the Fields, PIMS, the ISM, • A Joye (Joseph Fourier) Repeated interaction quan- the Mathematical Sciences Research Institute (MSRI), tum systems. II. the Université de Montréal (Département de mathéma- • I. Klich (Virginia) Entanglement in many body sys- tiques et de statistique), Concordia, and the CMS tems. Organizers: • E. Lieb (Princeton) The Polaron. Galia Dafni (Concordia), Robert McCann (Toronto), • C. Liverani (Tor Vergata) Fourier law from a dynam- Alina Stancu (Concordia) ical systems point of view. Number of participants: 60 • R. Livi (Firenze) Heat transport in low-dimensional systems. The 50th edition of the Séminaire de mathématiques • J. Møller (Aarhus) Pauli–Fierz systems at zero and supérieures (SMS) took place from June 27 to July 8, positive temperature. 2011, on the campus of the Université de Montréal. This • C.-A. Pillet (Toulon) Open systems. university has supported the summer school, which • R. Seiler (TU Berlin) Typicality in classical and quan- has acquired international renown, for over 50 years, tum information theory. often in collaboration with NATO. For the first time • R. Seiringer (McGill) Cold quantum gases and Bose- this year, a new funding structure was initiated by the Einstein condensation. SMS Director, Octav Cornea, and the school was sup- ported by the Canadian mathematical community, as The program also included twenty-four 45-minute well as at the North American level. This is reflected in talks given by Y. Avron (Technion), S. Bachmann the list of sponsors of the SMS 2011 Summer School, (UC Davis), J.-M. Barbaroux (Toulon), H. Cornean given above. (Aalborg), S. De Bièvre (Lille 1), W. De Roeck (Hei- delberg), M. Fraas (Technion), F. Germinet (Cergy- In recent decades, metric measure spaces have Pontoise), P. Grech (ETH Zürich), F. Hiai (Tohoku), emerged as a fruitful source of mathematical ques- S. Kuksin (École Polytechnique), E. Livi (Firenze), tions in their own right, and as indispensable tools for M. Merkli (Memorial), B. Nachtergaele (UC Davis), addressing classical problems in geometry, topology,

26 General Program dynamical systems, and partial differential equations. The abstracts and some lecture notes can be found on The summer school was designed to lead young sci- the SMS website, http://dms.umontreal.ca/~sms/ entists to the research frontier concerning the analy- Metric11/index_e.php. In addition, the proceedings sis and geometry of metric measure spaces, by expos- of the summer school will be collected in a volume ing them to a series of mini-courses featuring leading to be published in the CRM Proceedings and Lecture researchers who highlighted both the state-of-the-art Notes series. and some of the exciting challenges that remain. The The mini-courses came under three general themes, selection of funded participants from the pool of nearly with certain talks providing links between them. The 140 applicants, many of them highly qualified, was dif- first and perhaps most prevalent was the use oftech- ficult. In the end, with over 60 participants, mostly niques from optimal transportation to define geomet- graduate students, coming from 13 countries in Africa, ric notions on metric measure spaces, in particular the Asia, Europe, and North America, this 50th edition of notion of lower curvature bounds. Yann Ollivier began the Séminaire de mathématiques supérieures was a re- the school with a beautiful series of lectures introduc- sounding success. ing a definition of discrete Ricci curvature on metric There were 13 four-hour minicourses given by inter- spaces, based on the idea of comparing the (average national experts in their fields: transportation) distance between balls to the distance • L. Ambrosio (Scuola Normale Superiore di Pisa): Cal- between their centers. Ollivier’s talks were comple- culus in metric measure spaces with Ricci curvature mented on the one hand by Vitali Kapovitch’s lectures, bounded from below; emphasizing the Riemannian geometry point of view, • M. Barlow (University of British Columbia): Heat and on the other by Robert McCann’s lectures on op- equation on some fractal metric spaces; timal transportation. • T. Coulhon (Université de Cergy-Pontoise): Heat In a carefully prepared series of talks aimed at kernel estimates, Sobolev type inequalities and Riesz an audience consisting in part of non-geometers, transform on non-compact Riemannian manifolds; Kapovitch described the consequences of curvature • G. David (Université Paris-Sud): Regularity results for bounds on Riemannian manifolds, comparing in par- minimal sets; ticular Ricci curvature versus sectional curvature, and • P. Hajłasz (University of Pittsburgh): Sobolev map- metric analogs in Alexandrov spaces, and emphasiz- pings into metric spaces; ing the importance of splitting theorems. The high- • V. Kapovitch (University of Toronto): Fundamen- lights of the course were the results of Kapovitch and tal groups of manifolds with lower Ricci curvature Wilking on the finitely generated fundamental group bounds; of manifolds with Ricci curvature bounded from below. • Y.-H. Kim (University of British Columbia): Ma– McCann’s mini-course provided students with insight Trudinger–Wang curvature and regularity of optimal into the techniques and applications of optimal trans- transport; portation, starting with the classical transportation • P. Koskela (University of Jyväskylä): Quasiconformal problem of Monge and Kantorovich and progressing to mappings and function spaces; the recent theorems concerning smoothness of optimal • R. McCann (University of Toronto): Optimal Trans- maps by Ma, Trudinger, Wang, and Loeper. Along the portation; way there were excursions into two-player zero sum • E. Milman (Technion–Israel Institute of Technol- games, convex duality and linear programming, fully ogy): Isoperimetric, functional and concentration in- nonlinear partial differential equations, the economics equalities; of optimal pricing, and connections with minimal La- • Y. Ollivier (CNRS; Université Paris-Sud): Discrete grangian submanifolds in semi-Riemannian geometry. Ricci curvature with applications; • F. Otto (Max-Planck-Institut für Mathematik in den This theme was taken up in the second weekby Naturwissenschaften): Burgers’ equation as a gradi- Karl-Theodor Sturm, who spoke about the celebrated ent flow on two-phase Wasserstein space; and curvature-dimension condition for metric measure • K. T. Sturm (Universität Bonn): Ricci bounds for met- spaces, originating in his work and that of Lott–Villani ric measure spaces and geometric analysis. (with ideas tracing back to the work of McCann). He introduced a variant of this condition, the so-called “re- duced curvature-dimension condition,” which has the

27 Centre de recherches mathématiqes local-to-global property. The mini-course concluded quasi-conformal mappings in the context of (Ahlfors with a detailed exposition of the relevant notions and regular) metric-measure spaces, covering in detail the results in the setting of Finsler spaces. The discussion regularity of QC maps, the notion of quasi-symmetry, of optimal transportation started by McCann contin- and the function spaces preserved under these maps. In ued with a series of talks by Young-Heon Kim on Ma– addition to Sobolev spaces (using the definition given Trudinger–Wang curvature and regularity of optimal by Hajłasz), recent work by Koskela, Yang, and Zhou transport. In this theory, the non-negativity of certain was described, showing that certain appropriately de- sectional curvatures of a metric induced by the trans- fined Besov and Triebel–Lizorkin spaces are preserved. portation cost turns out to be necessary and sufficient The two themes described above came together in for the smoothness of optimal maps. Focusing his talks the mini-course by Luigi Ambrosio in the school’s in the Riemannian setting, Kim outlined the state-of- second week. Ambrosio reviewed and compared var- the art through a series of examples and counterexam- ious notions of weak gradients and Sobolev spaces ples, building up to his recent joint work on Hölder in metric measure spaces, such as upper gradients continuity of optimal maps between not-necessarily- (due to Heinonen and Koskela), absolute continuity on smooth distributions of mass. lines (a definition by Levi extended to metric measure The course by Felix Otto illustrated further uses ofno- spaces by Shanmugalingam), and Cheeger’s energy, tions coming from optimal transportation, in particu- and showed the identification of weak gradients using lar the Wasserstein distance, arising in partial differ- optimal transportation techniques, without relying on ential equations from applied mathematics modelling doubling or Poincaré assumptions. These exciting re- dissipative mixing of immiscible fluids. Here he re- sults (joint work of Ambrosio with Gigli and Savaré) visited his classical bound on the nonlinear mixing used a gradient flow based on the Wasserstein dis- rate. This appears uncontrolled in the linearized regime tance and the curvature-dimension conditions of Lott– due to the Rayleigh–Taylor instability, which predicts Sturm–Villani. that thin fingers of fluid grow faster, with the thinnest The final theme could be described as functional and fingers growing arbitrarily fast. More than a decade geometric inequalities. The mini-course of Ollivier ago, Otto coarse-grained the dynamics, to show that concluded with results on concentration of measure the average fluid density as a function of its height and the Brunn–Minkowski inequality for the discrete obeys a Burgers’ type equation that predicts mixing hypercube (the latter joint work with Villani), part at a bounded rate. In a recent preprint with Gigli, he of the body of work for which he was awarded the showed that this dynamics actually represents a gra- 2011 CNRS bronze medal. The course of Emanuel Mil- dient flow in a metric space setting, which picksout man, spanning the two weeks, described the relations the unique entropy solution to the scalar conservation between isoperimetric inequalities, concentration of law, as explained in his lectures. measure, and functional inequalities such as Poincaré, The second theme of the summer school, roughly com- Sobolev, and log-Sobolev. While isoperimetric inequal- ing under the “analytic aspects”of metric spaces, con- ities imply Sobolev type inequalities, and it is known cerned notions of differentiability on metric measure from work of Gromov–V. Milman that, in any metric spaces and the corresponding function spaces. This space, the Poincaré inequality implies exponential con- theme started in the first week with the parallel series centration, the reverse implications do not hold in gen- of lectures by Piotr Hajłasz and Pekka Koskela. With- eral. It was thus an impressive result that in the case out relying on much background from the audience, of a Riemannian manifold with density having lower Hajłasz succeeded in introducing students to the fas- bounds on the Bakry–Émery tensor, E. Milman showed cinating and sometimes surprising world of Sobolev that concentration inequalities imply isoperimetric in- mappings between manifolds, from manifolds into equalities. A main ingredient of his proof is a result metric spaces, and between metric spaces, in which ba- of Frank Morgan, well known in geometric measure sic facts such as approximation by smooth or Lipschitz theory. The latter topic was featured in the lectures by functions cannot be taken for granted, and may depend Guy David. Starting with the famous Plateau problem on topological properties involving homotopy groups in higher dimensions (not yet solved) as an illustration, (in the case of manifolds). Koskela’s dynamic lectures David’s course discussed the structure of minimizers exposed the audience to questions from the theory of to functionals on currents with a given lower dimen-

28 General Program sional rectifiable current as boundary. The focus was 17th International Conference on now on the lack of smoothness, and minimizers in the Difference Equations and Applications sense of Almgren, concluding with the proof of Jean (ICDEA) Taylor’s theorem that characterizes them. July 24–29, 2011, UQTR The relations between various inequalities was also the Sponsored by the International Society of Difference subject of the course by Thierry Coulhon in the sec- Equations, the CRM, the UQTR, the Département de ond week. Again working in the Riemannian context, mathématiques et informatique and the Départment de but this time on a non-compact manifold with vol- physique of UQTR, and the Association générale des ume doubling, Coulhon discussed the implications of étudiants de l’UQTR Lp various heat kernel estimates to boundedness of Organizer: Adel F. Antippa (UQTR) Riesz transforms, an important question that relates Main speakers: back to the second theme since it concerns the compat- Göran Högnäs (Åbo Akademi), Anna Mazzucato (Penn ibility of various definitions of weak derivatives (i.e., State), Stefan Siegmund (TU Dresden), Petr Stehlík the weak gradient and the square-root of the Lapla- (West Bohemia), Aleksandr N. Sharkovsky (Mathemat- cian) and the corresponding Sobolev spaces. An exam- ics Inst., ASU), Erik Van Vleck (Kansas), Pavel Winter- ple was given of a fractal-like manifold where local nitz (Montréal) and global bounds differ. Heat kernel estimates, and Number of participants: 48 in particular this type of discrepancy between local C’est sur le campus de l’Université du Québec à Trois- and global behaviour, also played a prominent role in Rivières que s’est déroulé pour la première fois au Ca- the lectures by Martin Barlow, where Gaussian bounds nada le congrès annuel de la Société internationale des were shown to be equivalent to a parabolic Harnack in- équations aux différences finies (ISDE). Au cours du equality on the one hand, and doubling and Poincaré congrès, marqué par la contribution d’éminents cher- on the other. These inequalities (or their failure) were cheurs et professeurs en provenance de 14 pays, une discussed in detail for the Sierpinski carpet. cérémonie a été organisée pour la remise du prix Bernd All talks were of an exceptionally high quality. More- Aulbach au Pʳ Aleksandr N. Sharkovsky. Ce prix a été over, many of the speakers attended the other mini- décerné pour la toute première fois par l’International courses and this generated interesting interactions. Society of Difference Equations (ISDE). En plus des ac- Students too posed questions to the speakers, rang- tivités scientifiques, les participants du congrès ont été ing from elementary to very knowledgeable, and con- invités au salon du maire de Trois-Rivières ainsi qu’à tinued the discussions between the talks and during une réception organisée par le recteur de l’Université the lunch breaks and social activities. Despite the full du Québec à Trois-Rivières, M. André Paradis. schedule, there was a lot of enthusiasm among partici- pants until the very last lecture, and a subsequent sur- Complex Analytic and Algebraic Trends in vey conducted by PIMS demonstrated high rates of sat- the Geometry of Varieties isfaction. Just as two of the speakers, Robert McCann August 15–17, 2011, UQAM and Young-Heon Kim, recounted positive memories of past SMS summer schools they attended as students, it Organizers: is hoped that the 2011 SMS will remain memorable for Karol Palka (UQAM), Peter Russell (McGill), Steven its participants, and some of them will even return as Shin-Yi Lu (UQAM) future speakers. Speakers: V. Charette (Sherbrooke), D. Daigle (Ottawa), F. Donzelli (Ottawa), B. Gilligan (Regina), R. Gurjar (Tata Inst.), Sh. Kaliman (Miami), M. Koras (Warsaw), A. Maharana (IISER Mohali), K. Masuda (Kwansei Gakuin), M. Miyanishi (Kwansei Gakuin), L. Moser- Jauslin (Bourgogne), A. Sathaye (Kentucky), J. Winkel- mann (Bochum), D.-Q. Zhang (NU Singapore), Y. Zong (Toronto)

29 Centre de recherches mathématiqes

Number of participants: 23 points of orbits of Ga-actions.) Donzelli in his talk stud- The conference was organized to take advantage ofthe ied the connection between flexibility and the Makar- presence in Montreal during August 2011 of three post- Limanov and related Derksen invariants in the case doctoral fellows (F. Donzelli, A. Maharana, K. Palka) of affine surfaces. The talk of Charette was onreal3- and several long-term visitors (R. Gurjar, M. Koras, manifolds. She described 3-manifold quotients of Eu- K. Masuda, M. Miyanishi, A. Sathaye, J. Winkelmann, clidian 3-space by non solvable groups of affine trans- D.-Q Zhang) specializing in complex analytic and alge- formations (discovered by Margulis) and discussed re- braic geometry. Several research projects resultig from cent results on the deformation spaces of such groups. this collaboration are ongoing. The talks of Gurjar and Maharana dealt with aspects There were 15 presentations of 50 minutes each. If of the classical subject of cyclic multiple planes, that is one looks for a common denominator for a major- cyclic ramified covers of the complex plane C2. Gur- ity of the talks, one will find it in the study of group jar described a common approach to multiple planes actions, including infinitesimal ones, on varieties, in and branched covers of the n-sphere based on Smith’s one of a manifold of incarnations of this subject. The theory of finite group actions on simplicial complexes. talks of Zhang and Gilligan dealt with compact Käh- This gives in particular a new proof of Zariski’s result ler manifolds, the first with the study of the dynamics on the irregularity of a multiple plane. Maharana gave of automorphisms from the view point of the minimal a classification in terms of the ramification locus ofthe model program and the second with the existence of multiple planes that have logarithmic Kodaira dimen- (local) Kähler structure on homogeneous spaces and sion less than 2. Koras described the almost completed ∗ tube neighborhoods of CR-solvmanifolds. classification of closed embeddings of C in C2. Fairly sophisticated results in the theory of open surfaces, in The talks of Miyanishi, Masuda, Daigle, and Moser- particular the logarithmic BMY-inequality, are used. Jauslin dealt with automorphisms of affine varieties. Miyanishi characterized derivations D on a factorial Sathaye in his talk raised, and largely solved, an ele- affine threefold Spec A that are locally nilpotent (and mentary question on extensions of a field k: If t is a hence come from a Ga-action) in terms of the fibra- root of an irreducible( ) polynomial f(x) over k, when ′ tion Spec(A) → Spec(Ker D). Masuda proved struc- is k(t) = k f (t) ? The question arose in connection ture theorems for affine domains that have an algebraic with the Jacobian problem. Winkelmann’s talk dealt derivation, a notion that generalizes local nilpotency with the relation between the Diophantine behaviour and corresponds to actions of more general algebraic of a variety X defined over a number field K and the groups. Daigle described a general construction of nor- properties of the complex manifold X(C), in particu- mal affine surfaces that admit a non-trivial Ga-action lar an analogy between infinite sets of integral points and have trivial canonical class (as, for instance, hyper- over a finite extension of K and holomorphic curves. surfaces in A3). Moser-Jauslin described the construc- He showed that these objects have similar lifting prop- tion of families of contractible (hence diffeomorphic to erties with respect to principal bundles. The subject C3) smooth hypersurfaces in C4 with pairwise non- of Zong’s talk was the monodromy of torsion points isomorphic members. A key tool here is the use of the of abelian varieties and the Mumford–Tate conjecture. Makar-Limanov invariant (the intersection of the ker- He outlined a proof of a theorem of Serre on big mon- nels of all locally nilpotent derivations) of these three- odromy of torsion points. folds. Combinatorial Algebra Meets Algebraic Kaliman gave a survey of the present state of Combinatorics Andersen–Lempert theory, that is the study of the den- January 20–22, 2012, UQAM sity properties of the Lie algebra generated by com- Sponsored by the CRM, LaCIM, and the Canada Re- pletely integrable vector fields in the space of all holo- search Chair in Combinatorial Algebra and Mathemat- morphic vector fields on a Stein manifold. This andthe ical Computer Science analogous question of algebraic density on an affine variety are very active areas of research at present, Organizers: in particular in connection with the study of flexible François Bergeron (UQAM), Johanne Patoine (UQAM), varieties. (A smooth point on a variety is flexible if the tangent space is generated by the tangents at the

30 General Program

Franco Saliola (UQAM), Luis Serrano (UQAM), Jérôme • Gorenstein sequences of socle degree 4 and 5 and Ar- Tremblay (UQAM) tinian Level algebras of codimension 3 (Y. S. Shin). Speakers: • A new combinatorial approach to cluster algebras of Ali Alilooee (Dalhousie), Federico Ardila (San Fran- finite types (C. Stump). cisco State), Elizabeth Beazley (Williams Coll.), Chris • Canonically positive bases in the cluster algebra as- Berg (UQAM), Zhi Chen (York), Emma Connon (Dal- sociated to an annulus (H. Thomas). housie), Federico Galetto (Northeastern), Christophe • On using quasisymmetric functions to determine Hohlweg (UQAM), Anthony Iarrobino (Northeastern), Schur expansions (G. Warrington). Ilias Kotsireas (Wilfrid Laurier), Alejandro Morales • Young’s lattice and the cyclic sieving phenomenon (MIT), Rosa Orellana (Dartmouth Coll.), Kevin Purb- (N. Williams). hoo (Waterloo), Yong-Su Shin (Sungshin WU), Chris- tian Stump (UQAM), Hugh Thomas (New Brunswick), SUMM 2012 Greg Warrington (Vermont), Nathan Williams (Min- Seminars in Undergraduate Mathematics in nesota) Montréal Number of participants: 45 January 21–22, 2012, Université de Montréal Le but de cette rencontre était de faire le point sur les progrès récents concernant plusieurs questions ou- Organizers: vertes à l’intersection de la combinatoire, de l’algèbre Jean-François Arbour (UQAM), Geoffroy Bergeron commutative, et de la géométrie algébrique. Parmi (Montréal), Vincent Gélinas (Concordia), Kevin Ger- les faits marquants, mentionnons des descriptions ex- vais (Montréal), Andréanne Lapointe (Montréal), Vin- plicites: (1) de constantes de structures pour des an- cent Létourneau (Montréal), Daniel Lévesque (Mont- neaux de cohomologie de variétés de drapeaux et de réal), Michael Snarski (McGill) grassmaniennes, (2) de résolutions linéaires équivari- Speakers (professors): antes d’idéaux de monômes, (3) de la “structure” de Steven Boyer (UQAM), Henri Darmon (McGill), Chan- systèmes de racines pour des groupes de Coxeter infi- tal David (Concordia), Paul Gauthier (Montréal) nis, (4) de la structures de certaines algèbres amassées. Speakers (students): Jean-François Arbour, Léo Belzile, Nicolas Bouchard, David Boulet, Philippe Voici la liste des conférences. Charron, Gabriel Gaudreault, Vincent Gélinas, Kevin • The graded Betti numbers of the path ideal of acycle Gervais, Bruno Joyal, Jamie Klassen, Andréanne La- (A. Alilooee). pointe, Alex Lavoie, Vincent Létourneau, Daniel • Power ideals of hyperplane arrangements (F. Ardila). Lévesque, Frédéric Quesnel, Jifeng Shen, Nicolas • Quantum cohomology and the poset of Newton Simard, Michael Snarski, David Thibodeau polygons (E. Beazley). Number of participants: 90 • Expansions of k-Schur functions in the affine nil Le Séminaire universitaire de mathématiques à Mont- Coxeter algebra (C. Berg). réal (SUMM) est un évènement organisé annuellement • A Plethysm formula on the induced linear character par des étudiants de premier cycle en mathématiques from U (F ) into GL (F ) (Z. Chen). n q n q et ayant lieu dans l’une des quatre universités mont- • Generalizing Fröberg’s theorem on ideals with linear réalaises. Il est né en 2009 de l’initiative d’étudiantes resolutions (E. Connon). de McGill et sa première édition a eu lieu à l’UQAM • Free resolutions of orbit closures for representations au mois de février 2010. L’objectif de ce séminaire est with finitely many orbits (F. Galetto). de permettre aux étudiants de se rencontrer dansle • Asymptotical behaviour of roots of Coxeter groups but d’échanger sur différents domaines des mathéma- (C. Hohlweg). tiques, tant fondamentales qu’appliquées. Les exposés • Bound on the Jordan type of a nilpotent matrix com- sont donnés par des étudiants et des professeurs (in- muting with a given matrix (T. Iarrobino). vités) des quatre universités montréalaises (voir le site • New results on D-optimal matrices (I. Kotsireas). http://summ.math.uqam.ca/). Le séminaire de 2012 • Flow polytopes and the Kostant partition function a attiré un grand nombre de participants : eneffet for signed graphs (A. Morales). beaucoup d’étudiants qui n’avaient pas rempli le for- • On a diagram centralizer algebra (R. Orellana). mulaire du CRM ont participé au séminaire. En 2012 • A tale of two staircases (K. Purbhoo). les sujets couverts allaient de la théorie des nombres et

31 Centre de recherches mathématiqes de la théorie des nœuds (sujets abordés par les profes- ter), Răzvan Gurau (Perimeter Inst.), David Kubiznak seurs invités) à la théorie des représentations, la théo- (Perimeter Inst.), Steve Rayan (Toronto), Amit Sever rie des groupes, la théorie des jeux, les algèbres amas- (Perimeter Inst.), Aaron Smith (Waterloo) sées, l’axiome du choix et la logique. Number of participants: 75 The “Geometry And Physics” conference has been held 69th Algebra Day each year since 2009, with the goal of bringing together April 14, 2012, Ottawa researchers working at the interface between math- Sponsored by the CRM, the University of Ottawa, and ematics and physics, fostering the exchange of inno- Carleton University vative ideas, and exposing participants to new devel- opments which may accelerate their research. An im- Organizer: Erhard Neher (Ottawa) portant secondary aim is to increase further Canada’s Speakers: presence and visibility in geometry within the interna- Alex Hoffnung (Ottawa), José Malagón López (Ot- tional mathematical community. Each year, the confer- tawa), Holger Petersson (FU Hagen), Zinovy Reich- ence focuses on three distinct themes in geometry and stein (UBC), Elizabeth Dan-Cohen (Louisiana State) physics as well as the connections between them. This The Algebra Day, which has a long tradition, enables results in an interesting diversity of talks, and is a dis- algebraists to meet in order to share their latest work. tinguishing feature of the conference which we aim to In 2012 H. Petersson spoke about Moufang sets and maintain. the problem of commuting U-operators in Jordan al- gebras; J. Malagón López about Exponents and formal The GAP 2012 conference witnessed several striking group rings; A. Hoffnung about Hecke algebras and co- breakthroughs in all three of the chosen theme areas: homology; Z. Reichstein about Simplifying polynomi- generalized geometry, integrable systems, and spe- als by Tschirnhaus transformations: old and new; and cial holonomy. The following are some of the high- E. Dan-Cohen about A Koszul category of representa- lights which made GAP 2012 such a success. In the tions of finitary Lie algebras. theme of generalized geometry, Barton Zwiebach un- veiled a new notion of Riemann tensor in the dou- Geometry and Physics — GAP 2012 ble field formalism, which has implications for the May 5–7, 2012, Waterloo & Perimeter Inst. study of generalized metrics, and posed several open Sponsored by the CRM, the Department of Mathemat- problems of interest to mathematicians and physi- ics of the University of Toronto, the Faculty of Math- cists. David Baraglia succeeded in extending the for- ematics of the University of Waterloo, the Faculty of malism of variation of Hodge structure, so crucial in Science of McMaster University, the Fields Institute for mirror symmetry, to generalized complex manifolds. Research in Mathematical Sciences, and the Perimeter Also Michael Bailey presented his recent thesis results, Institute for Theoretical Physics. which complete the local classification of generalized complex manifolds. Finally Gang Tian outlined his re- Organizers: cent research programme, in which he applies the B- Marco Gualtieri (Toronto), Spiro Karigiannis (Wa- field renormalization group flow to generalized Kähler terloo), Ruxandra Moraru (Waterloo), Rob Myers manifolds. (Perimeter Inst.), Pedro Vieira (Perimeter Inst.), In integrable systems, much excitement centred McKenzie Wang (McMaster) around the recent explicit computations of scattering Principal Speakers: amplitudes and Wilson loops in terms of minimal sur- David Baraglia (ANU), Robert Bryant (UC Berke- face areas, which in turn may be expressed in terms ley), Gil Cavalcanti (Utrecht), Mark Haskins (Impe- of integrable systems such as the Hitchin system. This rial Coll.), Jacques Hurtubise (McGill), Boris Khesin work, exemplified by the talks of Amit Sever and Mar- (Toronto; IAS), Dmitry Korotkin (Concordia), Martin tin Kruczenski, generated intense discussions among Kruczenski (Purdue), Naichung Conan Leung (Chinese the assembled experts in integrable systems. In an- U Hong Kong), Chuu-Lian Terng (UC Irvine), Gang other direction, Boris Khesin described his beautiful re- Tian (Princeton; Peking), Barton Zwiebach (MIT) cent work with Fedor Soloviev, which uncovers a great Local Postdocs: number of new discrete integrable systems with con- Michael Bailey (UQAM), Ronan Conlon (McMas-

32 General Program tinuum limit given by a specialization of the KdV hier- lectures were extremely successful, with many ques- archy. tions and lively participation from the audience, so that In the field of special holonomy, Mark Haskins an- the planned two-hour sessions often lasted three hours nounced his spectacular recent achievement in the or more. The more specialised evening lectures were construction of new compact G2 manifolds with also well received overall. known diffeomorphism type, as well as compact G2 The Bellairs Institute provides a unique environment manifolds containing calibrated submanifolds. This for scientific interaction, and the afternoons were set represents a major development in a field tightly linked aside for informal discussions, allowing many of the to M-theory and string compactifications. In a remark- participants to make progress on various collaborative ably energetic presentation, Ronan Conlon described research projects. an important enhancement to the famous result of Tian and Yau proving the existence of asymptotically SAGE Days at CRM conical Calabi-Yau manifolds, which extends our un- May 5–11, 2012, CRM derstanding of noncompact Calabi-Yau manifolds, also crucial in the study of string compactifications. Tian, Organizers: who was in attendance, seemed to approve. Finally, in Srecko Brlek (UQAM), Sébastien Labbé (UQAM), a tour-de-force performance, Robert Bryant produced Franco Saliola (UQAM) explicit resolutions of the canonical coassociative cone Main speakers: in 7 dimensions, making use of an unexpected integra- Meinolf Geck (Aberdeen), Viviane Pons (Marne-la- bility hidden in the ring of SO(3)-invariant polynomi- Vallée), Derek Ruths (McGill), Anne Schilling (UC als in dimension 7, settling a thirty-year-old question Davis), Øyvind Solberg (NTNU), Nicolas M. Thiéry in the study of calibrated geometry. (Paris-Sud), Doron Zeilberger (Rutgers) Number of participants: 58 The Bellairs Workshop in Number Theory In early May 2012, the CRM hosted Sage Days 38. The 2012 audience included researchers of all levels, from un- May 6–12, 2012, Bellairs Research Institute (Barbados) dergraduates embarking on summer research projects Sponsored by CICMA to established researchers, as well as university and CEGEP educators. The goal of the workshop was Organizers: twofold: to provide a gentle introduction to Sage for Henri Darmon (McGill), Eyal Z. Goren (McGill) newcomers, and to develop and implement algorithms Keynote speaker: Minhyong Kim (Oxford) for mathematics research. All participants were en- Evening speakers: couraged to come equipped with their own research Jennifer Balakrishnan (Harvard), Amnon Besser problems that could benefit from some computational (Ben Gurion), Bryden Cais (Arizona), Henri Darmon experimentation. (McGill), Romyar Sharifi (Arizona) Number of participants: 29 We designed the schedule of the workshop with these goals in mind. We had a rigid schedule for the first few The purpose of the workshop was to present aspects of days of the week and an evolving schedule for the last the algebraic theory of the pro-unipotent fundamen- two days. Almost all of the presentations were sched- tal group and its arithmetic applications to diophan- uled for the morning sessions. The afternoon sessions tine questions, following Minhyong Kim’s progam to were dedicated to follow-up discussions, work on tu- study rational points on varieties through anabelian torial exercises (for new users), and coding sprints (for descent and Chabauty-type techniques. The lectures developers). We ended every day with a “status report” aimed to be accessible to non-experts and newcomers where participants would describe their progress. to the subject, including graduate students, although some background in number theory and algebraic ge- Since one of the workshop goals was to provide a gen- ometry was assumed. tle introduction to Sage, there was a strong empha- sis on tutorials. This made the workshop very popular, A series of five two-hour lectures were delivered in the and we had a great turnout (58 participants). It seems mornings by Minhyong Kim, supplemented by lectures that there is a large appetite for workshops that intro- from attending experts in the evenings. The morning duce new research tools! We had seven one-hour tu-

33 Centre de recherches mathématiqes torials throughout the week, led by various Sage de- 2012 Montréal–Toronto Workshop in velopers: “Using the Sage notebook and navigating the Number Theory help system,” F. Saliola; “Calculus and Linear Algebra “Cycles on Kuga Fibre Varieties” in Sage,” F. Saliola; “Programming in Python and Sage,” May 28–29, 2012, CRM F. Hivert; “Contributing to Sage,” A. Schilling; “Intro- Sponsored by the CRM, the Fields Institute for Re- duction to Cython,” S. Labbé; “Cython,” F. Hivert; and search in Mathematical Sciences, and CICMA “Introduction to the Sage category theory framework,” N. M. Thiéry. Organizers: Eyal Z. Goren (McGill), Stephen S. Kudla (Toronto) The tutorials offered practical experience for the par- Speakers: ticipants: relevant notions were introduced and then Zavosh Amir-Khosravi (Toronto), Dylan Attwell- exercises were assigned to the participants. In addi- Duval (McGill), Henri Darmon (McGill), Andrew Fiori tion to the presentations and tutorials on Sage, there (McGill), Eyal Goren, Stephen Kudla, Kartik Prasanna were several mathematical presentations. These began (University of Michigan at Ann Arbor), Siddarth by acquainting the audience with the relevant mathe- Sankaran (Universität Bonn), Brian Smithling (Johns matics and then described some of the computational Hopkins University), Patrick Walls (Toronto), Ying aspects of the theory, together with relevant software Zong (Toronto) packages. Note that some of this software is indepen- Number of participants: 25 dent of Sage, and that these talks also served as a means This workshop was dedicated to the study of Kuga fi- to establish communication between the developers of bre varieties and their applications, in particular to the the different software packages. Hodge conjecture, the construction of points on elliptic At the end of the week we sent out a questionnaire curves and the Griffiths groups, and higher weight ver- asking for comments on the week. We asked for com- sions of Gross–Zagier theory. These recent, and very ments on the schedule, and whether the tutorials and recent, developments are due to Abdulali, Bertolini– presentations were adapted to the participants’ needs Darmon–Prassana, and Mellit. The program included, as beginners, users, or developers of Sage. The re- besides background material aimed mostly at graduate sponses were very positive. There was some criticism students and junior researchers, several expositions of the pace of the tutorials as a few participants felt devoted to these emerging directions. Kartik Prasanna the tutorials were a “bit rushed.” Nonetheless they ex- presented new work with Darmon, some of it com- pressed gratitude for the scheduled free time, which pleted the night before (!), and so we are happy to have they used to review the tutorials and work on the ex- instigated new research contributions. ercises. Some participants went from user to developer As before, the workshop was a resounding success, ev- over the course of the week, making their very first ident at the level of talks, the participants’ engagement contributions to Sage. Several participants emphasized and commitment, and the pleasant and cooperative at- that they liked the daily status reports, that it was a mosphere surrounding the whole 2-day activity. In ad- good motivator, a good way to see what the other par- dition, during the workshop, through the questions of ticipants where working on during the week, and a the audience and discussions, interesting new research good way to observe the progress made over the week. directions have emerged. Hopefully these will be taken We feel that the workshop was very successful. New up by some of the participants. users left emboldened with new skills that they can The Montréal–Toronto workshops, the fourth of which build upon in the future. The workshop resulted in has just been concluded, are gaining reputation as a several contributions to Sage, from the fixing of bugs fine collaborative initiative between the number the- to the development of new functionalities, and it es- ory groups in Montréal and in Toronto, and one of the tablished communication between different software successful collaborative programs between the CRM in projects. Many research publications will be appearing Montréal and the Fields Institute in Toronto. as new tools and algorithms are developed. We look forward to these developments.

34 General Program

International Workshop keynote lectures were of the highest quality and we Perspectives on High-Dimensional Data now summarize each of them. Analysis II The topic of the first keynote lecture (by Samuel Kou) May 30 – June 1, 2012, CRM was protein folding. Essentially all the biological func- tions in our bodies are carried out by proteins. The spe- Organizers: cific function of a protein is in turn determined byits S. Ejaz Ahmed (Brock & Windsor, Chair), Abbas 3D structure. Since it is quite time-consuming and ex- Khalili (McGill), David Stephens (McGill), Éric Marc- pensive to conduct laboratory experiments to obtain a hand (Sherbrooke), Peter X. K. Song (Michigan), Ji Zhu protein’s 3D structure, it is very desirable to be able to (Michigan) compute the 3D structure of a protein out of its amino Speakers: acid sequence. This problem, known as protein fold- Jeongyoun Ahn (Georgia), Shojaeddin Chenouri (Wa- ing, is a long-standing one in biology, dating back to terloo), Michael Daniels (Florida), Guoqing Diao Anfisen’s ground-breaking (Nobel prize) work in the (George Mason), Lee Dicker (Rutgers), Kjell Doksum 1950s. The difficulty of protein folding is twofold: first, (Wisconsin–Madison), Yingying Fan (Southern Cali- we do not have a good energy function that can accu- fornia), Yang Feng (Columbia), Xiaoli Gao (Oakland), rately capture the interactions between the different Yulia Gel (Waterloo), Zhigeng Geng (Wisconsin– parts of the protein, due to our lack of detailed scien- Madison), Ali Ghodsi (Waterloo), Md Shakhawat Hos- tific understanding; second, even with a perfect energy sain (Winnipeg), Xiaoming Huo (Georgia Tech), Timo- function, it is still extremely difficult to obtain the 3D thy D. Johnson (Michigan), Frank Konietschke (Göttin- structure because the energy function has a huge num- gen), Shingchang Samuel Kou (Harvard), Hannes Leeb ber of local minima, which can easily prevent a search (Wien), Hua Liang (Rochester), Yufeng Liu (UNC— algorithm from finding a global optimum. Efficient al- Chapel Hill), Jinchi Lv (Southern California), Shuangge gorithms that can explore the vast space of all possible Ma (Yale), Bin Nan (Michigan), Debashis Paul (UC conformations (3D structures) are critical. Davis), Benedikt M. Pötscher (Wien), Ruslan Salakhut- dinov (Toronto), Ali Shojaie (Washington), Nozer D. In Samuel Kou’s lecture, a new Markov Chain Monte Singpurwalla (George Washington), Peter X. Song Carlo algorithm for exploring the conformation space (Michigan), Lu Tian (Stanford), Joseph S. Verducci of a protein, Fragment Regrowth via Energy-guided (Ohio State), Anand Vidyashankar (George Mason), Sequential Sampling (FRESS), is introduced. The key Peng Wang (Bowling Green State), Yichao Wu (North ingredient of FRESS is to delete a randomly selected Carolina State) fragment of varying length from the current confor- Number of participants: 55 mation and then regrow the deleted fragment (in each This workshop went very smoothly and was a huge iteration of the algorithm). This regrowth of the frag- success. Besides domestic participants, it attracted ment is carried out by energy-guided importance sam- many international participants from the USA and pling so that conformations with lower energies have some European countries. At the end of the workshop, higher probabilities of being sampled. In particular, the many participants indicated their interest in taking fragment regrowth is done one backbone atom at a part in a future workshop of a similar nature, in or- time through sequential Monte Carlo. This sequential der to discuss research progress in these areas. This scheme allows FRESS to avoid being trapped at local workshop fulfilled the agenda of promoting research minima in the conformation space. To utilize the infor- activities in the area of high-dimensional data analysis mation from known protein structures, the sequential and created a rather focused venue for participants to placement of the backbone atoms is guided by the ex- discuss and exchange research ideas via presentations isting 3D structures in the PDB (protein databank) so and informal discussions (following the presentations). that the bond angles and torsion angles frequently ap- The list of speakers at the workshop was really impres- pearing in the existing protein structures have a higher sive, and most of the talks were based on unpublished probability of being sampled. It is demonstrated in the and on-going work. There was a significant proportion talk that for about 700 test proteins, the FRESS algo- of Canadian speakers, who had been given this oppor- rithm is able to fold them into a conformation within 5 tunity to develop future collaborations among them RMSD (root mean squared distance) of the true struc- and with researchers from other countries. The two ture (within 5 RMSD is considered a gold standard).

35 Centre de recherches mathématiqes

The topic of the second keynote lecture (by Kjell Dok- evant information, in the sense that they can be used to sum) was high-dimensional data analysis and biomed- remove any confounding effects. Kjell Doksum gave a ical genomics. A highly relevant concern in statistics is result showing when this approach provides non spu- how to deal with the high-dimensional data that have rious tests of association between a variable and a re- become so prevalent in recent experiments and stud- sponse. He also reviewed methods based on PCA and ies. These types of data occur in genomics, astronomy, compared them with a new proposed nonparametric and finance as well as other fields. Thus it isnotun- approach. This talk opens many new research prob- usual that the numbers of variables to be considered lems in a host of applications. are in the hundreds of thousands while the sample size In addition to the keynote lectures, 31 invited talks is at most three thousand. The classical statistical tech- were presented by influential researchers on various niques are designed for the case where the number of aspects of High-dimensional Data Analysis and were variables is less than the sample size, so new meth- well received by the audience. Most presentations were ods are now required. In Kjell Doksum’s talk, he dis- followed with insightful comments and interesting dis- cussed a set of approaches based on Principal Com- cussions. A poster session was also organized during a ponent Analysis (PCA). In this approach, when inves- reception in order to showcase the recent work of grad- tigating the association between a variable and a re- uate students. This was also well attended. Participants k sponse, the other variables are replaced by their first had active exchanges of ideas and in-depth discussions k principal components, where is at most ten. In this on current research activities and future research di- way the dimension is reduced to ten or less. The hope rections. is that the first k principal components capture the rel-

Colloquium Series

The CRM, together with the Institut des sciences mathématiques (the Québec universities graduate mathematics consortium), runs two Montréal colloquium series, one in mathematics and the other in statistics (the latter jointly with GERAD, an operations research centre located in the André-Aisenstadt building). During the academic year, these series offer survey talks on topics of current interest by distinguished mathematicians and statisticians.

CRM–ISM Mathematics Colloquium

In 2011–2012 the colloquium coordinators were Iosif Polterovich (Montréal) and Jean-Christophe Nave (McGill).

September 9, 2011 September 30, 2011 Fedor Nazarov (Kent State) Jean-Pierre Serre (Collège de France) Non-trivial convex bodies with maximal sections of con- Variation with p of the number of solutions mod p of a stant volume system of polynomial equations September 15, 2011 October 21, 2011 Joseph Silverman (Brown) Sergey Norin (McGill) Number theory and dynamical systems: a survey Divisors on graphs September 16, 2011 November 4, 2011 Paul Biran (ETH Zürich) Leonid Chekhov (Steklov Inst.) Symplectic topology in the large — from Morse to Floer Teichmüller spaces of Riemann surfaces with holes and and beyond algebras of geodesic functions September 23, 2011 November 11, 2011 Jayce Getz (McGill) Bun Wong (UC Riverside) On Langlands functoriality Domains with non-compact automorphism groups November 18, 2011 Michael Levitin (Reading) Tricks in spectral theory

36 General Program

November 25, 2011 February 10, 2012 Alex Furman (UI Chicago) Ludmil Katzarkov (Miami) Groups with good pedigrees, or superrigidity revisited On the Shafarevich conjecture December 2, 2011 February 17, 2012 Gerda de Vries (Alberta) Olga Kharlampovich (McGill) Formation of animal groups: the importance of commu- Definable subsets in free and torsion free hyperbolic nication groups December 9, 2011 March 9, 2012 Gilbert Strang (MIT) Philip Candelas (Oxford) Balanced splitting methods / infinite matrices Periods of Calabi–Yau manifolds in physics and number December 16, 2011 theory Alan Huckleberry (Bochum) March 23, 2012 Disordered bosons: a complex geometric viewpoint Steven Johnson (MIT) January 13, 2012 On the limits of invisibility Louis-Pierre Arguin (Montréal) March 30, 2012 Probability and statistical physics of disordered systems Dmitri Burago (Penn State) January 20, 2012 Boundary rigidity and minimal surfaces: a survey Jason Starr (Stony Brook) April 19, 2012 Rational curves and rational points Vitali Milman (Tel Aviv) January 27, 2012 The reasons behind some classical constructions in anal- Alex Eskin (Chicago) ysis Rational billiards and the SL(2, R) action on moduli April 20, 2012 space Mikaël Pichot (McGill) February 3, 2012 Discrete groups of intermediate rank Vadim Kaimanovich (Ottawa) Equivalence relations, random graphs and stochastic ho- mogenization

CRM–ISM–GERAD Statistics Colloquium

In 2010–2011 the organizing team of the Statistics Colloquium included Jean-François Angers (Montréal), Mylène Bédard (Montréal), Simon Guillotte (UQAM), Abbas Khalili (McGill), Johanna Nešlehova (McGill), Lea Popovic (Concordia), and Arusharka Sen (Concordia). Note that in most cases, two seminars were scheduled on the same date.

September 9, 2011 Richard A. Davis (Colorado State) Aurelie Labbe (McGill) Estimating extremal dependence in time series via the An integrated hierarchical Bayesian model for multi- extremogram variate expression-quantitative trait locus (eQTL) ge- November 11, 2011 netic mapping Hélène Guérin (Rennes 1) Edward Susko (Dalhousie) An ergodic variant of the telegraph process for a toy Properties of Bayesian posteriors and bootstrap support model of bacterial chemotaxis in phylogenetic inference Ana-Maria Staicu (Toronto) October 14, 2011 Skewed functional processes and their applications Debbie Dupuis (HEC Montréal) December 9, 2011 Modeling non-stationary extremes: the case of heat Giles Hooker (Cornell) waves Detecting evolution in experimental ecology: diagnostics for missing state variables

37 Centre de recherches mathématiqes

January 13, 2012 Hugh Chipman (Acadia) Yulei He (Harvard) Sequential optimization of a computer model and other Bayesian approaches to evidence synthesis in clinical “active learning” problems practice guideline development April 13, 2012 February 10, 2012 Longhai Li (Saskatchewan) Jochen Blath (TU Berlin) High-dimensional feature selection using hierarchical Longterm properties of the symbiotic branching model Bayesian logistic regression with heavy-tailed priors Winfried Stute (Gießen) Sunil Rao (Miami) Principal component analysis of the Poisson process Best predictive estimation for linear mixed models with March 9, 2012 applications to small area estimation Mori Jamshidian (CSU Fullerton) Using tests of homoscedasticity to test missing com- pletely at random

38 Multidisciplinary and Industrial Program Centre de recherches mathématiqes

he main vehicles for the CRM’s efforts in this area are the research networks to which it belongs, principally T Mprime, a national network focusing on the mathematics of information technology and complex systems, and the National Institute for Complex Data Structures (NICDS). The reports are presented in the language inwhich they were submitted.

Activities of the Multidisciplinary and Industrial Program

Statistics 2011 Canada tics, Bayesian statistics, bioinformatics, biostatistics, IMST 2011 – FIM XX combinatorics, computer and information sciences, de- July 1–4, 2011, Concordia sign of experiments, ergodic theory, functional analy- Sponsored by Concordia University, the Forum for In- sis, graph theory, multivariate analysis, number the- terdisciplinary Mathematics, the CRM, the SSC, and ory, partial differential equations, and topology. Georgia State The conference featured contributed and invited pa- Local Organizing Committee (Concordia): per sessions and poster presentations, along with a Yogendra P. Chaubey (Chair), Simon Bacon, Satyaveer special inaugurating lecture to honour Professor T. D. Chauhan, Patrice Gailliardetz, Jose Garrido, Nikolay Dwivedi (who has been a driving force behind the pre- Gospodinov, Cody Hyndman, Jochen Jaeger, Tak Mak, vious conferences in this series), sponsored by an en- Danielle Morin, Fassil Nebebe (Co-chair), Lea Popovic, dowment from the Dwivedi family and the Faculty of Arusharka Sen, Debaraj Sen, Mahesh Sharma, Murari Arts and Science of Concordia University. Singh, Wei Sun, Robert Weladji The conference was a large-scale one, with 9 plenary International Advisory Committee: talks, 50 invited sessions and 14 contributed sessions. Bovas Abraham (Waterloo), David Brillinger (UC The talks by Richard Cook, Rob Kass, and Christian Berkeley), M. C. Jones (Open), Rob Kass (Carnegie Mel- Genest were among the highlights of the plenary ses- lon), Govind S. Mudholkar (Rochester), J. N. K. Rao sions. The invited sessions spanned a wide spectrum (Carleton), Nancy Reid (Toronto), Louis-Paul Rivest of topics, such as data mining, forest fire modelling, (Laval), Pranab K. Sen (UNC—Chapel Hill), G. P. H. cryptography, functional data analysis, mathematical Styan (McGill), Rob Tibshirani (Stanford) finance, survival analysis, to name only a few. Our re- Plenary Speakers: port will focus on two invited sessions, one that was Richard Cook (Waterloo), Narsingh Deo (Central organized and chaired by Lajmi Lakhal Chaieb and an- Florida), Jean-Marie Dufour (McGill), Christian Gen- other that was organized and chaired by Arusharka est (McGill), M. C. Jones, Robert Kass, Govind S. Mud- Sen. holkar, J. Sunil Rao (Miami), Pranab K. Sen The one organized by Lajmi Lakhal Chaieb and entitled In July 2011 the Department of Mathematics and Statis- “Recent Advances in Survival Analysis (I34)” featured tics of Concordia University, the Department of Deci- three speakers: Prof. Adin-Cristian Andrei, Dr. Au- sion Sciences & MIS of the same university, and the guste Gaddah, and Prof. Eleanor Pullenayegum. A.-C. Forum for Interdisciplinary Mathematics (FIM) hosted Andrei’s talk was entitled “A semiparametric model for a joint conference, “Statistics 2011 Canada: 5th Cana- recurrent events.” In it he presented a regression model dian Conference in Applied Statistics,” together with for gap-time. Typically gap-times are subject to depen- the 20th conference of the Forum for Interdisciplinary dent censoring. The proposed inference methodology Mathematics. The title of the joint conference was “In- was based on Jackknife and illustrated with a real data terdisciplinary Mathematical & Statistical Techniques.” set on cystic fibrosis where he investigated the effect of In keeping with the long tradition of decennial confer- covariates on gap-times between repeated pulmonary ences since 1971, this conference was dedicated to all exacerbations. A. Gaddah’s talk was entitled “Random areas of mathematical and statistical sciences. In addi- censorship single-index quantile regression model.” In tion to traditional theoretical/applied areas, interdisci- it he considered the estimation of the conditional quan- plinary research was encouraged and promoted. His- tile from randomly right-censored survival data. The torically these meetings have focused on the follow- proposed methodology is based on an iterative algo- ing areas of scholarship: applied and theoretical statis- rithm to estimate jointly the link function and the re-

40 Multidisciplinary and Industrial Program gression parameter. A simulation study and a practical Emmanuel Lorin de la Grandmaison (Carleton), Apala data set analysis concluded this interesting talk. E. Pul- Majumdar (Oxford), Odile Marcotte, Beatriz Murrieta lenayegum’s talk was entitled “Longitudinal data sub- Cortes (Tecnologico de Monterrey), Aaron Newman ject to censoring and intermittent measurement.” In it (Dalhousie), Dominique Orban, Jean-François Plante she extended Diggle et al.’s analysis of increments to (HEC Montréal), Mason Porter (Oxford), Christopher the case of irregular follow-up. The proposed method- Prior (Oxford), Mary Pugh (Toronto), Jean-Pierre Ray- ology is based on combining binning with weighting, nauld (Montréal), Tim Reis (Oxford), Suzanne Shontz imputation, and multiple imputation. (Penn State), Rex Westbrook (Calgary) In the session “Survival Analysis (I50),” organized Industrial representatives: by Arusharka Sen, there were also three speakers: Gilles Boesch and Michel Carreau (Énergies renou- Prof. Lajmi Lakhal Chaieb, Dr. Yassir Rabhi, and velables, Hatch), Alain Cournoyer (Institut national Prof. Winfried Stute, but Dr. Rabhi was absent. L. d’optique), Ozgur Gurtuna (Turquoise Technology So- Lakhal Chaieb’s talk was entitled “On the associa- lutions Inc.), Arnaud Lina (Matrox Electronic Systems), tion between failure times in the presence of depen- Mario L. Morfin Ramírez (York & Acculogic), Vincent dent censoring: A sensitivity study” and he presented Zalzal (Matrox Electronic Systems) a framework for modelling bivariate survival-time data Number of participants: 24 researchers, 7 indus- under dependent censoring using copulas. A sensitiv- trial representatives, and 26 students and postdoctoral ity study was carried out on the copula parameter and fellows illustrated with simulated as well as real twin-registry The Fourth Montreal IPSW was attended by 57par- data-sets. W. Stute’s talk was entitled “Nonparametric ticipants, who worked on six problems proposed regression for consecutive survival data under trun- by five companies: Acculogic, Hatch, Institut na- cation and censorship effects” and he constructed a tional d’optique (INO), Matrox Electronic Systems, and nonparametric regression estimator for times between Turquoise Technology Solutions Inc. Note that Accu- consecutive events observed on a patient. The problem logic is based in Markham (Ontario) and INO in Que- is complicated because of the truncation of the first and bec City. Two of the problems, i.e., those supplied by the censoring of the second variable; it requires a mod- INO, required the use of tools from what one might call ification of both the Lynden-Bell and Kaplan-Meier es- “applied continuous mathematics” (in particular differ- timators. Both sessions were reasonably well attended ential equations). These problems dealt with the opti- and the speakers drew a lot of questions from the au- mization of the temporal shape of laser pulses and the dience. modelling of CO2 polishing of glass, respectively. The teams working on the INO problems benefited greatly Fourth Montréal Industrial Problem Solving from the expertise of researchers from Oxford, Paris, Workshop and Ontario (among others). August 15–19, 2011, CRM Two companies (Acculogic and Matrox Electronic Sys- Sponsored by CRM and Mprime tems) provided problems related to computer vision. Acculogic manufactures systems for testing Electronic Organizers: Circuit Boards (ECBs) and those systems must be able Fabian Bastin (Montréal), Eliot Fried (McGill), Michel to “see” the points where the tests will be carried out. Gendreau (Polytechnique Montréal), Huaxiong Huang The goal of the team was to propose methods forim- (York), Odile Marcotte (CRM; UQAM), Dominique proving the testing rate of the systems, i.e., minimiz- Orban (Polytechnique Montréal), Sylvain Perron ing the number of tests that cannot be carried out be- (HEC Montréal), Jean-Marc Rousseau (CIRANO; rcm₂; cause the points have not been located properly. Ma- chair), Louis-Martin Rousseau (Polytechnique Mont- trox Electronic Systems proposed a very nice mathe- réal), Luc Vinet (Montréal) matical problem arising in computer vision: given a Participating researchers: curve in the plane and a number of points (denoted Fabian Bastin, C. Sean Bohun (UOIT), Stephen Y. by N), how can one select N points on the curve so Chen (York), Ellis Cumberbatch (Claremont Gradu- that the points are spaced in a regular fashion? This ate), Michel Denault (HEC Montréal), Alistair Fitt (Ox- problem appealed to many participants and the team ford Brookes), Michel Gendreau, Huaxiong Huang, members studied it from different angles. Claude Le Bris (ÉNPC), Christian Léger (Montréal),

41 Centre de recherches mathématiqes

Finally the workshop included two problems related Number of participants: 44 to renewable energies. The problem supplied by Hatch In recent years there has been a shift of emphasis dealt with the assessment of the uncertainty in the in research on balanced dynamics. Whereas early re- measurement of a wind resource. This problem is of the search was strongly motivated by NWP and focused utmost importance in the field of wind power, since on the construction and analysis of balanced models, the companies that design wind farms must be able following the important work of Lorenz, Warn, Ford, to predict the energy output of such farms. On the Vanneste, and others, the concept of a “fuzzy slow other hand, Turquoise Technology Solutions Inc. pro- manifold” has become widely accepted; thus research posed to study the behaviour of a portfolio of renew- has been more concerned with imbalance (generation able energy investments (especially solar energy in- and interactions with the balanced flow) rather than vestments). This topic is more relevant than ever be- balance per se. This is especially the case in oceanog- cause if one can show that the output of multiple re- raphy, where there is still uncertainty concerning the newable energy investments is reliable, then the elec- closing of the energy budget. tricity systems operators may agree to integrate re- This meeting primarily dealt with the modelling newable energy into existing grids. of submesoscale oceanographic flows, where Rossby As was the case for the first three Montreal IP- and Froude numbers are O(1) and lengthscales of SWs, the atmosphere at the workshop was friendly O(1 km). Here, by contrast with the (mesoscale) eddy- and relaxed. The rooms where the teams worked permitting models that are customarily used in GCMs, were all located on the first floor of the André- small-scale eddies and gravity-wave generation are Aisenstadt building, and the wonderful logistical sup- ubiquitous; simulations are typically done in domains port of the CRM was appreciated by all the par- with dimensions of O(100 km) and grid spacings of ticipants. The reader may find more details onthe O(25 m). Talks discussed modelling strategies, insta- workshop web site (http://www.crm.umontreal. bility mechanisms (inertial instability in particular), ca/probindustriels2011/index_e.shtml). geostrophic turbulence phenomenology, and applica- tions. The breakdown of balance received most atten- Workshop on tion, but there were a few talks on balanced small- Balance, Boundaries and Mixing in the scale phenomena in the vicinity of boundaries, i.e., Climate Problem surface quasi-geostrophic-like dynamics. Mixing was September 28–30, 2011, CRM discussed specifically in only a few presentations, but Sponsored by CRM and Mprime it was implicit in most of the oceanographic talks: by contrast with atmospheric scientists, who tend Organizers: to view gravity waves as a means for transporting Peter Bartello (McGill), K. Shafer Smith (NYU), David (pseudo)momentum, oceanographers are interested in Straub (McGill) gravity waves on account of their (diapycnal) mixing Speakers: properties. Rafail V. Abramov (UI Chicago), Farid Ait Chaalal (McGill), Gualtiero Badin (Boston), Erich Becker (Ros- Although this was not the intention of the organizers, tock), Alexander Bihlo (Montréal), Eric A. D’Asaro there was very little representation from atmospheric (Washington), Baylor Fox-Kemper (CU-Boulder), scientists (just 2 presentations). This probably reflects a Nicolas Grisouard (NYU), Ian Groom (NYU), Igor Ka- cultural difference: NWP, which is strongly synoptic- menkovich (Miami), Patrice Klein (Ifremer), Amala scale-centric, has been hugely influential in the devel- Mahadevan (WHOI), James C. McWilliams (UC Los opment of dynamical meteorology. The oceanographi- Angeles), Sonajit Mukherjee (UMass Dartmouth), Bal- cal talks were eye-opening for many participants, inas- asubramanya T. Nadiga (Los Alamos Natl. Lab.), Keith much as they started from different premises, ones Ngan (Met Office), Sanjiv Ramachandran (UMass that are closer to the modern view of geophysical fluid Dartmouth), Gjergj Smailekaj (IAMS), Amit Tandon dynamics. Jim McWilliams’ joke about meteorologists (UMass Dartmouth), Leif Thomas (Stanford), Vladimir and their concern with balanced dynamics went down Tseitline (ÉNS), Geoffrey K. Vallis (Princeton), Jacques very well with the audience; nonetheless, it would have Vanneste (Edinburgh), Jena Vinod (CIET), Jinho Wang been nice if there had been some representation of (WHOI), Stephanie Waterman (Imperial Coll.) work from the perspective of large-scale balanced dy-

42 Multidisciplinary and Industrial Program namics. Below we summarize the most interesting pre- (with approximately 250 m grid spacing in the mid- sentations. dle atmosphere) and L30 (with dz ∼ 1km). A -5/3 V. Zeitlin talked about inertial instability in 2-layer ro- mesoscale spectrum could be obtained only in a few tating shallow water. In the first part of the talk he re- special cases: unphysical hyperdiffusion, anisotropic viewed the classical linear stabilitiy criterion and re- subgrid (Smagorinsky) model, and the finer vertical minded the audience that inertial instability is often grid. A detailed analysis of the spectral fluxes in the up- called symmetric instability in the case of the along- per troposphere indicated that fluxes due to horizon- front k = 0 modes. The numerical simulations, for a tal advection and adiabatic convergence are compara- barotropic Bickley jet with different densities in the ble, which is consistent with Lindborg’s work on strat- two layers, were designed to elucidate the connection ified turbulence. Although the tuning of the Smagorin- between inertial instability and baroclinic instability. sky scheme seemed a little contrived, the sensitivity of For small Ro, the linear analysis is recovered and the the mesoscale dynamics to physical parameterization barotropic mode is the most unstable mode; for large would seem to hold more generally. Ro, the most unstable mode becomes baroclinic. More- J. Vanneste spoke mostly about gravity-wave genera- over, the baroclinic instability for k = 0 can be identi- tion in shear flows. The first half of his talk wasare- fied with the symmetric inertial instability. view of work on the breakdown of balance and expo- J. McWilliams discussed a number of theoretical ideas nential asymptotics. The second half dealt mostly with in the context of the California undercurrent, a sepa- a specific problem, a 2-d SQG-like model that has been rating boundary current. The generation of unbalanced modified to account for the exponentially-small radi- motion represents one way in which the energy bud- ation of gravity waves. An important point was that get of the ocean may be closed and the tendency for the solution for the stream function, which is obtained (barotropic) energy to be cascaded to large scales via by matching to the far field, must contain an expo- geostrophic turbulence counteracted. Numerical sim- nentially increasing component as well as an exponen- ulations showed generation of mesoscale and subme- tially decaying one. In previous work on SQG this has soscale eddies where the undercurrent separated from not always been done. the shore due to the bottom topography. B. Nadiga gave a very interesting talk on energy fluxes P. Klein reviewed recent work on the impact of sub- in geostrophic turbulence. The starting point was re- mesoscales on larger oceanic scales. Observations sug- cent work by Scott and Wang claiming, in contrast to gest that eddies are ubiquitous on submescoscales, but the well-known picture due to Salmon, that there is an until recently they were assumed to have no effect on inverse cascade of baroclinic energy. This was investi- larger scales. Following work on surface quasigeostro- gated using the Princeton Ocean Model and LES-type phy, the talk focused on the impact of surface dy- diagnostics, yielding energy fluxes across scales. The namics on submesoscale eddies at depth. Generally main message was that the situation is more compli- SQG works well, suggesting that the ageostrophic mo- cated than Scott and Wang implied. While Salmon’s tion is weak, departures being related to the presence picture generally holds, an inverse baroclinic cascade of ageostrophic instability and spontaneous gravity- can be induced by basin geometry (the so-called beta- wave emission. The quantification of the imbalance flux) and topographic interactions. caught the participants’ attention: it is estimated that I. Grooms spoke about weakly stratified rotating tur- the energy in internal gravity waves is 5 orders of mag- bulence. Although the title is suggestive of rotation- nitude smaller than that in balanced modes. At the sur- dominated, large-scale PG or SG dynamics, he only face small-scale ageostrophic motion can lead to depar- considered the wave modes defined by normal modes. tures from SQG, i.e., to vortex asymmetry and modifi- The claim, which is completely standard, is that these cation of the eddy forcing. fast modes, which are obtained from a linear stabil- E. Becker gave a very interesting talk on numerical ity analysis (strictly valid only for Rossby and Froude simulations of the atmospheric energy spectrum in numbers going to 0), include a balanced component. a mechanistic model in which heating rates are pre- He demonstrated this by looking at various linear mea- scribed. The numerical simulations were carried out at sures of imbalance, e.g., the mismatch between the T330 in the horizontal with two vertical grids, L100 Coriolis, buoyancy, and pressure-gradient terms, for

43 Centre de recherches mathématiqes

Boussinesq as well as limit equations for rotating con- G. Vallis gave two talks for the price of one. In the vection. first half, he examined the contribution of realistic bot- L. Thomas discussed the relevance of symmetric insta- tom topography to the kinetic energy budget, more bility as a possible mechanism for the transfer of en- specifically, to avoiding inertial runaway; the tenta- ergy from balanced to unbalanced modes. In particu- tive conclusion is that the resulting unbalanced flow lar, he analyzed a simple model including stratification may be small. In the second half, he examined an ide- and strain. Most of us were surprised at the attention alized model of the meridional overturning circula- devoted to symmetric instability and imbalance; there tion and compared it to GCM simulations. Finally A. wasn’t much interest in the subject several years ago. Bihlo presented a poster on invariant parameterization Recent observations, however, indicate that this mech- schemes. The idea was to use Lie-group methods, in anism may be relevant to the ocean. E. d’Asaro showed particular the differential invariants, to derive param- Lagrangian-float observations of shallow fronts. The eterization schemes that respect the continuous sym- main result was that there is evidence of symmetric in- metries; it was illustrated with an application to the stability where there is negative PV and, furthermore, barotropic vorticity equation. that models do not exhibit glaring inconsistencies with this.

44 CRM Prizes Centre de recherches mathématiqes

he CRM created and administers, either alone or jointly, four of the eight major national prizes in the math- T ematical sciences, namely: the CRM–Fields–PIMS Prize, the Prize for Theoretical Physics awarded in collab- oration with the Canadian Association of Physicists (CAP), the Prize for young researchers in Statistics awarded jointly with the Statistical Society of Canada (SSC), and the CRM André-Aisenstadt Prize awarded to rising young Canadian stars, selected by the International Scientific Advisory Committee of the CRM. The CRM has invested enormously in time, effort, and its own resources in order to propel leading Canadian scientists into the spotlight, giving them international recognition when they most need it.

CRM–Fields–PIMS Prize 2012 Awarded to Stevo Todorcevic

Professor Todorcevic obtained his Ph.D. in 1979 in Bel- metrization problem. Among the most striking recent grade and currently holds a Canada Research Chair at accomplishments of Todorcevic (and co-authors) are the University of Toronto. His contributions to set the- major contributions to the von Neumann and Ma- ory made him a world leader in this topic with a par- haram problems on Boolean algebras, the theory of ticular impact on combinatorial set theory and its con- non-separable Banach spaces, including the solution nections with topology and analysis. of an old problem of Davis and Johnson, the solution of a long-standing problem of Laver, and the develop- ment of a duality theory relating finite Ramsey theory and topological dynamics. For a detailed description of Dr. Todorcevic’s scientific contributions, we refer the reader to the article by Claude Laflamme (Calgary) in the Spring 2012 issue of Le Bulletin du CRM.

The CRM–Fields–PIMS Prize

This prize was established in 1994 as the CRM–Fields Prize to recognize exceptional research in the math- ematical sciences. In 2005 PIMS became an equal partner in the awarding of the prize and its name Stevo Todorcevic was changed to the CRM–Fields–PIMS Prize. A com- His work is recognized for its striking originality and mittee appointed by the three institutes chooses the technical brilliance. He was an invited speaker at the recipient. The previous recipients of the prize are 1998 ICM in Berlin for his work on ρ- functions. He H. S. M. (Donald) Coxeter (1995), George A. El- made major contributions to the study of S- and L- liott (1996), James Arthur (1997), Robert V. Moody spaces in topology, proved a remarkable classification (1998), Stephen A. Cook (1999), Israel Michael Si- theorem for transitive relations on the first uncount- gal (2000), William T. Tutte (2001), John B. Friedlan- able ordinal, and made a deep study of compact sub- der (2002), John McKay (2003), Edwin Perkins (2003), sets of the Baire class 1 functions, thus continuing Donald A. Dawson (2004), David Boyd (2005), Nicole work of Bourgain, Fremlin, Talagrand, and others in Tomczak-Jaegermann (2006), Joel S. Feldman (2007), Banach space theory. Together with P. Larson he com- Allan Borodin (2008), Martin Barlow (2009), Gordon pleted the solution of Katetov’s old compact spaces Slade (2010), Marc Lewis (2011).

46 CRM Prizes

André-Aisenstadt Prize 2012 Awarded to Marco Gualtieri and Young-Heon Kim

In 2012 the André-Aisenstadt Prize was jointly Annals of Mathematics. More recently Marco Gualtieri awarded to Marco Gualtieri and Young-Heon Kim. has studied D-branes in generalized complex mani- folds and their relation to noncommutative geometry, as well as further generalizations of classical geome- tries. At the age of 32, he was awarded the prestigious André Lichnerowicz Prize (shared with Xiang Tang) at the IMPA in Rio de Janeiro. He also won an Early Re- search Award of the Ontario Government for the pe- riod 2010–2015. Dr. Young-Heon Kim obtained his bachelor’s degree in mathematics at the Pohang University of Science and Technology and a Master’s degree at the Korea Ad- vanced Institute of Science and Technology in South Korea. In 2005 he was awarded a Ph.D. from North- Marco Gualtieri western University (under the supervision of Ezra Get- Dr. Gualtieri obtained a bachelor’s degree in science at zler). He joined the mathematics department of the McGill University in 1999 and his Ph.D. from Oxford University of British Columbia in 2008. His specialty is University in 2004 under the supervision of Nigel J. in analysis and his most important contributions con- Hitchin. He was awarded the Lichnerowicz Prize in cern the fast developing topic of optimal transporta- Poisson geometry in 2010 and joined the University tion. Dr. Kim received a Sloan Fellowship in 2012. For of Toronto in 2008. Prior to that appointment Profes- a detailed description of Dr. Kim’s scientific contribu- sor Gualtieri had held postdoctoral positions at MSRI tions, we refer the reader to the article by Robert Mc- (Berkeley), the Fields Institute (Toronto), and MIT. His Cann (Toronto) in the Spring 2012 issue of Le Bulletin area of research is differential geometry and he has du CRM. made essential contributions to the development of generalized complex geometry, an active area of re- search at the interface of complex geometry and sym- plectic geometry. More specifically, Marco Gualtieri’s research focuses on the geometry of generalized complex structures, a fairly recent and active area of mathematics pioneered by Nigel Hitchin in the 2000s, which provides a novel and unified approach to symplectic and complex ge- ometry. Applications to mathematical physics (string theory and mirror symmetry) and noncommutative ge- ometry are at the forefront of current developments in Young-Heon Kim this vibrant domain. In this vein, Marco Gualtieri’s Ph.D. thesis provides The André-Aisenstadt Prize the first systematic study of generalized complex ge- ometry, and introduces a number of new notions of Created in 1991, the André-Aisenstadt Mathematics fundamental importance, such as the Kuranishi the- Prize is intended to recognize and reward research ory for generalized complex structures and the gen- achievements in pure and applied mathematics by tal- eralized Kähler geometry. His foundational work has ented young Canadian mathematicians. This prize con- been the source of inspiration for many related stud- sists of a $3,000 award and a medal. The recipient is ies. Currently, Google Scholar lists 535 citations to this chosen by the International Scientific Advisory Com- work and one part of it has recently appeared in the mittee of the CRM. At the time of consideration, can-

47 Centre de recherches mathématiqes didates must be Canadian citizens or permanent resi- (2000), Eckhard Meinrenken (2001), Jinyi Chen (2002), dents of Canada, and no more than seven years from Alexander Brudnyi (2003), Vinayak Vatsal (2004), Ravi their Ph.D. Vakil (2005), Iosif Polterovich (2006), Tai-Peng Tsai The previous recipients of the André-Aisenstadt Prize (2006), Alexander E. Holroyd (2007), Gregory G. Smith are Niky Kamran (1992), Ian Putnam (1993), Michael (2007), József Solymosi (2008), Jonathan Taylor (2008), Ward (1995), Nigel Higson (1995), Adrian S. Lewis Valentin Blomer (2009), Omer Angel (2010), Joel Kam- (1996), Lisa Jeffrey (1997), Henri Darmon (1997), nitzer (2011). Boris Khesin (1998), John Toth (1999), Changfeng Gui

The CAP–CRM Prize 2012 Awarded to Luc Vinet

The 2012 CAP–CRM Prize in Theoretical and Mathe- application of this work to a proof of the long-standing matical Physics was awarded to Luc Vinet, Université Macdonald conjecture on properties of multivariate or- de Montréal, for his outstanding and continued contri- thogonal polynomials. His contributions to the sym- butions to mathematical physics, mainly based on the metry theory of difference and q-difference equations study of symmetries, algebraic structures, and special are truly pioneering. functions. Remarkably, Vinet’s scientific career was not inter- rupted by his heavy administrative duties as director of the Centre de recherches mathématiques, then provost of McGill University, and finally rector of the Univer- sité de Montréal. He continued to publish highly in- novative work during his administrative tenure and is now going through a new burst of creativity. Quite recently, in 2011, he has discovered new families of orthogonal polynomials, associated with reflections. These have already found many applications. Inthe context of quantum information theory, he has shown how spin chains can be used to design perfect quan- tum wires. Dr. Vinet gave a prize lecture entitled Fils Luc Vinet quantiques, polynômes orthogonaux et approximation Luc Vinet is one of Canada’s leading mathematical and diophantienne at the CRM on October 5, 2012. theoretical physicists, who has made outstanding con- tributions in numerous areas. The unifying feature of The CAP–CRM Prize his research is the innovative use of group-theoretical and algebraic methods, the emphasis on exact solu- The Centre de recherches mathématiques (CRM) and tions of physical problems, and the originality of his the Canadian Association of Physicists (CAP) created approach. He has made important contributions that in 1995, on the occasion of the 50th anniversary of the have had great impact on both physics and mathemat- CAP, a joint prize for recognizing exceptional achieve- ics. His early remarkable work was on gauge field theo- ments in theoretical and mathematical physics. The ries, in particular on exact invariant solutions of Yang- prize consists of a $2,000 award and a medal. Mills equations in Minkowski space. Also early in his The previous recipients of the prize are Werner Is- career he identified the symmetries and supersymme- rael (1995), William G. Unruh (1996), Ian Affleck tries of magnetic monopole systems. He explored var- (1997), J. Richard Bond (1998), David J. Rowe (1999), ious algebraic structures that can be used to describe Gordon W. Semenoff (2000), André-Marie Tremblay symmetries in different physical problems. These go (2001), Pavel Winternitz (2002), Matthew Choptuik well beyond standard Lie groups and algebras. They (2003), Jiří Patera (2004), Robert Myers (2005), John include polynomial, quantum, and super- and para- Harnad (2006), Joel S. Feldman (2007), Richard Cleve super-algebras. He is very well known for his influen- (2008), Hong Guo (2009), Clifford Burgess (2010), tial work on quantum many-body problems and for his Robert Brandenberger (2011).

48 CRM Prizes

The CRM–SSC Prize 2012 Awarded to Changbao Wu

tics, and of course The Canadian Journal of Statistics. Advisor or co-advisor of three Ph.D. students and more than 10 M.Math. students at the University of Water- loo, Wu is also appreciated for his community con- tributions. He served on numerous committees at his institution and within the SSC; among others, he was President of the Survey Methods Section in 2005 –2006. Born in 1963, Wu was raised in a small village in the Chinese province of Anhui. After the Cultural Rev- olution, he was able to study mathematics at Anhui Laodong University. He graduated in 1982 and was hired as a faculty member at the Anhui Institute of Ed- Changbao Wu ucation, a training centre for high school teachers; the Professor Changbao Wu, from the Department of institution later became Hefei Normal University. At Statistics and Actuarial Science at the University of the beginning of his career, Wu was younger than most Waterloo, is the 2012 winner of the CRM–SSC Prize. of his students. He was recognized as an energetic and This prize highlights Professor Wu’s outstanding con- passionate teacher and completed an M.Sc. diploma in tributions to survey sampling and his exceptional men- Mathematical Statistics at East China Normal Univer- toring of graduate students. Professor Wu also distin- sity in 1986. Nine years later, he left his job to pursue guished himself with extended service to his institu- doctoral studies in statistics in Canada. He completed tion, the SSC, and several scholarly journals. The au- his Ph.D. at Simon Fraser University in 1999. His thesis, thor or co-author of over 30 scientific articles, Wu has entitled “The effective use of complete auxiliary infor- carried out fundamental work on calibration meth- mation from survey data,” was written under the su- ods; in particular, he showed how to construct opti- pervision of the late Randy Sitter. Since 1999, he has mal estimators of various finite-population parameters held a position at the University of Waterloo, where by exploiting auxiliary information efficiently through he is now a Full Professor. a model-calibration approach. The general framework he developed for model-assisted calibration methods The CRM–SSC Prize stimulated much research. More recently, Wu has fo- cused his interest on empirical likelihood methods for The SSC, founded in 1977, is dedicated to the promo- survey data. He is one of the leading developers of tion of excellence in statistical research and practice. pseudo-empirical likelihood techniques and the effi- The prestigious CRM–SSC Prize, jointly sponsored by cient computational algorithms he developed in this the SSC and the CRM, is given each year to a Canadian context are widely used. statistician in recognition of outstanding contributions to the discipline during the recipient’s first 15 years af- Throughout the years, Changbao Wu also seized many ter earning a doctorate. opportunities to get his hands dirty with data. For ex- ample, he gained first-hand experience with fishery Changbao Wu is the fourteenth recipient of the CRM– abundance survey design and analysis. He also played SSC Prize. The previous winners of the award are a key role in the Chinese leg of the International To- Christian Genest (1999), Robert J. Tibshirani (2000), bacco Control Policy Evaluation Project. In recognition Colleen D. Cutler (2001), Larry A. Wasserman (2002), of his leadership role in survey sampling, he was in- Charmaine B. Dean (2003), Randy Sitter (2004), Jiahua vited to serve as Associate Editor for Biometrika, the Chen (2005), Jeffrey Rosenthal (2006), Richard Cook Journal of Nonparametric Statistics, Survey Methodol- (2007), Paul Gustafson (2008), Hugh Chipman (2009), ogy, The Australian and New Zealand Journal of Statis- Grace Y. Yi (2010), Edward Susko (2011).

49 The CRM Outreach Program The CRM Outreach Program

he CRM is eager to fulfill the public’s desire for understanding the latest developments in the mathematical T sciences. To this end, the CRM initiated in the spring of 2006 a series of lectures called the Grandes Conférences du CRM, which feature outstanding lecturers able to convey the beauty and power of mathematical research to a wide audience. The Grandes Conférences du CRM are now well established and there were three lectures geared towards a general audience in 2011–2012: a lecture by Professor Gerda de Vries on December 1st, 2011, a lecture by Professor Moshe Y. Vardi on February 16, 2012, and a lecture by Professor Daniel Pauly on May 11, 2012. The three lectures took place at the Université de Montréal. The reader will find summaries of these lectures below. Each Grande Conférence attracted hundreds of people of all ages, and was followed by a “vin d’honneur” that enabled the participants to ask questions, reconnect with friends and colleagues, and meet people interested in mathematics and science in general. In 2011–2012 the Grandes Conférences program was under the stewardship of Christiane Rousseau and Yvan Saint-Aubin, professors at the Département de mathématiques et de statistique of the Université de Montréal.

The language of life: When mathematics speaks to biology Gerda de Vries (University of Alberta) by Michael C. Mackey (McGill University)

Last December 1, Montréal mathematicians were given ing how simple considerations derived from epidemi- the chance to hear Professor Gerda de Vries of the ological models allow public health policy makers to University of Alberta (http://www.math.ualberta. decide between various strategies. ca/~devries/) speak on “The language of life: When From there she turned to a discussion of the formation mathematics speaks to biology.” A member of the Al- of patterns in biology (think zebra stripes and giraffe berta Centre for Mathematical Biology (http://www. spots) using the framework of Alan Turing’s seminal math.ualberta.ca/~mathbio/), Professor de Vries, paper of 1952 to explain simply how reaction-diffusion President of the Society for Mathematical Biology and systems can generate spatio-temporal patterns. These an acclaimed teacher, researcher, and lecturer led all problems are, of course, areas of active research in of us on a breath-taking tour of just a few of the fas- many centres around the world even today, in fields as cinating areas currently occupying the attention of diverse as the formation of patterns in embryogenesis biomathematicians. and the formation of spatial structures in animal popu- The starting point for lations. These same questions also occur in the context the talk was a reminder of the formation of animal group patterns, i.e., in the that mathematical biol- swarming behaviour of fish and insects. ogy is not a new dis- In the hour that Professor de Vries had she could cipline in mathemat- hardly scratch the surface of what modern mathemat- ics, but rather has a ical biology is all about. Currently, any area of biology long and rich history. that one cares to name (ranging from molecular biol- She noted that Leon- ogy through organ physiology to clinical medicine and hard Euler was led, in ecological situations) has an active and vibrant compo- part, to his study of in- nent of mathematicians working hand in hand with ex- compressible fluid flow perimentalists to make more sense of the data collected Gerda de Vries by his interest in blood either in the laboratory, the clinic, or the field, and to flow in arteries, and that Daniel Bernoulli had major offer hypotheses that can be tested and are based on interests in promoting vaccination for smallpox based realistic mathematical models of the phenomena of in- on his analysis of morbidity and mortality data using terest. When I first started out as a young researcher in mathematical models. Using the example of Bernoulli this field 40 plus years ago, reading a few journals and as a spring-board, she then moved into recent con- going to the bi-annual Gordon Conference on Theoret- siderations about the spread of the avian flu virus, ical Biology sufficed to keep one up-to-date with what SARS, the H1N1 virus, and the West Nile virus, show- was happening. Nowadays there are literally scores

51 Centre de recherches mathématiqes of journals devoted to various aspects of mathemati- ranging interests not only in mathematics and bi- cal biology, a large number of conferences, and sum- ology but also in the fine arts. She is an accom- mer/winter schools that one can attend to be brought plished quilter (see http://www.telusplanet.net/ up to speed. public/gdevries/) and gives wonderful lectures on As is the case with many mathematicians, Profes- the mathematics in her quilts that are just as fascinat- sor de Vries is a multidimensional person with wide ing as her “Grande Conférence” lecture.

From Aristotle to the Pentium Moshe Y. Vardi (Rice University) by Benoit Larose (Concordia University and Champlain College)

On February 16, 2012, Universität des Saarlandes, Germany, and the Univer- the CRM had the priv- sité d’Orléans, France. Vardi is an editor of several in- ilege of hosting the ternational journals, and Editor-in-Chief of the Com- lecture of Professor munications of the ACM. He is a Guggenheim Fellow, Moshe Y. Vardi of as well as a Fellow of the ACM, the American Asso- Rice University enti- ciation for the Advancement of Science, the Associa- tled “From Aristotle to tion for the Advancement of Artificial Intelligence, and the Pentium.” Moshe Y. the IEEE. He was elected a member of the US National Vardi is the George Academy of Engineering, the American Academy of Professor in Compu- Arts and Science, the European Academy of Sciences, tational Engineering and the Academia Europaea. and Director of the Ken M. Vardi’s lecture consisted of a broadly accessible his- Moshe Y. Vardi Kennedy Institute for torical outline of the connection between formal logic Information Technology at Rice University. He chaired and computer science. We were treated to a bird’s eye the Computer Science Department at Rice University view of the last 2500 years, from Epimenides’ Liar’s from January 1994 till June 2002. Prior to joining Rice Paradox to the Pentium chip, interleaved with amusing in 1993, he was at the IBM Almaden Research Cen- and insightful quotes from such logicians as Aristotle ter, where he managed the Mathematics and Related and Lewis Carroll. Using Leibniz’s unfulfilled dream of Computer Science Department. His research interests mechanizing reasoning as a recurring theme, Profes- include database systems, computational-complexity sor Vardi took us through a humorous and fascinating theory, multi-agent systems, and design specification tour of the history of formal logic, visiting such charac- and verification. Vardi received his Ph.D. from the He- ters as Ramon Llull, George Boole and Charles Peirce. brew University of Jerusalem in 1981. He is the author We eventually returned to Euclid, whose great text has and co-author of about 400 articles, two books, and is been in use for over 2000 years, in a discussion of what the editor of several collections. Wigner referred to as mathematics’ unreasonable ef- Vardi is the recipient of numerous awards, including fectiveness, the notion of mathematical proof, and the three IBM Outstanding Innovation Awards, the 2000 consequences of the attempt by mathematicians of the Gödel Prize, the 2005 ACM Kanellakis Award for The- late 19th and early 20th century to clarify this concept. ory and Practice, the 2006 LICS Test-of-Time Award, This thread was followed, from Frege’s introduction of the 2008 ACM PODS Mendelzon Test-of-Time Award, first-order logic, via the discovery of Russell’s paradox the 2008 ACM SIGMOD Codd Innovations Award, the and Russell and Whitehead’s Principia Mathematica, to 2008 Blaise Pascal Medal for Computer Science by the fall, at the hands of Gödel, Church, and Turing, the European Academy of Sciences, the 2008 ACM of Hilbert’s program to consolidate the foundations of Presidential Award, the 2010 CRA Distinguished Ser- mathematics. Professor Vardi argued that it is precisely vice Award, the 2010 ACM Outstanding Contribution out of this quest that computer science was born; by Award, and the 2011 IEEE Computer Society Harry H. the early 50s, computers were being built around the Goode Award. He holds honorary doctorates from the world, based on von Neumann’s ideas, thus fulfilling

52 The CRM Outreach Program

Leibniz’s dream: “from reasoning, to patterns of rea- The talk was a hit with the audience, and infact soning, to logic, to computers, to computers that rea- members of the public were overheard saying that son.” M. Vardi closed the lecture with a moving quote Moshe Vardi’s lecture was the best of the “Grande from C. Papadimitriou on the sad fate of so many logi- Conférences” series. The lecture was followed by are- cians such as Boole, Cantor, Frege, Gödel, and Turing, ception in the hall of the Jean-Coutu building, where and a remarkably prescient quote from Leibniz on the the participants had the opportunity to exchange ideas advent of the modern computer. with the speaker.

Major trends in world fisheries and their effects on ecosystems Daniel Pauly (University of British Columbia)

Since the end of the ues to increase and the effects of global warming are second World War, the starting to be felt in numerous fisheries. Daniel Pauly’s spread of industrial fish- lecture, delivered in French, illustrated these trends, eries has led to increases discussed their implications, and proposed some reme- in catches and also suc- dies. cessive crashes, which Daniel Pauly was born in France and completed his began to affect global Ph.D. in the biology of fisheries at the University of catches in the 1970s, and Kiel (Germany) in 1979. After spending many years at intensified in the 1980s the International Center for Living Aquatic Resources and 1990s. In response, Management in Manila (Philippines), he became a pro- the industrialized coun- fessor at the UBC Fisheries Centre, of which he was tries of the Northern the director from 2003 to 2008. He is a Fellow of the Hemisphere redeployed Royal Society of Canada and has been awarded many their fishing effort in Daniel Pauly prizes, including the Award of Excellence of the Amer- the waters of developing ican Fisheries Society in 2004, the International Cos- countries, and beyond into the Southern Hemisphere, mos Prize in 2005, the Excellence in Ecology Prize in all the way to Antarctica. This geographic expansion 2007, and the Ramon Margalef Prize in Ecology in 2008. has now been completed and global catches, which Four universities have awarded Daniel Pauly an hon- peaked in the late 1980s, are now declining, while the orary doctorate, including the Université de Montréal damage to marine ecosystems and biodiversity contin- (in 2007).

53 CRM Partnerships CRM Partnerships

he CRM is strongly committed to its national mission and takes measures to ensure that as many Canadian T scientists as possible benefit from its activities and become involved in their planning. For instance, itap- points to its International Scientific Advisory Committee eminent Canadian scientists from various parts ofthe country; it is present in all important forums where the future directions of the Canadian mathematical sciences are discussed; it urges its organizers to ensure that Canadian specialists are included in their activities; it organizes and supports scientific events across the country; it collaborates with Canadian institutes, societies, and associa- tions. A specific budget is set aside each year for the participation of Canadian graduate students in its programs. The CRM is the only national institute that operates in the two official languages of Canada and it is highlyvisible on the international scene. In keeping with its national role, it coordinates its activities with the Fields Institute for Research in Mathematical Sciences, the Pacific Institute for the Mathematical Sciences (PIMS), the Mprime Network, the Canadian Mathematical Society (CMS), the Canadian Applied and Industrial Mathematics Society (CAIMS), the Statistical Society of Canada (SSC), the Canadian Association of Physicists (CAP), as well as other societies and institutes abroad.

CRM Partners

The Fields Institute for Research in mer School on Non-equilibrium Statistical Mechanics Mathematical Sciences and the Pacific (see the section General Program). Also in 2011 an Institute for the Mathematical Sciences Unité Mixte Internationale (UMI) of the CNRS was es- tablished at the CRM. There are only 30 UMIs (in all Since the early 1990s two other research institutes subjects) around the world. Laurent Habsieger (CNRS) have joined the CRM on the Canadian scene: Toronto’s and the CRM director are the codirectors of the UMI. Fields Institute for Research in Mathematical Sciences The UMI supports visits of French mathematicians to and the Pacific Institute for the Mathematical Sciences members of the CRM and vice versa. In 2012 the French (PIMS). As well as coordinating their scientific activi- researchers Claude-Alain Pillet and Pierre Ille visited ties, the three institutes have worked closely on a va- the UMI located at the CRM. Louigi Addario-Berry, a riety of initiatives, the most important of which is the professor at McGill and a member of the UMI, visited Mprime Network. The three institutes are also involved some French colleagues in 2012. For more information in other initiatives, such as the CRM–Fields–PIMS we refer the reader to www.crm.umontreal.ca/UMI/. Prize awarded in recognition of outstanding accom- The CRM has signed agreements with the European plishments in the mathematical sciences in Canada. It Union. For instance, in 2006 the CRM and the ISM was created in 1994 as the CRM–Fields Prize and be- signed an agreement with the ALGANT consortium came the CRM–Fields–PIMS Prize in 2006. The admin- (where ALGANT stands for Algebra, Geometry, Num- istrative responsibility for this prize rotates between ber Theory) to further the exchange of graduate stu- the three institutes. dents. In 2010 the CRM was one of the 12 partners National and International Collaborations to sign an agreement with SISSA (an Italian centre) to promote exchanges of visiting researchers specializing The CRM collaborates with research centres inthe in mathematical physics. SISSA (International School Montréal area, especially the Groupe d’études et de re- for Advanced Studies, in English) is based in Trieste cherche en analyse des décisions (GERAD). The CRM, and is a university dedicated to the training of gradu- the ISM, and GERAD jointly organize a weekly statis- ate students. tics colloquium (see the section General Program). The The CRM has signed two agreements with the TataIn- CRM is a partner of the Banff International Research stitute of Fundamental Research (TIFR), a prestigious Station (BIRS). research centre in India. The scope of the first agree- The researchers belonging to the CRM or a CRM lab- ment was applied mathematics and it was signed in oratory enjoy close collaborations with French col- 2006 between the CRM and the TIFR Centre for Appli- leagues, in particular CNRS and INRIA researchers. In cable Mathematics in Bangalore. The scope of the sec- July 2011 some CRM members and researchers from ond agreement was pure mathematics and was signed the Université de Cergy-Pontoise organized the Sum- in 2011 between the CRM and the Mumbai TIFR.

55 Centre de recherches mathématiqes

In its publishing activities, the CRM is continuing its linkages with industrial, governmental, and not-for- partnership with the American Mathematical Society profit organizations. Mprime research focuses onfive (AMS), in particular through its two series of joint pub- key sectors of the economy: biomedical and health sec- lications, the CRM Monograph Series and the CRM tor; environment and natural resources; information Proceedings & Lecture Notes. A CRM Series in Mathe- processing; risk and finance; and communication, net- matical Physics is published by Springer. The CRM has works, and security. exchange agreements with the Fields Institute, PIMS, Mprime also extends financial support to some events MSRI, the Institute for Mathematics and its Applica- organized by the CRM and other institutions. For in- tions (University of Minnesota), École normale supé- stance, in 2011–2012, Mprime was the principal source rieure (France), the Isaac Newton Institute, the Institut of support for the Fourth Montreal Industrial Problem des Hautes Études Scientifiques (France), and BIRS. Solving Workshop (see the section on the CRM multi- disciplinary and industrial program). Associations and Professional Societies Atlantic Association for Research in the The CRM maintains close ties with the different pro- Mathematical Sciences (AARMS) fessional societies in the mathematical sciences: CMS, CAIMS, SSC, and CAP . The president of the CMS is AARMS was founded in March 1996 at a time when an ex-officio member of the CRM International Sci- the National Network for Research in the Mathemati- entific Advisory Committee. The CRM has also sup- cal Sciences was being discussed and planned. AARMS ported financially certain initiatives of the CMS, such exists to encourage and advance research in all mathe- as the mathematical camps. Together with the other matical sciences (including statistics and computer sci- institutes, the CRM organizes or sponsors special ses- ence) in the Atlantic region. In addition AARMS acts as sions at the CMS, CAIMS, and SSC meetings. The CRM a regional voice in discussions of the mathematical sci- awards a prize each year jointly with the SSC; simi- ences on a national level. Since its inception, AARMS larly, it awards a prize each year with the CAP in math- has played an important role in the research activities ematical and theoretical physics. in the Atlantic region, sponsoring or co-sponsoring numerous meetings and workshops. In the summer The Mprime Network of 2002, AARMS initiated an annual Summer School The Mprime Network (www.mprime.ca) is the only for graduate students and promising undergraduates. Network of Centres of Excellence for the mathemat- AARMS is grateful to Canada’s three mathematical in- ical sciences, bringing together academia, industry, stitutes (the CRM, the Fields Institute for Research in and the public sector to develop cutting-edge mathe- Mathematical Sciences, and PIMS), as well as to the matical tools vital to our knowledge-based economy. member universities, for providing funding for its ac- Known as Mitacs (Mathematics of Information Tech- tivities. Its member universities are Acadia University, nology and Complex Systems) from 1999 to 2011, it Cape Breton University, Dalhousie University, Memo- is a pan-Canadian network whose creation was pro- rial University of Newfoundland, Mount Allison Uni- posed by the three Canadian mathematical sciences in- versity, St. Francis Xavier University, Saint Mary’s stitutes (the CRM, the Fields Institute for Research in University, the Université de Moncton, the University Mathematical Sciences, and PIMS). The organization of New Brunswick, and the University of Prince Ed- now called Mitacs is not focused solely on mathemat- ward Island. Finally AARMS receives some financial ics but on the development of the next generation of support from the provinces of New Brunswick and innovators with vital scientific and business skills (see Nova Scotia. One can find information on the activi- www.mitacs.ca). ties of AARMS at the following web site: http://www. aarms.math.ca. The purpose of the Mitacs and then Mprime Networks was to lead Canada’s effort in the generation, applica- Academic Partners tion, and commercialization of new mathematical tools and methodologies within a world-class research pro- The activities of the CRM rest on a solid basis ofco- gram. In order to do so, Mprime initiated and fostered operation with regional universities, in particular the

56 CRM Partnerships

Montréal universities, and most particularly the Uni- Entropy rigidity for non-positively curved compact man- versité de Montréal, whose support for the CRM has ifolds, by François Ledrappier (University of Notre been unfailing. The Université de Montréal releases Dame), on February 10, 2012 five of its faculty members to work at the CRMeach The Transverse Geometry of Tiling Spaces, by Jean Bel- year, and the support of these faculty members is an es- lissard (Georgia Institute of Technology), on April 13, sential asset for the CRM’s scientific activities. There is 2012 in addition a regular program of teaching releases for the other Montréal universities, bringing the equiva- Network for Computing and Mathematical lent of another two positions to the CRM each year. Modeling (ncm₂) On an ad-hoc basis linked to the thematic program, the CRM has also been arranging the release of re- The CRM is one of the founding members ofthe search personnel from nearby universities such as La- Network for Computing and Mathematical Modeling val, Sherbrooke, Queen’s, and Ottawa. The partner- (ncm₂), a network created by several research cen- ships of the CRM with the other research institutes in tres in order to respond to the needs of industry in the Montréal area have been very profitable. fields related to computing and mathematical mod- With the financial support of the Université de Mont- elling. The research of the network focuses onfive réal, McGill University, the Université du Québec à major themes: risk management, information process- Montréal, Concordia University, and Université Laval, ing, imaging and parallel computing, transport and as well as grants from NSERC and the Fonds de re- telecommunications, and health and electronic com- cherche du Québec – Nature et technologies (FRQNT), merce. The ncm₂ was founded by the CRM, the Centre the CRM finances the activities of its nine laboratories, de recherche en calcul appliqué (CERCA), the Cen- which collectively represent the most active branches ter for Interuniversity Research and Analysis on Or- of the mathematical sciences. These laboratories are ganizations (CIRANO), the Centre for Research on the perfect illustration of scientific vitality and serve to Transportation (CRT), the Computer Research Insti- feed the national and international scientific programs tute of Montréal (CRIM), and the Institut national de la of the CRM. The reader may refer to the section Re- recherche scientifique – Télécommunications (INRS- search Laboratories for a description of the activities Télécom). At the present time the following centres are of each of these laboratories. members of the ncm₂: CIRANO, CRM, CIRRELT, INRS- ÉMT, and GERAD. Association with the University of Ottawa Regroupement Neuroimagerie/Québec In 2003, the Department of Mathematics and Statistics (RNQ) of the University of Ottawa became a member of the CRM. In partnership with the University of Ottawa, In recent years, CRM’s PhysNum laboratory has devel- the CRM cofinances the CRM–University of Ottawa oped a strong collaborative network with various part- Distinguished Lecture Series, postdoctoral fellowships, ners in neuroimaging in the Montréal area. This net- and teaching releases so that University of Ottawa fac- work became an officially recognized network with the ulty members can undertake research with colleagues founding of the Regroupement Neuroimagerie/Québec in the CRM’s laboratories or participate in the scien- (RNQ), under the umbrella of the Institut universitaire tific activities of the CRM. de gériatrie de Montréal. The RNQ, with its 70 re- searchers, has recently purchased some key equipment CRM–University of Ottawa Distinguished in neuroimaging thanks to a very large grant ($11M). Lecture Series One of the strongest alliances of the CRM within that network is its association with the Inserm laboratory The series features talks by prominent mathematicians for brain imaging at the FMPMC Pitié-La Salpêtrière from Canada and abroad on topics at the forefront (Paris), whose director is Dr. Habib Benali. of today’s mathematical research. In 2011–2012 there were two such talks at the University of Ottawa.

57 Centre de recherches mathématiqes

Joint Initiatives

The annual meetings of the CMS, SSC, and CAIMS, as for Women in Mathematics (AWM) Embedded Meet- well as some of their training and promotion activi- ing at ICIAM 2011. ties, are jointly sponsored by the CRM, the Fields In- 2011 CMS Summer Meeting stitute for Research in Mathematical Sciences, PIMS, June 3–5, 2010, University of Alberta and Mprime. The annual meetings of the societies http://cms.math.ca/Events/summer11/ allow Canadian mathematicians and statisticians to 39th Annual Meeting of the Statistical Society of Canada keep abreast of their colleagues’ work, to organize ses- June 12–15, 2011, Acadia University sions on emerging topics, and attend lectures given http://www.ssc.ca/en/meetings/2011/ by world-renowned mathematicians or prize winners. 2011 CMS Winter Meeting One can find more information on the societies bycon- December 10–12, 2011, Delta Chelsea Hotel, Toronto sulting their respective web sites (http://www.cms. http://cms.math.ca/Events/winter11/ math.ca/, http://www.ssc.ca/, and http://www. caims.ca/). Note that there was no CAIMS Annual ICIAM 2011 Meeting in 2011 because an international congress in July 18–22, 2011, Vancouver Convention Centre applied mathematics (ICIAM) took place in Canada AWM Embedded Meeting @ ICIAM 2011 during that year. The CRM supported the Association July 18–19, 2011, Vancouver Convention Centre

58 Mathematical Education Centre de recherches mathématiqes

s part of its mandate to promote and stimulate research in the mathematical sciences, at every level, the CRM A provides funding and support for many activities and programs related to mathematical education and the training of researchers. Many of these activities and programs are carried out jointly with the ISM (Institut des sciences mathématiques). As a result, much of the information contained in the present section is taken from the ISM annual report.

Institut des sciences mathématiques (ISM)

Created in 1991 by the departments of mathemat- the CRM–ISM Probability Seminar, and the ISM Grad- ics and statistics of the four Montréal universities, uate Student Conference. the ISM is a consortium of eight Québec universities • Promotion of the mathematical sciences (Bishop’s University, Concordia, Laval, McGill, Uni- The ISM produces the Accromαth magazine and dis- versité de Montréal, UQAM, UQTR, and Université de tributes it freely in all the cégeps and secondary Sherbrooke), six of which offer a Ph.D. program in schools in Québec. In this way, it contributes to spread- Mathematics. As an institute to which belong almost ing mathematical knowledge among teachers, young all the Québec researchers in the mathematical sci- students, and the general public. Each year, ISM pro- ences, the ISM has at its disposal vast material and fessors give talks attended by thousands of cégep stu- intellectual resources, and as a result, Montréal and dents; these talks present the latest breakthroughs in Québec itself have become one of the main centres of mathematics and the careers available to mathematics training and research in the mathematical sciences in graduates. North America. The ISM is funded by the Ministère de l’Éducation, du Loisir et du Sport du Québec and by the As the above list demonstrates, the CRM has several eight universities in the consortium. joint activities with the ISM, in particular two collo- quia, a joint program of postdoctoral fellowships, and The reader will find below an overview of the activities the planning of graduate courses related to the the- and programs of the ISM. matic programs of the CRM. Since the summer of 2003, • Coordination and harmonization of graduate pro- the CRM has also supported the Undergraduate Sum- grams mer Scholarships program, which allows postdoctoral The ISM was created to bring together the strengths of fellows to supervise undergraduate students doing re- its member departments, in order to turn them into a search. great school of mathematics. Thus the ISM coordinates the graduate studies of the mathematics departments, CRM–ISM Postdoctoral Fellowships supports the sharing of expertise among its researchers The CRM–ISM postdoctoral fellowships enable and facilitates student mobility between the Montréal promising young researchers to devote themselves to universities. their research work. The ISM organizes a single com- • Scholarships and financial support petition on behalf of the eight universities of the con- The ISM helps students and beginning researchers sortium, and it receives a large number of applications, carry out their research activities in several ways, for which are then evaluated by the 150 ISM professors. instance through the ISM Scholarships for Graduate The selection of the fellows is rigorous and only onein Studies, the Carl Herz Scholarship (financed by the forty applicants is awarded a fellowship. The applica- Carl Herz Foundation), the Travel Bursaries, the Un- tions are handled electronically in order to streamline dergraduate Summer Scholarships, and the CRM–ISM the selection process and economize the resources con- postdoctoral fellowships. sumed during the selection. The postdoctoral fellows • Scientific activities play a crucial role in the Montréal universities: they Since its creation, the ISM has initiated several activ- collaborate with the established researchers, stimulate ities that are by now an integral part of the Québec their work, and bring new ideas from other great cen- scientific scene: the CRM–ISM Mathematics Collo- tres of mathematical research. They also are a vital quium, the CRM–ISM–GERAD Statistics Colloquium, link between the professors and the students, espe-

60 Mathematical Education cially when they organize on their own study groups which takes the department recommendations into ac- on emerging topics. count, makes the final selection of scholars. Each year the ISM has been able to attract an exceptional student CRM–ISM 2011–2012 Postdoctoral Fellows to Québec. A doctoral fellowship for the academic year Vorrapan Chandee (Ph.D., Stanford) works with 2012–2013 was awarded to Almaz Butaev, who comes Chantal David and Andrew Granville on analytic and from Malaysia and will pursue a Ph.D. in mathematics probabilistic number theory, L-functions, the theory at Concordia University under the supervision of Galia of random matrices, and quadratic forms. Dafni. Tiago Fonseca (Ph.D., UPMC) works with Marco In spite of its success, this program will be discontin- Bertola, John Harnad, and Jacques Hurtubise. His re- ued next year because of budgetary constraints. search interests are in algebraic and enumerative com- binatorics and in integrable quantum systems. Undergraduate Summer Scholarships Nabil Kahouadji (Ph.D., Paris Diderot) collaborates In collaboration with the CRM and the ISM professors, with Niky Kamran. He works in differential geome- the ISM awards summer scholarships to promising un- try, Cartan-Kähler theory, conservation laws, geomet- dergraduates who want to do research during the sum- ric aspects of PDEs, and mathematical physics. mer and plan to study mathematics at the graduate Dimitris Koukoulopoulos (Ph.D., UI Urbana- level. These undergraduates are supervised by postdoc- Champaign) works with Andrew Granville on ana- toral fellows, who in general are supervising students lytic, probabilistic, and additive number theory. for the first time. The reader will find below the listof Antonio Lei (Ph.D., Cambridge) works with Henri the undergraduate scholars. Darmon in algebraic number theory. Valentine Chiche-Lapierre (Concordia) Guyslain Naves (Ph.D., Joseph Fourier) works with Scholarship co-financed by Galia Dafni Adrian Vetta. His research interests are in combina- Supervisor : Suresh Eswarathasan torial optimization, graph theory, and approximation Topic : Applications of analysis to error-correcting algorithms. codes Vivien Ripoll (Ph.D., Paris Diderot) works with Duration : May 1 – June 30, 2012 (2 months) Christophe Hohlweg on combinatorics and the geom- Spencer Frei (McGill) etry of Coxeter groups and real and complex reflection Scholarship co-financed by Gantumur Tsogtgerel groups. Supervisor : Brian Seguin Matthew Roberts (Ph.D., Bath) works with Louigi Topic : Existence, regularity, and approximation for el- Addario-Berry in probability theory. liptic systems with variational structure Yakov Savelyev (Ph.D., Stony Brook) works with Oc- Duration : May 1 – July 31 (3 months) tav Cornea and François Lalonde in symplectic and dif- Nicolas Gonzalez (McGill) ferential geometry. His main interests are Floer theory Scholarship co-financed by Tony Humphries and Gromov-Witten theory in dynamical systems and Supervisor : Renato Calleja mathematical physics. Topic : Numerical study of a family of differential equa- tions with two state-dependent delays that are inde- ISM Doctoral Fellowships pendent of each other Duration : May 1 – August 3 (3 months) In 2007–2008 the ISM initiated a doctoral fellowship program in order to recruit outstanding Ph.D. students. Vincent Grenier-Gauthier (Laval) The doctoral fellowships provide financial support for Scholarship co-financed by André Fortin up to four years to outstanding, new students to pur- Supervisor : Driss Yakoubi sue a doctoral program at one of the ISM member uni- Topic : Formulation complètement eulérienne de versities. The students fill an application form online l’interaction fluide-structure pour le problème du pis- and the applications are made available to all the ISM ton professors. An inter-university selection committee, Duration : May 1 – August 31 (4 months)

61 Centre de recherches mathématiqes

Marc-Adrien Mandich (McGill) The following students gave talks during the Con- Scholarship co-financed by Vojkan Jakšić ference: Anas Abdallah (Laval), Abdolrasoul Bahari- Supervisor : Philip Grech fard (Laval), Mohammad Bardestani (Montréal), Cyril Topic : Entropy flux in the stationary state of afinite Joël Batkam (Sherbrooke), Erwan Biland (Laval), univariate sample S connected at its left and right ends Éloïse Boiteau (Laval), Laurence Boulanger (Montréal), to two infinitely extended reservoirs at distinct tem- Alexandre Desfossés-Foucault (Montréal), Ibrahima peratures and chemical potentials Dione (Laval), Kael Dixon (McGill), Yasser Farhat Duration : May 1 – August 31 (4 months) (Laval), Ludovick Gagnon (Laval), Philippe Gagnon Francis Rodrigue (Montréal) (Montréal), Sophie Léger (Laval), Mostafa Mache Scholarship co-financed by Matilde Lalín (Laval), Jim Parks (Concordia), Benoît Pouliot (Laval), Supervisor : Mathew Rogers Eric Rowland (UQAM), Maxime Scott (UQAM), Topic : An exploration of Bernoulli numbers and Michael Snarski (McGill), Hugo Tremblay (UQAM), Bernoulli polynomials and Malik Younsi (Laval). Duration : May 1 – August 31 (4 months) Promotion of the Mathematical Sciences Xi Sisi Shen (McGill) Scholarship co-financed by Pengfei Guan, Adrian Produced by the ISM and financed by the ISM, the Vetta, and Bruce Reed CRM, the CMS, and the Mitacs network, the Accromαth Supervisor : Aaron Williams magazine aims to draw more young people to the Topic : Combinatorial generation mathematical sciences. Accromαth, whose editor-in- Duration : May 1 – August 31 (4 months) chief is André Ross, has two issues per year and is available free of charge in all the high schools and ISM Graduate Student Conference cégeps of Québec. Accromαth is designed by an excep- tional team of researchers and instructors with a broad Each year the ISM sponsors and supports the organi- experience in the promotion of mathematics; it pro- zation of the ISM Graduate Student Conference (“Col- vides high school and cégep teachers with stimulating loque pan-québécois des étudiants de l’ISM”). Orga- and topical articles on the most recent discoveries and nized by and for the students of the partner universi- applications, as well as articles on the history of math- ties, the 13th Conference was held on June 1–3, 2012, at ematics and its links with the arts. UQAM. It was organized by Jérôme Fortier, Sandra Lar- rivée, and Maxime Scott, and attended by around 100 Accromαth is widespread in Québec but is also dis- participants. The program featured plenary lectures tributed in other French-speaking regions and coun- given by professors and presentations by students. The tries. Currently 2400 persons or institutions (mostly plenary lectures were given by Thomas Brüstle from teachers from Québec) subscribe to the magazine. the Université de Sherbrooke (On maximal Green se- This year Accromαth was awarded the Anatole-Decerf quences), André Joyal from UQAM (Petite histoire des Prize, a prestigious prize awarded every two years by cogèbres colibres), Jean-François Renaud from UQAM the Société mathématique de France in recognition of (Théorie des fluctuations pour le processus de Lévy spec- work in the pedagogy or popularization of mathemat- tralement négatif ), Dominic Rochon from the Univer- ics. For the first time ever the recipient of the prize sité du Québec à Trois-Rivières (Dynamique bicom- was a team working outside of Europe. The members plexe), and Adrian Vetta from McGill University (A of the selection committee stressed the high scientific quick introduction to algorithmic game theory). and educational quality of the magazine. France Caron received the prize on behalf of the Editorial Board at the Institut Henri–Poincaré on June 15, 2012.

62 Mathematical Education

Other Joint Initiatives

Canadian Undergraduate Mathematics science, economics, etc.). During the conference stu- Conference 2011 dents get the valuable opportunity to practice giv- June 15–19, 2011, Université Laval ing mathematical talks on a topic of their choice, en- Sponsored by Université Laval, Département de ma- counter ideas from areas of mathematics outside of thématiques et statistique de l’Université Laval, AES- their expertise, and listen to renowned keynote speak- MUL, CMS, AESGUL, CRM, Mitacs Student Advisory ers from a variety of disciplines. The keynote speak- Committee, AARMS, ASSQ, Exfo, FRQNT, CAIMS, ers invited each year are either prominent figures or Fields, Thomas Ransford (Analysis Research Chair), rising stars in their fields, and most importantly they CMS Student Committee, ISM, GIREF, SSC, Service de care about undergraduates and their exposure to math- placement de l’Université Laval, Line Beauchamp (mi- ematics. nistre 55e Congrès de l’Association Mathématique de l’Éducation, du Loisir et du Sport), Michelle Cour- du Québec chesne (présidente du Conseil du Trésor), ADSEG, October 14–15, 2011, Polytechnique Montréal CADEUL, AÉLIÉS, AMQ, Fondation de l’Université La- val, Air Canada, Coop Zone As usual the CRM was a sponsor of the “Associ- Organizers: ation Mathématique du Québec” conference, which Anika Pascale Papillon (Laval), Andréa Deschênes (La- took place at the École Polytechnique de Montréal val), Laurent Pelletier (Laval), Dominique Maheux (La- and whose theme was Les mathématiques à construire val), Jean-Sébastien Lévesque (Laval) (Mathematics to build). Keynote Speakers: Yvan Saint-Aubin (Montréal), Yves Demay (Nice “Sciences et mathématiques en action” and Sophia Antipolis), Jean-Marie De Koninck (Laval), “Association québécoise des jeux Frédéric Gourdeau (Laval), Aurélie Labbe (McGill), mathématiques” Pamela Gorkin (Bucknell), Frederick Rickey (USMA), Thomas Brüstle (Sherbrooke; Bishop’s) The CRM contributes to the “Sciences et mathéma- Number of participants: 165 tiques en action” program, created by Professor Jean- The Canadian Undergraduate Mathematics Confer- Marie De Koninck from Université Laval in order to ence (CUMC) is one of North America’s largest un- popularize mathematics and science for high school dergraduate conferences and Canada’s premier confer- students and the general public. We refer the reader ence for undergraduate students interested in mathe- to the site www.smac.ulaval.ca for more information. matics and related fields (statistics, physics, computer The CRM also supports the Association québécoise des jeux mathématiques (aqjm.fsg.ulaval.ca).

63 Research Laboratories Research Laboratories

n 2011–2012 the CRM was encompassing nine research laboratories at the heart of the Québec mathematical I community. These research groups act as focal points for local scientific activity and participate actively inthe scientific programs of the CRM .

Applied Mathematics

Description terests include dynamical systems, partial differential equations, and delay differential equations. Emmanuel The CRM Applied Mathematics Laboratory is are- Lorin de la Grandmaison is an Associate Professor in search network of some 21 applied mathematicians, the School of Mathematics and Statistics of Carleton engineers, computer scientists, and chemists, based in University. His research interests include partial dif- Montréal. The Laboratory exists primarily to stimulate ferential equations, numerical analysis (in particular, research and collaboration in the applied mathematical for hyperbolic systems and complex applications of fi- research areas of its members by fostering discussion nite volumes), and mathematical modelling. and the creation of ideas through conferences, work- This year Laboratory members received many hon- shops, and seminars, and the furtherance of research ours, prizes, and nominations. through its visitors’ program and the appointment of talented postdoctoral fellows. The Laboratory is also • The American Society of Mechanical Engineers very concerned with the training of young researchers (ASME) Design Engineering Division Technical Com- and supports travel and conference attendance of its mittee on Multibody Systems and Nonlinear Dynamics postdoctoral fellows. (TC-MSND) gave Eusebius Doedel an honorary award at the ASME 2011 International Design Engineering The research interests of the Laboratory members are Technical Conferences & Computers and Information quite diverse although there are a number of com- Engineering Conferences, held in August 28–31, 2011 mon threads that make interchange and collaboration in Washington, DC, USA. both possible and fruitful. Active areas of research • Peter Bartello was named President of the Canadian represented within the Laboratory include, for exam- Meteorological and Oceanographic Society from June ple, the application of dynamical systems theory to 2012. complex phenomena, high-dimensional chaos, and bi- • Jacques Bélair was nominated a member of the steer- ology. There is an interest in numerical linear alge- ing committee of the Centre for Applied Mathematics bra and its applications, including the design, analysis, in Bioscience and Medicine (McGill). and implementation of effective computer algorithms. Amongst the membership one will also find expertise • Tucker Carrington was a visiting professor at the in numerical simulation, applied dynamical systems, ETH Zürich from May to November 2012. quantum chemistry, turbulence, combustion, biome- • Eliot Fried was a visiting professor in the Mechanical chanics, numerical methods in fluid mechanics and Engineering Department at the University of Washing- electromagnetism, hp-finite element methods, molec- ton from 2011 to 2012. ular dynamics, control, optimization, preconditioners, • George Haller has been appointed professor of non- and large-scale eigenvalue problems. linear dynamics at ETH Zürich (he is on leave of ab- sence from McGill). News and highlights • Emmanuel Lorin was a visiting professor for two months at the Université de Grenoble. He has also been In 2011–2012 the Laboratory welcomed two new mem- nominated to the selection committee of the FRQNT bers. Jean-Philippe Lessard joined the Department of for Ph.D. mathematics bursaries. Mathematics and Statistics of Université Laval in Au- • Jean-Paul Zolésio was a visitor professor in the De- gust 2011 after having previously been an NSF post- partment of Mathematics, Nebraska University, Lin- doc in the Institute for Advanced Study, Princeton and, coln in October 2011 and in the Department of Mathe- more recently, serving as Group Leader of the Compu- matics, North Carolina State University in May 2012. tational Mathematics section in the Basque Center for Applied Mathematics in Bilbao, Spain. His research in-

65 Centre de recherches mathématiqes

The 2011–2012 year was an outstandingly productive all the seminars and conference presentations given one for the Laboratory! At least 97 refereed journal over the past 12 months due to their overwhelming publications bearing the names of members of the number. Here are some of the most important keynote applied maths laboratory have appeared during that or plenary speaker invitations received. period. To this impressive total should be added an • Peter Bartello delivered a keynote talk and pedagog- important number of accepted articles, refereed con- ical lecture entitled “From balance to stratified tur- ference proceedings, and book chapters. In addition, bulence” at the Joint US National Center for Atmo- Jean-Paul Zolésio coauthored (with Michel Delfour) spheric Research-Institute for Mathematics Applied the book: Shapes and Geometries: Metrics, Analysis, to Geosciences Theme-of-the-Year 2012: “Connec- Differential Calculus, and Optimization, 2nd edition, tions between Rotating, Stratified Turbulence and Cli- July 2011, SIAM. To quote from the SIAM website: mate: Theory, Observations, Experiments, and Mod- “This considerably enriched new edition provides a self- els,” Boulder, Colorado, USA, May 2012. contained presentation of the mathematical foundations, • Tucker Carrington was a plenary speaker at the constructions, and tools necessary for studying problems International Symposium on Molecular Spectroscopy where the modeling, optimization, or control variable is 67th Meeting held in Columbus, Ohio, June 18–22, the shape or the structure of a geometric object.” 2012. His talk had the title “Calculating ro-vibrational Beyond the usual NSERC Discovery grants, some sig- spectra using an Eckart frame.” nificant additional grant money was attracted byvari- • Rustum Choksi was an invited speaker at the ous members of the laboratory. Workshop on Geometry of Interfaces and Capillarity, • André Bandrauk was successful in attracting grant Granada, Spain, June 2012. The subject of his talk was money for Québec-Germany cooperation, awarded “On Minimizing Interfaces for a Variational Problem by the Ministère du Développement économique, de with Long-Range Interactions.” l’Innovation et de l’Exportation - Québec. The project • Eliot Fried was an invited speaker and tutor at the funding comes to $150, 000 in total. A. Bandrauk has conference Nonlocal Continuum Models for Diffusion, also secured funding from the FRQNT for the Équipe Mechanics, and Other Applications (SAMSI, North Attoseconde (the amount of the grant is $225,000). Carolina, June 25–29, 2012) and gave a tutorial with • An amount of $5000 from the Mprime Network (for- the title “Established Continuum Approaches to Spa- merly Mitacs) was awarded to Peter Bartello for the tial Nonlocality.” Workshop on Balance, Boundaries and Mixing in the Climate Problem, organised by P. Bartello and two oth- Students, postdoctoral fellows, and visitors ers, and held at the CRM in September 2011. A priority for the applied maths laboratory, reflected • An amount of $19,000 was awarded by PIMS to Pe- clearly in the use of its funds over the last few years, ter Bartello and three Canadian colleagues for some has been the training and encouragement of younger Special sessions on Mathematics of Planet Earth at scientists in applied mathematical research. To date the 2013 Congress of the Canadian Meteorological and this has been primarily through the support of post- Oceanographic Society. doctoral researchers with the aim of seeing them pre- • Tucker Carrington is the principal investigator for a pared for a life in academia or industry. A new initia- project entitled “Understanding the methane cycle in tive this year is the provision of up to four bursaries planetary atmospheres,” which will last for three years for doctoral students of full laboratory members. and has been allocated $350,000. • Robert G. Owens is the principal investigator for a Dr. Renato Calleja, who was a postdoctoral fellow at Mitacs-funded project ($80,000) entitled “Improvement McGill from 2009 to 2012 under the supervision of of the capabilities of an analytical instrument and its Tony Humphries, is leaving us. From September to De- applications in polymer materials characterization and cember 2012, R. Calleja will be a postdoctoral fellow formulation.” at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota. Then from Jan- The members of the CRM applied maths laboratory uary to August 2013 he will be a Visiting Assistant continue to have a very significant presence at interna- Professor at the School of Mathematics of the Geor- tional scientific conferences and it is not possible tolist gia Institute of Technology. Finally, in August 2013, he

66 Research Laboratories will have a tenure-track position at the Instituto Tec- In the 2011–2012 academic year 12 M.Sc. students, 25 nológico Autónomo de México (ITAM) in Mexico City. Ph.D. students, and 11 postdoctoral fellows were su- Dr. Brian Seguin will continue one more year at McGill pervised or cosupervised by members of the Applied under the supervision of Eliot Fried. Dr. François Mathematics Laboratory. Fillion-Gourdeau, a postdoc of André Bandrauk and Emmanuel Lorin, enjoys partial support from the lab- Seminars oratory and is also supported by the Fields Institute and the CRM. Recently, he was invited by the Isaac The main regular laboratory activity is the weekly Newton Institute for Mathematical Sciences in Cam- research seminar. This functions extremely well, de- bridge to take part in the conference on New Develop- spite the diversity of the research interests of labora- ments in Relativistic Quantum Mechanics and Appli- tory members, and attendance is good. Over the past cations (July 30–August 3, 2012). F. Fillion-Gourdeau is two semesters the laboratory has hosted almost 30 dif- being joined by two new arrivals: Dr. Ihsan Topaloğlu, ferent speakers, drawn mainly from North America, who will work with Gantumur Tsogtgerel and Rustum but also including collaborators from Europe and Aus- Choksi, and Dr. Dmitry Kolomenskiy, whose work is tralia/Oceania. Rustum Choksi, Jean-Christophe Nave, of interest to Jean-Christophe Nave and Robert Owens. and Gantumur Tsogtgerel are thanked for organizing Dr. Topaloğlu’s research interests lie mainly in the cal- an excellent seminar program over the past twelve culus of variations and partial differential equations. months and for volunteering to continue the good Dr. Kolomenskiy is one of only 4 new CRM postdoc- work in 2012-2013. toral fellows appointed in 2012. During his time in Montreal he will develop numerical techniques for the Workshops, special sessions, and others incompressible Navier-Stokes equations with irregular The members of the laboratory have been very ac- time-dependent boundaries (in order to study insect tive during the past year in helping organize inter- flight and unmanned aerial vehicles aerodynamics). national conferences, workshops and other scientific This year the laboratory decided to make available 4 events. Here are the highlights. (These meetings have bursaries of $5000 each for up to three years with the been arranged in chronological order and the name of following rules: the responsible lab member is given in parentheses.) (a) An application for a bursary will consist of the stu- • Workshop on Balance, Boundaries and Mixing in dent’s CV and a letter of recommendation from the the Climate Problem, September 2011, CRM (Peter supervisor; Bartello). (b) The competition deadline will be in November to • Workshop on “Advanced Techniques in Nonlinear coincide with the NSERC scholarship application Dynamics,”Instituto de Física, Benemérita Universidad deadline; Autónoma de Puebla, Mexico, February 2012 (Eusebius (c) The bursaries will be available at any time afterthe Doedel). first year of the Ph.D. program being followed by • Conference on Nonlocal PDE and Variational Prob- the successful student; lems, Institute for Pure and Applied Mathematics, (d) The bursaries will be awarded for one year inthe UCLA, March 2012 (Rustum Choksi). first instance and renewed each year, provided the progress of the Ph.D. candidate is satisfactory (a • Workshop on “Connections Between Regularized letter from the supervisor to this effect will besuf- and Large-Eddy Simulation Methods for Turbulence,” ficient); Banff International Research Station, May 13–18, 2012 (e) Decisions will be made by a small ad-hoc commit- (Eliot Fried). tee drawn from laboratory members not request- • Workshop entitled “Calcul rigoureux dans les sys- ing a Ph.D. bursary and based on the size of the tèmes dynamiques” at the Université Laval, May 23, current grants held by the supervisor (the smaller 2012 (Jean-Philippe Lessard). the total, the higher the laboratory funding prior- • The 46th Congress of the Canadian Meteorological ity) and the excellence of the Ph.D. student (as as- and Oceanographic Society (CMOS) took place from sessed from the CV and letter of recommendation) May 29th to June 1st 2012. This Congress was or- with a 50-50 weighting. ganized jointly with the 21st American Meteorologi-

67 Centre de recherches mathématiqes cal Society (AMS) Conference on Numerical Weather Antony R. Humphries (McGill) Prediction (NWP) and the 25th AMS Conference on Numerical analysis, differential equations Weather Analysis and Forecasting (WAF). These two Emmanuel Lorin de la Grandmaison (Carleton) conferences are organized every other year outside Numerical analysis for hyperbolic systems, quantum the annual AMS meeting. In 2012 the Conferences chemistry, complex applications of finite volumes, were held in Montreal and organized in collaboration computer science with CMOS. The conferences benefit from a joint sci- Sherwin A. Maslowe (McGill) entific committee to plan the sessions on NWPand Asymptotic methods, fluid mechanics WAF, themes that are common to both groups (Peter Jean-Christophe Nave (McGill) Bartello). Numerical analysis, PDE, interface problems, level set Members of the Laboratory methods, fluid mechanics, computer graphics Gantumur Tsogtgerel (McGill) Regular members Applied mathematics, partial differential equations, general relativity Robert G. Owens (Montréal), Director Jian-Jun Xu (McGill) Mechanics, numerical simulation of complex fluids Asymptotics and numerical analysis, nonlinear PDEs, André D. Bandrauk (Sherbrooke) materials science Quantum chemistry Peter Bartello (McGill) Associate members Turbulence, CFD Tucker Carrington (Queen’s) Jacques Bélair (Montréal) Chemical dynamics Dynamical systems in physiology Martin J. Gander (Genève) Anne Bourlioux (Montréal) Domain decomposition, preconditioning Modelling, numerical simulation in turbulent combus- Jean-Philippe Lessard (Laval) tion Dynamical systems, rigourous computational meth- Xiao-Wen Chang (McGill) ods, PDEs, delay differential equations, topological Numerical linear algebra and applications methods Rustum Choksi (McGill) Nilima Nigam (Simon Fraser) Calculus of variations, nonlinear partial differential Applied analysis, numerical methods in electromag- equations, problems arising in materials science, self- netism assembly of diblock copolymers, and magnetic domain Paul F. Tupper (Simon Fraser) formation in type-1 superconductors and ferromag- Numerical analysis, stochastic processes, statistical nets mechanics Eusebius J. Doedel (Concordia) Thomas P. Wihler (Bern) Numerical analysis, dynamical systems, differential Numerical analysis, computational methods for PDEs equations, bifurcation theory, scientific software Jean-Paul Zolésio (INRIA Sophia Antipolis) Eliot Fried (McGill) Control, optimization Mechanics and thermodynamics of continuous media George Haller (McGill) Theory of nonlinear dynamical systems, fluid mechan- ics, Hamiltonian systems, singular perturbation theory

68 Research Laboratories

CICMA – Centre Interuniversitaire en Calcul Mathématique Algébrique

Description laboration with Youness Lamzouri (a former CICMA student), K. Soundararajan, and Frank Thorne, ran one CICMA brings together researchers working in num- of the workshops in the AMS’s new “Mathematics Re- ber theory, geometric group theory, and algebraic search Communities” series. The workshop topic was geometry. Algebraic geometry is a broad discipline “The Pretentious View of Analytic Number Theory” with strong connections to a variety of areas ranging and it covered Granville and Soundararajan’s ambi- from arithmetic to theoretical physics. Eyal Goren and tious program to reorganize a large swath of analytic Adrian Iovita are leading experts in applying algebro- number theory around the surprisingly powerful and geometric techniques to problems motivated by num- versatile notion of pretentiousness. ber theory, notably the study of Shimura varieties and • On October 7-9, 2011, Andrew Granville and p-adic cohomology theories. John McKay is one of the Valentin Blomer organised the Third Montreal- instigators of the moonshine program, which ties to- Toronto Workshop in Number Theory at the Fields gether in a surprising way certain notions in the theory Institute, on the theme of “New developments in an- of modular forms, arithmetic geometry, and theoreti- alytic number theory.” This was the third installment cal physics. Geometric group theory is a vibrant sub- of a workshop series initiated by Goren and Kudla, ject that has melded geometric and algebraic methods which has grown into a regular and reliably successful in deep and powerful ways, leading to novel insights in bi-annual event. both subjects. Dani Wise and Mikael Pichot are world- • On November 6-11, 2011, CICMA members Chan- renowned specialists in this central area. tal David and Matilde Lalín organized the second of Contemporary algebraic number theory has devel- the “Women in Numbers” conferences at the Banff opped over the last decades following two major International Research Station. Aimed exclusively at trends. On one hand, there is the theory of special women working in number theory in a broad sense, values of L-functions attached to arithmetic objects, the WIN conferences are now arguably the most influ- originating in the work of Gauss and Dirichlet and ential events of their kind on the international stage. leading to the modern conjectures of Deligne, Beilin- • On January 9-14, 2012, Henri Darmon organised and son, and Bloch-Kato. On the other hand, the Langlands participated in an International Winter School on the program postulates a close link between arithmetic L- Birch and Swinnerton-Dyer conjecture at the Basic Sci- functions and automorphic representations. Analytic ence Research Institute in Pohang, South Korea. number theory studies profound and subtle questions • On April 28-29, 2012, Eyal Goren organised, in col- about the distribution of prime numbers, using pow- laboration with Steven Kudla, the Fourth Montreal- erful techniques from analysis, notably the theory of Toronto Workshop in Number Theory at the CRM, on functions of a complex variable and spectral theory. the theme “Cycles on Kuga fibre varieties.” Number theory in all its different flavours is particu- • On May 5-12, 2012, CICMA members Henri Dar- larly well represented in the laboratory, with Darmon, mon and Eyal Goren ran the annual Bellairs Workshop Goren, Iovita, and Kassaei on the arithmetic and auto- in number theory at McGill’s Bellairs Research Insti- morphic side, and David, Granville, Kisilevsky, Kouk- tute in Barbados. The theme of this well-attended in- oulopoulos, and Lalín on the more analytic side of the structional workshop was “Pro-unipotent fundamen- subject. tal groups: arithmetic and diophantine aspects.” Min- Workshops and instructional conferences hyong Kim (Oxford), who has pioneered a program to study diophantine questions via a technique of an- The 2011–2012 academic year saw many members of abelian descent, gave the principal lecture series (de- CICMA involved in the organization of workshops and scribing this innovative approach). prestigious instructional conferences at the local, na- tional, and international level. Students and postdoctoral fellows • From June 26 to July 2, 2011, CICMA members An- Several graduate students supervised by CICMA mem- drew Granville and Dimitris Koukoulopoulos, in col- bers defended their Ph.D. theses in the 2011–2012 year:

69 Centre de recherches mathématiqes

• Mohammed Bardestani (supervised by Granville); David Ford (Concordia) • Daniel Fiorilli, who was supervised by Granville and Computational number theory, algorithmic number was awarded an NSERC postdoctoral fellowship to theory work at the IAS in Princeton. He has now moved on Jayce R. Getz (McGill) to Michigan and received the Governor General’s gold Number theory medal for his Ph.D. thesis; Eyal Z. Goren (McGill) • Cameron Franc, who was supervised by Darmon and Arithmetic geometry, algebraic number theory, mod- went on to a postdoctoral position at UC Santa Cruz uli spaces of abelian varieties, Hilbert modular forms, and Stanford; p-adic modular forms • Tristan Freiberg, who was supervised by Granville Andrew Granville (Montréal) and has taken up a postdoctoral fellowship at the KTH Analytic number theory, arithmetic geometry, combi- in Sweden; natorics • Yu Zhao, who was supervised by Darmon and was Heekyoung Hahn (McGill) awarded a postdoctoral fellowship at the Academia Eisenstein series, L-functions, trace formula, q-series, Sinica in Beijing. theta functions and partitions In the 2011–2012 academic year 26 M.Sc. students, 48 Adrian Iovita (Concordia) Ph.D. students, and 15 postdoctoral fellows were su- Number theory, p-adic cohomology pervised or cosupervised by CICMA members. Olga Kharlampovich (McGill) Combinatorial group theory and Lie algebras Seminars Hershy Kisilevsky (Concordia) L-functions, Iwasawa theory, elliptic curves, class field The Quebec-Vermont Number Theory Seminar, CI- theory CMA’s main scientific activity, is held every second John Labute (McGill) Thursday for a full day and is attended byabout Pro-p-groups, Lie algebras, Galois theory 30-45 participants from Montreal, Vermont, Quebec City, and Ottawa. In 2011–2012 Henri Darmon and Matilde Lalín (Montréal) L Eyal Goren were the organizers of the seminar, which Mahler measures, -functions, zeta functions included many well-attended lectures. Information Claude Levesque (Laval) on the Quebec Vermont seminar can be found at Algebraic number theory, units, class number, cyclo- http://www.math.mcgill.ca/darmon/qvnts/qvnts.html. tomic fields Michael Makkai (McGill) Regular members of the Laboratory Mathematical logic Henri Darmon (McGill), Director John McKay (Concordia) Algebraic number theory, arithmetic geometry, Computational group theory, sporadic groups, compu- L-functions, Diophantine equations, elliptic curves tation of Galois groups Hugo Chapdelaine (Laval) M. Ram Murty (Queen’s) Algebraic number theory, algebraic geometry Number theory: Artin’s conjecture, elliptic curves, modular forms, automorphic forms, Langlands pro- Chris J. Cummins (Concordia) gram, Selberg’s conjectures, sieve methods, cryptogra- Group theory, modular functions, moonshine phy Chantal David (Concordia) Damien Roy (Ottawa) Analytic number theory, L-functions Transcendental number theory Jean-Marie De Koninck (Laval) Peter Russell (McGill) Analytic number theory: distribution of prime num- Algebraic geometry bers, factorization of numbers, asymptotic behaviour of arithmetic functions, Riemann zeta function Francisco Thaine (Concordia) Cyclotomic fields, cyclotomy, rational points on curves David S. Dummit (Vermont) Algebraic number theory, arithmetic algebraic geome- try, computational mathematics

70 Research Laboratories

CIRGET – Centre Interuniversitaire de Recherches en Géométrie Et Topolo- gie

Description Students, postdoctoral fellows, and visitors

Geometry and topology are fundamental disciplines Graduate students and postdoctoral fellows are an in- of mathematics whose richness and vitality, evident tegral part of CIRGET scientific life, organizing work- throughout human history, reflect a deep link to our ing groups and seminars, mentoring undergraduate experience of the universe. They are a focal point of students, and occasionally giving specialized courses. modern mathematics and indeed several domains of Many of our postdoctoral fellows are staying at CIR- mathematics have recently shown a strong trend to- GET in 2012–2013, but those who have completed their wards a geometrization of ideas and methods: two stays at CIRGET are moving on to good positions: cases in point are mathematical physics and number Mathieu Anel is continuing his postdoctoral studies theory. CIRGET, based at UQAM, is composed of sev- at the ETH in Zurich; Fabrizio Donzelli has a posi- enteen full members, four associate members, and a tion at the University of Ottawa; Roman Golovko is large number of postdoctoral fellows and graduate stu- now a Lecturer at the Israel Institute of Technology dents working in this broad field. The main themes to (Technion); Eric Harper has a postdoctoral position at be pursued in the coming years include the topological McMaster; Sungmo Kang is now a professor at Chon- classification of 3-dimensional manifolds; the quanti- nam National University in Korea; and Karol Palka has zation of Hitchin systems and the geometric Langlands taken up a position at the University of Warsaw. program; the classification of special Kähler metrics; Our Ph.D. graduates have also found good posi- the study of symplectic invariants, especially in dimen- tions. Radu Cebanu is now a postdoctoral fellow sion 4; non-linear partial differential equations in Rie- at Boston College; Xiangwen Zhang and François mannian geometry, convex geometry, and general rel- Charest are both postdocs at Columbia University; ativity; and Hamiltonian dynamical systems. François Charette is doing a postdoc at Tel Aviv and at the ETH in Zurich; and Mark Hagen has accepted a News and highlights position as an RTG Assistant Professor at the Univer- This year CIRGET was most pleased to welcome sity of Michigan (Ann Arbor). Frédéric Rochon, our new Tier 2 Canada Research CIRGET members also greatly benefit from the many Chair. Rochon is one of the top young experts in the international visitors who come to work with them. In field of global analysis on singular spaces, notably in- 2011–2012, 29 visitors stayed for short periods at the dex theory on manifolds with boundary. In collabo- Centre. ration with Richard Melrose, Rochon has established In the 2011–2012 academic year 7 summer research an impressive program of generalizing the K-theoretic students, 27 M.Sc. students, 28 Ph.D. students, and 26 approach of the Atiyah- Patody-Singer theorem to the postdoctoral fellows were supervised or cosupervised case of manifolds with boundary. A regular collabora- by CIRGET members. tor with several members of the group, Dmitry Jakob- son, an analyst from McGill University with interests Seminars in spectral geometry, quantum chaos, number theory, and graph theory, also joined the centre as an associate In 2011–2012, CIRGET invited five colloquium speak- member. We warmly welcome both new members to ers for the CRM–ISM mathematics colloquium lec- the group. ture series: Paul Biran (ETH, Zurich), Bun Wong Our graduate students continue to thrive and we are (Riverside), Alan Huckleberry (Ruhr University of delighted to announce that our recent Ph.D. graduate Bochum), Jason Starr (SUNY at Stony Brook), and Lud- Mark Hagen, who worked under the supervision of mil Katzarkov (Miami and Vienna). Dani Wise, was awarded the Carl Herz Prize for his CIRGET’s everyday scientific life revolves around its work in geometric group theory. weekly seminars and working groups where profes- sors, postdoctoral fellows and students meet on a reg-

71 Centre de recherches mathématiqes ular basis. The CIRGET Geometry and Topology Semi- Steven Boyer (UQAM) nar, organized by Steven Lu, is a general seminar series Topology of manifolds, low-dimensional geometry and attended by all CIRGET members. Of the 37 talks given topology this year, 28 were given by invited speakers who stayed Abraham Broer (Montréal) at the centre for short research visits. The Algebraic Algebraic transformation groups, invariant theory Geometry Seminar, organized by Karol Palka, hosted Virginie Charette (Sherbrooke) 21 talks. In addition, Mathieu Anel, a CIRGET post- Discrete group actions on affine varieties, Lorentz doctoral fellow, organized the CIRGET–LaCIM semi- manifolds, Riemann surfaces discretization, discrete nar with Viven Ripoll, a LaCIM postdoc. The aim of differential geometry the seminar was to bring together members of the two Olivier Collin (UQAM) laboratories so as to allow them to share research in- Invariants of knots and 3-manifolds arising from global terests. A total of 18 talks were given during the year. analysis Finally CIRGET graduate students from UQAM, the Octav Cornea (Montréal) Université de Montréal, and McGill participated in the Algebraic topology, dynamical systems CIRGET Junior Seminar, organized by doctoral stu- dents Kael Dixon and Ben Smith. This seminar gives Pengfei Guan (McGill) graduate students a forum to present their research to Partial differential equations, geometric analysis, sev- their peers. A total of 22 talks were given this year. eral complex variables Jacques Hurtubise (McGill) CIRGET working groups meet on a regular basis to ex- Algebraic geometry, integrable systems, gauge theory, plore specific topics over a period of several months moduli spaces or more. This year two working groups were active: Adam Clay organized a group that worked on low- André Joyal (UQAM) dimensional topology and Vestislav Apostolov orga- Algebraic topology, category theory nized a group that worked on Hermitian geometry. Niky Kamran (McGill) Geometric approach to partial differential equations Workshops, special sessions, and other François Lalonde (Montréal) Symplectic topology and geometry, global analysis on The following workshops were organized by CIRGET manifolds, infinite-dimensional transformation groups members at the CRM in 2011–2012. The interested Steven Lu (UQAM) reader will find their reports in the section General Chern number inequalities, semistability of tensorial Program. sheaves, log jets, log and hyperbolic geometry, alge- Workshop on Moving Frames in Geometry braic degeneracy June 13–17, 2011 Iosif Polterovich (Montréal) Organizers: Niky Kamran (McGill), Abraham Smith Geometric analysis, spectral theory, functional analy- (McGill), Francis Valiquette (McGill) sis, differential geometry, partial differential equations Complex Analytic and Algebraic Trends in the Geome- Frédéric Rochon (UQAM) try of Varieties Geometric analysis, global analysis on singular spaces, August 15–17, 2011 index theory on manifolds with boundary Organizers: Karol Palka (UQAM), Peter Russell Peter Russell (McGill) (McGill), Steven Shin-Yi Lu (UQAM) Algebraic geometry Johannes Walcher (McGill) Members of the Laboratory Mirror symmetry for open strings, nongeometric string compactifications Regular members Daniel T. Wise (McGill) Vestislav Apostolov (UQAM), Director Geometric group theory, low-dimensional topology Complex geometry, Kähler geometry

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Associate members retical methods, random matrices, isomonodromic de- formations, isospectral flows S. Twareque Ali (Concordia) Coherent states, wavelets, quantization techniques, Dmitry Jakobson (McGill) harmonic analysis, Wigner functions Pure mathematics, global analysis, spectral geometry, quantum chaos, harmonic analysis, eigenvalues and John Harnad (Concordia) eigenfunctions Mathematical physics, classical and quantum physics, geometrical methods, integrable systems, group theo- John A. Toth (McGill) Microlocal analysis, partial differential equations

GIREF – Groupe Interdisciplinaire de Recherche en Éléments Finis

Description chairholder, prepared an application for the renewal of the chair, in partnership with Michelin. The NSERC The recent advances in computer hardware and soft- Research Chair was renewed for five years with a total ware allow researchers to model and simulate physi- amount of approximately two million dollars. cal phenomena whose complexity is unheard of. These problems are characterized by nonlinear laws, non- Here is a list of the projects currently pursued at differentiable friction laws, large-deformation geome- GIREF; the reader will find more details on the GIREF tries, complex solid-solid or fluid-solid interactions, web site (giref.ulaval.ca). The names of investiga- problems in multiphysics, etc. Such problems can be tors are given within parentheses. found everywhere in industrial environments, espe- • The MEF++ project (A. Fortin, M. Fortin, R. Guénette, cially in the design and fabrication of high-technology J. Urquiza, A. Cloutier) products. Thus the members of GIREF (“Groupe Inter- • NSERC Research Chair in high performance scien- disciplinaire de Recherche en Éléments Finis,” or in En- tific computing (A. Fortin, principal investigator, and glish “Interdisciplinary Research Group in Finite El- J. Urquiza, associate investigator) ement Methods”) aim to develop original numerical • Numerical modelling in the wood sciences (P. methods for solving cutting-edge industrial problems Blanchet, M.-L. Dano, A. Cloutier, A. Fortin, Y. Fortin, in nonlinear mechanics. Their work concerns pure G. Gendron, D. Pelletier) mathematics, computer science, software engineering, • Modelling of flows in natural environments (J.-L. and engineering. The GIREF members propose gen- Robert, R. Therrien, Y. Secretan) eral methods that can be used for diverse industrial applications. The some 27 member researchers reflect • Biomedical modelling (A. Garon, M. Delfour, A. the interdisciplinary nature of the Laboratory and are Fortin, Y. Bourgault, Y. Belhamadia) based at the Université Laval, the École Polytechnique • Numerical modelling in biology (L. Buono, G. Daigle, de Montréal, as well as the Universities of Moncton, A. Fortin, D. Fortin, M. Fréchette, J. Urquiza) Ottawa, and Alberta. • Parallel computing (all the members of GIREF) • Design of bistable structures (M.-L. Dano, A. Fecteau, News and highlights M. Jean Saint- Laurent) GIREF is continuing its partnership with the Société • Modelling of thermally-induced torsion within com- Michelin through the development or their joint mod- posite tubes (M.-L. Dano, N. Verreault) elling tool (MEF++). A team led by Éric Chamberland is rewriting some components of MEF++ in order to Students, postdoctoral fellows, and visitors take advantage of parallel computing. The GIREF mem- The GIREF students were particularly honoured this bers have started to make computations of more than year. Benoît Pouliot was awarded the “Médaille du one hundred million degrees of freedom on the su- lieutenant-gouverneur du Québec,” Éloïse Boiteau was percomputer of the CLUMEQ network. We will follow awarded a Hydro-Québec scholarship, and Sophie up on that story… The first phase of the NSERC Re- Léger was awarded the Fernand-Landry scholarship. search Chair in high performance scientific comput- ing came to an end in October 2011. André Fortin, the

73 Centre de recherches mathématiqes

In the 2011–2012 academic year one undergraduate ulation of laminar and turbulent viscous flows, mod- student, 15 M.Sc. students, 15 Ph.D. students, and 3 elling and simulation of fluid-structure interactions postdoctoral fellows were carrying out research at Roger Pierre (Laval) GIREF. Numerical analysis of partial differential equations José Urquiza (Laval) Seminars Numerical analysis, control of partial differential equa- tions In 2011–2012 the seminar held by GIREF included 21 talks. Associate members Members of the Laboratory Pierre Blanchet (FPInnovations) Nanotechnology for wood products Regular members Alain Charbonneau (UQO) André Fortin (Laval), Director Numerical simulation of optical wave guides, finite ele- Finite elements method, instationary viscous flows, ments method, numerical methods, statistical machine mixing problems translation, automated text categorization André Garon (Polytechnique Montréal), Deputy Di- Alain Cloutier (Laval) rector Forestry, forest engineering Thermohydraulics, fluid mechanics, finite elements Marie-Laure Dano (Laval) method, hydraulic turbines, mechanics of biofluids: Mechanics and production of composite materials, in- stents and pumps telligent mechanical systems Youssef Belhamadia (Alberta) Claire Deschênes (Laval) Mathematical modelling and numerical simulation of Axial hydraulic turbines phase change problems, adaptive meshing for insta- Guy Dumas (Laval) tionary problems in 2 and 3 dimensions, numerical Mechanical engineering, physics of fluids modelling of cryosurgery, numerical modelling of the Mohamed Farhloul (Moncton) electromechanical wave in the heart Finite elements and finite volumes method, partial dif- Yves Bourgault (Ottawa) ferential equations, applications of the mixed finite el- Computational fluid dynamics, numerical methods, fi- ements method to fluid mechanics, numerical analysis nite elements method, mathematical modelling, me- Marie-Isabelle Farinas (UQAC) chanics of continuous media Modelling, numerical simulation, computational fluid Michel C. Delfour (Montréal) mechanics, design of turbo engines (cardiac pump), op- Control, optimization, design, shells, calculus, biome- timization chanics Vincent François (UQTR) Michel Fortin (Laval) Integration of the finite elements method into Numerical analysis of partial differential equations, computer-aided design numerical methods in fluid mechanics, optimization Yves Fortin (Laval) and optimal control for partial differential equations Forestry, forest engineering Robert Guénette (Laval) Augustin Gakwaya (Laval) Numerical methods in non-Newtonian fluid mechan- Aerospatial and aeronautical engineering, numerical ics, rheological models, Hamiltonian formulation modelling, computer-assisted design Hassan Manouzi (Laval) Guy Gendron (Laval) Numerical analysis, applications of mathematics to en- Composite materials, optimization and modelling of gineering structures Dominique Pelletier (Polytechnique Montréal) Jean-François Hétu (NRC-IMI) Fluid mechanics and heat transfer, finite elements Numerical modelling of processes method, adaptive finite elements methods for com- Jean-Loup Robert (Laval) pressible and incompressible flows, modelling and sim- Numerical models of free surface flows, transport and

74 Research Laboratories diffusion models with stochastic components, unified tion and adaptation, error estimation, hydrodynamics modelling in a saturated and aerated environment in 2 dimensions, advection-diffusion phenomena Yves Secretan (INRS-ETE) René Therrien (Laval) Numerical methods for finite elements, mesh genera- Underground water flows, hydrology, geothermics

LaCIM – Laboratoire de Combinatoire et d’Informatique Mathématique

Description Students, postdoctoral fellows, and visitors

LaCIM (French acronym meaning “Combinatorics and During the summer of 2011 LaCIM hosted the fol- Mathematical Computer Science Laboratory”) is home lowing researchers: Carsten Lange (Freie Universität to mathematics and theoretical computer science re- Berlin); Matthew Dyer (Notre-Dame); Cesar Cebal- searchers whose interests comprise discrete mathe- los (Freie Universität Berlin). In the fall of 2011, matics and the mathematical aspects of computer sci- LaCIM hosted: Mark Haiman (Berkeley); Frédéric Pa- ence. Founded in 1989, LaCIM includes 15 regular tras (Nice); Viviane Pons (Marne-la-Vallée); Samuele members, 5 associate members, and 16 collaborating Giraudo (Marne-la-Vallée); Susanna Fishel (Arizona members. It welcomes postdoctoral fellows and its reg- State); Valérie Berthé (LIAFA Paris). Finally, in the win- ular members supervise or cosupervise many M.Sc. ter of 2012, LaCIM hosted the following researchers: and Ph.D. students, as well as undergraduate and cégep Federico Ardila (San Francisco); Tom Denton (York); summer research students. Many renowned mathe- Carolina Benedetti (York); Roland Friedrich (Hum- maticians visit LaCIM and collaborate with its mem- boldt); Luigi Santocanale (Marseille); Doron Zeilberger bers in the following areas: enumerative and bijec- (Rutgers); Nicolas Thiéry (Orsay); Brant Jones (James tive combinatorics, theory of species, algebraic com- Madison). binatorics, combinatorics of finite and infinite words, In the 2011–2012 academic year 9 undergraduate stu- discrete geometry, theory of languages and automata, dents, 21 M.Sc. students, 37 Ph.D. students, and 14 post- Gray codes, bioinformatics, and combinatorial opti- doctoral fellows were supervised or cosupervised by mization. LaCIM members.

News and highlights Workshops, special sessions, and others

Thanks to the LIRCO, an international laboratory of The following events were organized by LaCIM mem- the French CNRS that includes French researchers as bers. The reader will find reports on them in the section well as members of LaCIM, many French researchers General Program. (a dozen in 2011–2012) have visited LaCIM. LaCIM has now 8 postdoctoral fellows, including 4 that arrived Combinatorial Algebra Meets Algebraic Combinatorics this year: Alejandro Morales, Puiman Ng, Mathieu January 20–22, 2012, UQAM Guay-Paquette, and Qiu Yu. Furthermore 8 undergrad- Organizers: François Bergeron (UQAM), Franco Saliola uates carried out research internships during the sum- (UQAM), Luis Serrano (UQAM) mer of 2012, including some who had received an SAGE Days at CRM NSERC scholarship for doing so. François Bergeron May 5–11, 2012, CRM took part in an evening dedicated to science (Science et Organizers: Srečko Brlek (UQAM), Sébastien Labbé contes) at the “Cœur des science” (UQAM); he also took (UQAM), Franco Saliola (UQAM) part in the “Gala des Concours scientifiques Mont- morency.” François Bergeron and Gilbert Labelle regu- LaCIM members also organized mini-courses and a larly gave lectures on mathematics in cégeps and col- workshop under the title “Coxeter groups meet con- leges. vex geometry”, from August 13 to 22, 2011. The orga- nizers were Christophe Hohlweg, Jean-Philippe Labbé, Carsten Lange, and Vivien Ripoll. The mini-courses were given by Christophe Hohlweg (Geometry of Cox- eter groups and root systems), Carsten Lange (Introduc-

75 Centre de recherches mathématiqes tion to polytopes, Cambrian lattices and Cambrian fans, Franco Saliola (UQAM) generalized permutahedra), Vincent Pilaud (Brick poly- Algebraic combinatorics, group representations topes and generalized associahedra), and Matthew Dyer Timothy R. S. Walsh (UQAM) (Bruhat intervals and polyhedral cones). Algorithmics, enumerative combinatorics, graph the- The XXIIIrd Meeting on Representation Theory ofAl- ory gebras (September 16 and 17, 2011, at Bishop’s Univer- sity) was organized by a team of 7 researchers, includ- Associate members ing three LaCIM members: Ibrahim Assem, Thomas Pierre Lalonde (Maisonneuve) Brüstle, and Shiping Liu, all from the Université de Enumerative and bijective combinatorics, alternating Sherbrooke. sign matrices, enumeration of involutions with respect to various parameters, use of Pfaffians and determi- Members of the Laboratory nants in enumeration Regular members Cédric Lamathe (UQAM) Combinatorics of tree-like structures, theory of Srečko Brlek (UQAM), Director species, indicator series of partially labeled structures Combinatorics of words, algorithmics and asymmetric structures Ibrahim Assem (Sherbrooke) Luc Lapointe (Talca) Representation theory Algebraic combinatorics, symmetric functions, inte- Anne Bergeron (UQAM) grable systems, supersymmetries Bioinformatics Odile Marcotte (UQAM & CRM) François Bergeron (UQAM) Combinatorial optimization, integer programming, Combinatorics, algebra, representations of finite graph theory groups Dominic Rochon (UQTR) Thomas Brüstle (Sherbrooke & Bishop’s) Complex analysis, hypercomplex numbers Algebraic combinatorics, cluster algebras, triangula- tions of surfaces, stochastic differential equations, Collaborating members mathematical models in finance Marcello Aguiar (Texas A&M) Cedric Chauve (Simon Fraser & UQAM) Algebraic combinatorics, non-commutative algebra, Enumerative combinatorics, trees, bioinformatics Hopf algebras and quantum groups, category theory Sylvie Hamel (Montréal) Robert Bédard (UQAM) Bioinformatics and algorithms, theory of languages Representations of finite groups, Lie theory and automata, algebraic combinatorics Luc Bélair (UQAM) Christophe Hohlweg (UQAM) Mathematical logic, model theory Algebra, algebraic combinatorics, convex geometry Nantel Bergeron (York) Gilbert Labelle (UQAM) Applied algebra Enumerative combinatorics, analysis Pierre Bouchard (UQAM) Shiping Liu (Sherbrooke) Commutative algebra, algebraic geometry and combi- Representation theory natorics Vladimir Makarenkov (UQAM) Michel Bousquet (Vieux-Montréal) Computational biology, mathematical classification Enumeration of combinatorial structures, planar maps Marni Mishna (Simon Fraser) and cacti, theory of species, Lagrange inversion formu- Algorithms and enumerative, analytical, and algebraic las combinatorics Yves Chiricota (UQAC) Christophe Reutenauer (UQAM) Computer graphics, mathematical methods in com- Algebraic combinatorics, noncommutative algebra, au- puter graphics, combinatorics, computational geome- tomata theory, coding theory, free algebras try, symbolic computation

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Sylvie Corteel (LIAFA & CNRS) Louise Laforest (UQAM) Enumerative and bijective combinatorics, partitions of Data structures, combinatorics, asymptotic analysis, integers, q-series quaternary trees Adriano Garsia (UC San Diego) Daniel Lemire (TÉLUQ) Algebraic combinatorics, symmetric functions, har- Database theory, data warehousing, multidimensional monic and coinvariant spaces, quasiharmonic and databases (OLAP), data mining, time series, collabora- quasi-invariant functions tive filtering, information retrieval Alain Goupil (UQTR) Simon Plouffe Combinatorics, algebra, linear representations of Integer sequences, generalized expansions of real num- groups, symmetric group bers André Joyal (UQAM) Xavier G. Viennot (Bordeaux 1) Algebraic topology, category theory Enumerative, algebraic, and bijective combinatorics, Jacques Labelle (UQAM) interactions between combinatorics, theoretical infor- Combinatorics, topology matics, and theoretical physics

Mathematical Analysis

Description ested reader will find reports on all those activities in the section Thematic Program. Some Laboratory mem- At the same time classical and central to modern math- bers were also among the organizers of the Summer ematics, analysis involves the study of continuous sys- School (SMS) on “Metric Measure Spaces: Geometric tems, from dynamical systems to solutions of par- and Analytic Aspects” (CRM, June 27–July 8, 2011). tial differential equations and spectra of operators. In Some members of the Analysis Laboratory (e.g., Galia 2011–2012 the Laboratory included 28 regular and 10 Dafni, Javad Mashreghi, and Vojkan Jakšić) were suc- associate members working at 9 different universities cessful in attracting external funding for hosting visi- in Québec, Ontario, the United Kingdom, and France. tors from France. The members of the Laboratory work in the following areas: harmonic analysis, complex analysis and several Students, postdoctoral fellows, and visitors complex variables, potential theory, functional analy- sis, Banach algebras, microlocal analysis, analysis on In the 2011–2012 academic year 3 undergraduate stu- manifolds, nonsmooth analysis, spectral theory, partial dents, 38 M.Sc. students, 43 Ph.D. students, and 19 post- differential equations, geometric analysis, ergodic the- doctoral fellows were supervised or cosupervised by ory and dynamical systems, control theory, mathemat- members of the Mathematical Analysis Laboratory. ical physics, applied mathematics, probability, nonlin- ear analysis, nonlinear differential equations, topolog- Seminars ical methods in differential equations, fluid dynamics, and turbulence. The members of the Mathematical Analysis Labora- tory organize several seminars at four main locations. News and highlights The Université Laval hosts an Analysis Seminar, which Robert Seiringer received an E.W.R. Steacie Memorial featured 15 talks in 2011-2012. Alina Stancu (Concor- Fellowship award in 2012. Laboratory members coor- dia), Alexey Kokotov (Concordia), and Dmitry Jakob- ganized a series of lectures by Tadashi Tokieda (Cam- son (McGill) jointly organized the McGill/Concordia bridge) that took place in April 2012. Obviously Lab- Analysis Seminar, which featured 38 talks in 2011– oratory members devoted much time and energy to 2012. Dmitry Jakobson and Iosif Polterovich (Univer- the organizing of the thematic semester on “Geomet- sité de Montréal) organized a seminar in spectral the- ric Analysis and Spectral Theory”, which took place at ory that included 20 meetings. The Seminar on geo- the CRM in 2012. The semester featured 6 workshops metric and computational topology held at the Uni- (including one in June 2012 and one in July 2012) and versité de Sherbrooke featured one talk in 2011–2012 series of lectures by three Aisenstadt chairs. The inter- and the McGill/Concordia Working seminar in analy-

77 Centre de recherches mathématiqes sis featured two talks (during the winter of 2012). In ad- S. W. Drury (McGill) dition, eight CRM-ISM Colloquium speakers were in- Harmonic analysis, matrix theory vited by Laboratory members. Richard Fournier (Dawson & CRM) Complex analysis, function theory Workshops, special sessions, and others Marlène Frigon (Montréal) Apart from the SMS and the thematic semester work- Nonlinear analysis, differential equations, fixed point shops mentioned above, the Laboratory sponsored the theory, critical point theory, multivalent analysis following event, whose report is included in the sec- Paul M. Gauthier (Montréal) tion General Program. Complex analysis, holomorphy, harmonicity, analytic approximation Complex Analysis and Potential Theory Pawel Gora (Concordia) A Conference in Honour of Paul M. Gauthier and Kohur Ergodic theory, dynamical systems, fractal geometry Gowrisankaran June 20–23, 2011, CRM Frédéric Gourdeau (Laval) Organizers: André Boivin (Western Ontario), Javad Banach algebras, cohomology, amenability, functional Mashreghi (Laval) analysis Vojkan Jakšić (McGill) Vojkan Jakšić and Robert Seiringer, both of them Lab- Mathematical physics, quantum statistical mechanics, oratory members, were among the organizers of the random Schrödinger operators following school, whose report is also to be found in the section General Program. Tomasz Kaczynski (Sherbrooke) Topological methods, Conley index, applications to dy- Summer School on Non-Equilibrium Statistical Mechan- namical systems ics Ivo Klemes (McGill) July 1–29, 2011, CRM Harmonic analysis, trigonometric series Organizers: Laurent Bruneau (Cergy-Pontoise), Alexey Kokotov (Concordia) Vojkan Jakšić (McGill), Roberto Livi (Firenze), Claude- Spectral geometry of Riemann surfaces, hyperbolic Alain Pillet (Toulon), Robert Seiringer (McGill) partial differential equations Members of the Laboratory Paul Koosis (McGill) Harmonic analysis Regular members Javad Mashreghi (Laval) Dmitry Jakobson (McGill), Director Complex analysis, harmonic analysis, Hardy spaces Pure mathematics, global analysis, spectral geometry, Iosif Polterovich (Montréal) quantum chaos, harmonic analysis, eigenvalues and Geometric analysis, spectral theory, functional analy- eigenfunctions sis, differential geometry, partial differential equations Line Baribeau (Laval) Thomas J. Ransford (Laval) Complex and functional analysis, Banach algebras, Complex and harmonic analysis, functional analysis holomorphic iterations, discrete groups and theory of operators, spectral analysis, potential Abraham Boyarsky (Concordia) theory Dynamical systems Dominic Rochon (UQTR) Francis H. Clarke (Lyon 1) Complex analysis, hypercomplex numbers Nonlinear and dynamic analysis, control theory, calcu- Jérémie Rostand (Laval) lus of variations Complex analysis, experimental mathematics Galia Dafni (Concordia) Christiane Rousseau (Montréal) Harmonic analysis, partial differential equations, com- Dynamical systems, bifurcations, qualitative theory, plex variables polynomial systems, analytic invariants, integrable Donald A. Dawson (Carleton) systems Probability, stochastic processes

78 Research Laboratories

Dana Schlomiuk (Montréal) Kohur Gowrisankaran (McGill) Global analysis, dynamical systems, singularities, bi- Potential theory furcations, algebraic curves, primary integral Pengfei Guan (McGill) Robert Seiringer (McGill) Partial differential equations, geometric analysis, sev- Many-body quantum systems, Bose-Einstein conden- eral complex variables sates John Harnad (Concordia) Alexander Shnirelman (Concordia) Mathematical physics, classical and quantum physics, Applications of geometric analysis to fluids and “weak” geometrical methods, integrable systems, group theo- solutions of the Euler and Navier-Stokes equations retical methods, random matrices, isomonodromic de- Alina Stancu (Concordia) formations, isospectral flows Geometric analysis Niky Kamran (McGill) Ron J. Stern (Concordia) Geometric approach to partial differential equations Functional analysis and theory of operators, linear and Dmitry Korotkin (Concordia) nonlinear systems, non-smooth analysis, stability, op- Integrable systems, isomonodromic deformations, timal order classical and quantum gravity, Frobenius varieties John A. Toth (McGill) Nilima Nigam (Simon Fraser) Spectral theory, semi-classical analysis, microlocal Applied analysis, numerical methods in electromag- analysis, Hamiltonian mechanics netism Yiannis N. Petridis (University College London) Associate members Automorphic forms and their spectral theory, analytic Octavian Cornea (Montréal) number theory, spectral and scattering theory of man- Algebraic topology, dynamical systems ifolds Richard Duncan (Montréal) Samuel Zaidman (Montréal) Ergodic theory, martingale theory, probability theory Functional analysis and differential equations in ab- in Banach spaces stract spaces, pseudo-differential operators

Mathematical Physics

Description herent states; wavelets; supersymmetry; the symmetry analysis of PDEs and difference equations; representa- The mathematical physics group is one of the oldest tion theory of Lie groups and quantum groups; and the and most active at the CRM. It consists of 18 regu- mathematical structure of classical and quantum field lar members, 8 local associate members, all full-time theories. faculty members at one of the participating universi- ties, and 6 external associate members working per- News and highlights manently at universities and research laboratories in Europe or the United States. The group carries out Professor Alexander Maloney, of the physics depart- research in many of the most active areas of mathe- ment at McGill University, became an associate mem- matical physics: coherent nonlinear systems in fluids, ber in March 2012. Professor Alexander Turbiner (In- optics, and plasmas; classical and quantum integrable stituto de Ciencias Nucleares, UNAM, Mexico) and Pe- systems; the spectral theory of random matrices; per- ter Zograf (Steklov Mathematical Institute, St. Peters- colation phenomena; conformal field theory; quantum burg) also became associate members (in this case, ex- statistical mechanics; spectral and scattering theory ternal associate members) in March, 2012. of random Schrödinger operators; quasi-crystals; rela- Laboratory members received many prizes and distinc- tivity; spectral transform methods; foundational ques- tions in 2011–2012. Marco Bertola was accorded the tions in quantization; asymptotics of eigenstates; co- Dean’s Award for Distinguished Scholarship at Con-

79 Centre de recherches mathématiqes cordia University in November 2011. Robert Branden- • Marco Bertola was an invited lecturer at the Win- berger held a Killam Research Fellowship until August ter School on Random Matrices and Integrable Systems 2011. He was also awarded the CAP/CRM Prize for (Les Houches, France, March 4-9, 2012). Mathematical Physics in 2011. Michel Grundland’s pa- • Robert Brandenberger gave invited lectures at a per, coauthored with Sarah Post and entitled “Gener- number of international workshops and conferences in alized symmetries of integrable equations and soliton 2011–2012, in particular: “Scenarios of Early Universe surfaces” (J. Phys. A: Math. Theor. 44, 165203) was cho- Cosmology: Physical and Philosophical Challenges” sen for inclusion in the Institute of Physics (IOP) Select (Workshop on Philosophy of Cosmology, Granada, list. John Harnad was reappointed for a further three Spain, September 22–23, 2011), and “Fluctuations in years as Affiliate Member, Perimeter Institute ofThe- Non-Singular Bouncing Cosmologies from Type II Su- oretical Physics, and also as Fellow of the Science Col- perstrings” (Workshop on String Theory and Cosmol- lege, Concordia University. Other Lab members who ogy, Pennsylvania, March 16–18, 2012). have been named affiliates of the Perimeter Institute • Robert Conte was invited to give a lecture at the “Ge- are: Robert Brandenberger, Keshav Dasgupta, Alexan- ometrical Methods in Mathematical Physics” Interna- der Maloney, Manu Paranjape, and Johannes Walcher. tional Conference (Moscow State University, Decem- Yvan Saint-Aubin won the Excellence in Teaching ber 12–17, 2011). Award of the Canadian Mathematical Society in 2011. • Keshav Dasgupta was an invited lecturer at the Great In 2011–2012 Jacques Hurtubise served as President of Lakes String Conference (Chicago, April 29–May 1, the Canadian Mathematical Society. Robert Seiringer 2011). was awarded a Steacie Memorial Fellowship by NSERC • Bertrand Eynard was an invited speaker at the work- in 2012, and a Willian Dawson Scholarship at McGill. shop “Stochastic Analysis” at Oberwolfach on May 29– Pavel Winternitz was awarded the Česká Hlava Prize June 4, 2011, and at the Moscow, September 2011 work- on November 18, 2011, for two cycles of articles on su- shop on Random Processes, Conformal Field Theory perintegrable systems and on symmetries of difference and Integrable Systems. He also gave an invited lecture equations. He was also awarded the Best Paper Prize by series on “Map Enumerations” at the Summer School the Journal of Physics A for the paper “An infinite fam- in Random Geometry (Iceland, August 2011). ily of solvable and integrable quantum systems on a • Jean-Pierre Gazeau gave an invited talk entitled plane” (together with Frédérick Tremblay and Alexan- “Frame quantization or exploring the world like a der Turbiner). Luc Vinet was awarded the CAP-CRM starfish” at the conference FLAME12 (Acoustics Re- Prize for 2012 (see the section CRM Prizes). search Institute, Vienna, May 2012). Several Laboratory members were also appointed to • Michel Grundland was an invited speaker at the In- editorial or scientific governing boards in 2011–2012. ternational Conference on Quantum Theory and Sym- For instance John Harnad was named member of the metries 7 (Prague, August 2011). editorial board of the new journal Analysis and Mathe- • John Harnad gave the invited talk “Tau functions and matical Physics, published by Springer Verlag. Bertrand convolution symmetries” at the XIIIth International Eynard was named member of the board of the journal Conference on Geometry, Integrability and Quantiza- Random Matrices, Theory and Applications (World Sci- tion (Varna, Bulgaria, June 3–8, 2011). He was also an entific). Robert Seiringer continued to be Associate Ed- invited participant at the Program on Complex Analy- itor for Letters in Mathematical Physics and member of sis and Integrable Systems held at the Mittag-Leffler In- the editorial boards of the Journal of Statistical Physics stitute (Stockholm, September 9–November 30, 2011). and the Journal of Mathematical Physics. • Jacques Hurtubise gave invited talks at the Newton Invited talks by Laboratory members at international Insitute and the University of Leeds (in the summer of conferences and workshops in 2011–2012 are too nu- 2011). merous to be all listed here but we will mention some • Dmitry Korotkin gave invited talks at the conference of them. “Painlevé equations and related topics” (Euler Inter- • Syed Twareque Ali was an invited plenary lecturer national Mathematical Institute, St. Petersburg, Rus- (giving an Expository Quantum Series of five lectures) sia, June 17–23, 2011), at the conference “Geometri- at Putra University, Selangor, Malaysia (January 9–13, cal Methods in Mathematical Physics” (Moscow State 2012).

80 Research Laboratories

University, Moscow, December 12–17, 2011), and at The former students and postdoctoral fellows ofthe the AMS Special Session on “Algebraic and Geometric PhysMath Laboratory are doing well. Oksana Yermo- Aspects of Integrable Systems and Random Matrices” layeva received a renewal of her Marie Curie Research (Boston, January 5–7, 2012). Fellow position (Université Paris 6) for 2011–2012. In • Manu Paranjape was an invited speaker at the 2011 the summer of 2011, Mattia Cafasso was appointed CAP congress (St. John’s, Newfoundland, June 13–17, maître de conférences at the Université d’Angers. 2011). Seung-Yeop Lee was appointed Assistant Professor at • Luc Vinet gave invited talks at the International Con- the University of Southern Florida after having com- ference on Asymptotics and Special Functions (Hong pleted his appointment as Sherman Fairchild Research Kong, China, May 29–June 3, 2011), the OPSFA 11 Fellow at Caltech. Dong Wang continued a similar conference on Orthogonal Polynomials, Special Func- extended research appointment at the University of tions and Applications (Madrid, Spain, August 29– Michigan. In 2011–2012 Benjamin Young continued an September 2, 2011), the International Conference on extended postdoctoral appointment in Stockholm; in Special Functions and Orthogonal Polynomials of Lie 2012 he was appointed assistant Professor at the Uni- Groups and their Applications (Decin, Czech Republic, versity of Oregon. Olivier Marchal continued his post- August 14–20, 2011), and the conference on Quantum doctoral position at the University of Alberta, begun in Theory and Symmetries 7 (Prague, Czech Republic, Au- January 2011; he was appointed maître de conférences gust 7–13, 2011). at the Institut Camille Jordan (Lyon). Tiago Dinis da Fonseca was recruited for a further postdoctoral ap- • Pavel Winternitz gave the closing talk (“Review of pointment by the Laboratoire de Physique Théorique current status of Superintegrability, Symmetries and (CNRS, Université de Savoie). Ferenc Balogh obtained Perturbation Theory (SPT)”) at the conference on Sym- a further postdoctoral appointment at the Scuola Inter- metries and Perturbation Theory (Otranto, Italy, June nazionale Superiore di Studi Avanzate (SISSA) in Tri- 5–12, 2011), an invited talk (“Superintegrability with este. In 2012 Sarah Post was named Assistant Profes- higher order integrals of motion”) at the conference sor in the Mathematics Department of the University on Quantum Theory and Symmetries 7 (Prague, Czech of Hawaii at Monoa. Republic, August 7–13, 2011), and an invited talk on superintegrability at the Symposium on Superintegra- In the period between June 2011 and August 2012 there bility, Exact Solvability, and Special Functions (Cuer- were a total of 38 scientific visitors at the PhysMath navaca, México, February 21–24, 2012). Laboratory. These included seminar speakers, collabo- rators in joint research projects, and external associate Students, postdoctoral fellows, and visitors members. In the 2011–2012 academic year 11 under- graduate students, 29 M.Sc. students, 44 Ph.D. students, The following were the postdoctoral fellows and re- and 27 postdoctoral fellows were supervised or cosu- search associates working under the supervision of pervised by members of the Mathematical Physics Lab- one or more of the regular members of the Laboratory oratory. (the names of the supervisors are listed in brackets): Ferenc Balogh (J. Harnad); Alexander Bihlo (P. Win- Seminars ternitz); Tiago Dinis da Fonseca (M. Bertola, J. Har- nad); Melita Hadzagic (J. Patera); Caroline Kalla (D. The usual weekly Seminar Series in Mathematical Korotkin, V. Shramchenko); Aleksi Kurkela (R. Bran- Physics took place at the CRM every Tuesday after- denberger); Josh Lapan (R. Brandenberger, J. Walcher); noon from September 2011 until May 2012, with ac- Shunji Matsuura (R. Brandenberger, K. Dasgupta, J. tive participation by members, visitors, postdoctoral Walcher); Sarah Post (A. Grundland, L. Vinet, P. Win- fellows, and students. Yvan Saint-Aubin was the or- ternitz); Danilo Riglioni (P. Winternitz); Pat Scott (R. ganizer of this seminar series in 2011–2012. Approx- Brandenberger); Jihye Seo (R. Brandenberger, K. Das- imately half the talks were given by visiting invited gupta, J. Walcher, J. Harnad); Marzena Szajewska (J. speakers, and the rest by regular and associate Lab- Patera); Brett Underwood (R. Brandenberger); Yi Wang oratory members, postdoctoral fellows, and Labora- (R. Brandenberger); Matthias Westrich (V. Jakšić, R. tory visitors. In addition, the Working Seminar on Inte- Seiringer); Guofo Yu (L. Vinet). grable Systems, Random Matrices, Random Processes continued, taking place every Thursday afternoon at

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Concordia, with active participation of many Labora- Robert Brandenberger (McGill) tory members, postdoctoral fellows, students, and visi- Theoretical Cosmology tors. In 2011–2012 this seminar was organized by Tiago Keshav Dasgupta (McGill) Dinis da Fonseca. Heavy ion collision theory in the energy range 30MeV/nucleon to many GeV/nucleon Workshops and Special Sessions Alfred Michel Grundland (UQTR) We mention here some of the events organized by Lab- Symmetry of differential equations in physics oratory members. Richard L. Hall (Concordia) • Syed Twareque Ali was coorganizer of the XV In- Spectra of Schrödinger, Klein-Gordon, Dirac and ternational Workshop on Wavelets, Differential Equa- Salpeter operators, many-body problems, relativis- tions, Number Theory, Mechanics and Applications tic scattering theory, iterative solution to ODEs and (University of Havana, February 20–24, 2012). boundary-value problems • Marco Bertola was coorganizer of the workshop on Jacques Hurtubise (McGill) Formal and Analytic Solutions of Differential and Dif- Algebraic geometry, integrable systems, gauge theory, ference Equations (Banach Mathematical Research and moduli spaces Conference Center, Bedlewo, Poland, August 2011). Véronique Hussin (Montréal) • Robert Brandenberger was the main organizer of the Group theory, Lie algebras and applications in physics, BIRS 5-day workshop entitled “Self Adjoint Extensions supersymmetries in classical and quantum mechanics and Singularity Resolution in String Theory and Quan- Dmitry Korotkin (Concordia) tum Gravity” (BIRS, Canada, August 21–26, 2011). Integrable systems, isomonodromic deformations, • Jacques Hurtubise was coorganizer of the workshop classical and quantum gravity, Frobenius varieties “Advances in hyperkähler and holomorphic symplec- Pierre Mathieu (Laval) tic geometry” (BIRS, Canada, March 11–16, 2012). Conformal field theory, classical and quantum inte- • Robert Seiringer was coorganizer of the summer grable systems, affine Lie algebras school “Current Topics in Mathematical Physics” at the Manu Paranjape (Montréal) Erwin Schrödinger Institute (Vienna, Austria, August Theoretical particle physics: field theory, solitons, non- 16–24, 2011). commutative geometry, alternative gravity • Johannes Walcher was a coorganizer of the work- Jiří Patera (Montréal) shop “Hodge theory and string duality” (BIRS, Canada, Applications of group theory, quasi-crystals, Lie alge- December 4–9, 2011). bras Members of the Laboratory Yvan Saint-Aubin (Montréal) Conformal field theory, statistical mechanics, 2- Regular members dimensional phase transition model Robert Seiringer (McGill) John Harnad (Concordia), Director Quantum many-body systems, Bose-Einstein conden- Mathematical physics, classical and quantum physics, sates, Ginzburg-Landau theory, Gross-Pitaevskii the- geometrical methods, integrable systems, group theo- ory, bosons retical methods, random matrices, isomonodromic de- formations, isospectral flows Vasilisa Shramchenko (Sherbrooke) Frobenius manifolds, integrable systems, Riemann- S. Twareque Ali (Concordia) Hilbert problems, isomonodromic deformations of sys- Coherent states, wavelets, quantization techniques, tems of linear differential equations, function theory harmonic analysis, Wigner functions on Riemann surfaces Marco Bertola (Concordia) Luc Vinet (Montréal) Axiomatic quantum field theory, invariant theory of Symmetry properties of systems, special functions discrete groups, random matrices, isomonodromic de- formations Johannes Walcher (McGill) Mirror symmetry for open strings, non-geometric string compactifications

82 Research Laboratories

Pavel Winternitz (Montréal) Dmitry Jakobson (McGill) Methods of group theory in physics, nonlinear phe- Pure mathematics, global analysis, spectral geometry, nomena, symmetries of difference equations, superin- quantum chaos, harmonic analysis, eigenvalues and tegrability eigenfunctions Vojkan Jakšić (McGill) Associate members Mathematical physics, quantum statistical mechanics, Robert Conte (CEA/Saclay) random Schrödinger operators Integrable and partially integrable systems, Painlevé Niky Kamran (McGill) analysis, exact solutions, finite difference equations Geometric approach to partial differential equations Chris Cummins (Concordia) François Lalonde (Montréal) Group theory, modular functions, moonshine Symplectic topology and geometry, global analysis on Stéphane Durand (Édouard-Montpetit) manifolds, Hamiltonian systems Classical and quantum physics, mathematical physics, Decio Levi (Roma Tre) symmetries, parasupersymmetries, fractional super- Symmetries of differential and difference equations, symmetries, KdV equations, quantum mechanics, rel- integrable nonlinear equations on the lattice and re- ativity ductive perturbation theory on the lattice Bertrand Eynard (CEA/Saclay) Alexander Shnirelman (Concordia) Matrix models, integrable systems, string theory, rela- Applications of geometrical analysis to fluids and tionship between matrix models, integrability, and al- “weak” solutions of the Euler and Navier-Stokes equa- gebraic geometry tions Jean-Pierre Gazeau (Paris Diderot) John A. Toth (McGill) Coherent states, wavelets, relativistic quantum frames, Spectral theory, semi-classical analysis, microlocal symmetry groups for beta-lattices analysis, Hamiltonian mechanics Alexander Its (IUPUI) Carolyne M. Van Vliet (Montréal & Miami) Soliton theory, integrable systems, special functions, Non-equilibrium statistical mechanics, fluctuations mathematical physics and stochastic processes, quantum transport in con- densed matter, electronic behavior in submicron quan- tum devices

PhysNum

Description • Grova studies neurovascular models in epilepsy; • Lina studies sparse representations, inverse prob- Applied mathematics now plays an important role lems, and brain wave synchronization; and in the biomedical field and especially the neuro- • Lina analyzes scale-invariant processes in electro- sciences. The research activity at PhysNum has two physiology. main themes: pharmacometrics and brain imaging. In particular Fahima Nekka and her team conduct research in phar- • Jean-Marc Lina (École de technologie supérieure) macometrics, a discipline whose goal is to interpret and Habib Benali (Université Pierre et Marie Curie) and describe pharmacological phenomena in a quanti- work on the multimodal imaging of the spinal cord; tative manner, so as to support rational therapeutic de- cisions and improvement of patient health. They have • Lina and Christophe Grova (McGill University) developed a whole framework of probabilistic pharma- work on multiresolution and multimodal imaging in cometrics in which different sources of variability and magneto-electrophysiology; the nonlinearity of the system are accounted for. The • Benali and Maxime Descoteaux (Université de Sher- team is working on compliance metrics and ranking brooke) study models of the anatomical and functional and on direct and inverse problems related to patient connectivity of the brain; drug behaviour and the therapeutic effect of drugs. It

83 Centre de recherches mathématiqes is conceiving tools that shed new light on drug devel- • Fahima Nekka and her team are studying the vari- opment and evaluation in terms of efficacy and bioe- ability in drug use and its therapeutic consequences. quivalence; revisiting classical concepts in pharmacol- ogy and updating their formulation; developing mod- Students els for drug interactions; integrating physiology with behaviour to create a real fingerprint of drugs; inte- In the 2011–2012 academic year 19 M.Sc. students, 12 grating advanced hematopoietic models with PK/PD Ph.D. students, and 8 postdoctoral fellows were super- to improve concurrent therapy consisting of oncologi- vised or cosupervised by PhysNum members. Among cal drugs and their adjuvants. the students of the brain imaging group within Phys- Num, let us mention C. Bonnery (M.Sc.); T. Hedrich News and highlights (M.Sc.); J. Godbout (M.Ing.); Y. Zérouali (Ph.D.); R. Chowdhury (Ph.D.); A. Machado (Ph.D.); P. J. Toussaint Here are a few of the current projects of PhysNum (doctoral student at LINeM); and C. Matteau-Pelletier members. (Ph.D.). • One of the main research endeavours of PhysNum researchers is the development of mathematical mod- Members of the Laboratory els in multimodal brain imaging, with the goal of un- derstanding brain plasticity in humans. There are nu- Regular members merous applications of this research: sleep and ag- Jean-Marc Lina (ÉTS), Director ing (Lina); the consequences of a brain or spinal cord Wavelets, statistical modelling and brain imaging, ma- trauma (Benali); diagnosis of Alzheimer’s Disease (Be- chine learning nali); preoperative investigation in the case of in- Alain Arnéodo (ÉNS Lyon & CNRS) tractable epilepsy (Grova). Fractals and wavelets • An MRI methodology has been developed for ob- Habib Benali (UPMC) taining high-resolution images of the cat’s spinal cord. Quantitative analysis in brain imaging, medical imag- PhysNum researchers have applied this methodology ing and multimodal systems to cats with complete and partial spinal injuries and showed that the injuries can be identified in a robust Maxime Descoteaux (Sherbrooke) fashion and the integrity of white matter can be quan- Medical imaging, image analysis and processing, com- tified. They have extended their results to humans by puter vision, applied mathematics using MRIs with 3 teslas. Christophe Grova (McGill) • Lesage and Benali have used diffuse imaging for vi- Statistical signal processing, localization of epileptic sualizing the cat’s spinal cord and demonstrated that spikes using distributed sources modelling, and mul- metabolic activities can be quantified. timodal analysis of EEG source localization and simul- taneous EEG-fMRI data analysis • Lina and Grova are trying to detect the sources of epileptic activity in drug-resistant patients. To do this Frédéric Lesage (Polytechnique Montréal) they are using multiscale approaches for producing Conformal theory, integrable systems, inverse prob- functional images relevant to a sparse representation lems, optical imaging of the cortical activity. These approaches enable one to Fahima Nekka (Montréal) locate precisely the generators of fast oscillations that Pharmacokinetics, development of mathematical tools characterize epilepsy. from fractal geometry and harmonic analysis for ex- • Fahima Nekka and her team are developing and tracting information, applications to pharmacology adapting mathematical methodologies for drug eval- and medicine uation and use.

84 Research Laboratories

Statistics

Description • N. Ghazzali was appointed Rector of the Université du Québec à Trois-Rivières for a 5-year term, effective Statistics is central to many endeavours in society. February 1, 2012. Be it through surveys from sampling, clinical trials to • C. Léger became President of the Statistical Society study various biomedical treatments, or experimental of Canada, effective July 1, 2012. designs in agriculture or industry, statistical method- • C. Genest was appointed Director of the Institut des ology can be found everywhere in science. Recently, sciences mathématiques for a three-year term, effec- statistics has undergone a revolution in its techniques tive June 1, 2012. and approaches. This revolution has been driven by • R. Steele became President of the Biostatistics Sec- the need to analyze very large data sets and data with tion of the Statistical Society of Canada for a one-year more complex structure, and by the advent of power- term, effective July 1, 2012. ful computers. For example, statistical methodology is now addressing problems whose structure is very com- • Independently of the above, R. Steele is now serving plex, such as the analysis of brain images or genome as Director of the Electronic Services for the Statistical data, and new methodology is being developed, such Society of Canada, and he was recently appointed chair as data mining, for large data sets. Note that the name of the Graduate Affairs Committee in the Department of the Laboratory must be interpreted broadly, as some of Mathematics and Statistics at McGill. of its members are actuaries, probabilists, or biostatis- • É. Marchand was appointed to NSERC’s Evaluation ticians. Group 1508: Mathematics and Statistics for a three- year term, effective July 1, 2012. One of the aims of the Laboratory is to structure the Québec statistical community so that it can participate In 2011–2012 Laboratory members received many hon- in this revolution at a time when an important renewal ours and awards. Among them we would like to men- of academic personnel is taking place. This structure al- tion the following. lows the Québec community to participate in Canada- • J. O. Ramsay became the 38th Honorary Member of wide programs organized by the three Canadian math- the Statistical Society of Canada (SSC) in June 2012 (26 ematics institutes. The Laboratory is formed of the of them are alive; the SSC has over 1000 members). leaders of the Québec school of statistics, who work • C. Genest became (after L.-P. Rivest last year) the on topics such as statistical learning and neural net- second Honorary Member of the Association des works, survey sampling, analysis of functional data, statisticiennes et statisticiens du Québec (ASSQ) in statistical analysis of images, dependence structures, June 2012. Bayesian analysis, analysis of time series and financial • R. Platt received a prestigious award as a “Chercheur data, and resampling methods. national” from the Fonds de recherche en santé du Québec (FRSQ). This high-profile research funding and News and highlights salary supplement program recognizes the excellence of a limited number of outstanding researchers. On May 31, 2012, L.-P. Rivest completed a 5th year as Laboratory Director. C. Genest replaced him on June • T. Duchesne was the only Canadian to become a 1st. This decision was ratified by a unanimous voteheld member of the International Statistical Institute this in April. A vote of thanks to L.-P. Rivest was recorded year. Membership in the ISI is by cooptation only; at a regular meeting of Laboratory members on April places are limited. 13, 2012. • Y. Bengio received an award for his “Manifold Tan- gent Classifier” at the 25th Annual Conference onNeu- The Statistics Laboratory is a highly distinguished ral Information Processing Systems (held in Granada, group. It is home, among others, to three winners of the Spain, in December 2011). Furthermore he won the first Statistical Society of Canada’s prestigious Gold Medal, place in the Transfer Learning Challenge at this con- three Canada Research Chairs, and the holder of a ference’s workshop on “Challenges in Learning Hier- James McGill Chair. There were also some important archical Models: Transfer Learning and Optimization.” nominations this past year.

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• Y. Bengio also won the first place in the final phase 2, 2012. J. Garrido also gave an invited lecture at the of the 2011 Unsupervised and Transfer Learning Chal- CCRM and AFOSR Workshop on Catastrophic Risks lenge, an international machine learning competition. held in Stanford, California, in June 2012. • D. Dupuis and B. Rémillard were awarded Research • D. Haziza gave a plenary talk on the treatment of Professorships at HEC Montréal for the period 2012– influential observations in surveys at the “Journées de 2015. Their positions are in Statistics and Financial En- méthodologie statistique” held in Paris, France, in Jan- gineering, respectively. uary 2012. • D. Dupuis received “Le prisme,” an annual award • P. Lafaye de Micheaux gave a plenary talk on the use given to a graduate of the Faculty of Science at the Uni- of the R software in neuro-imaging at the “Premières versité de Moncton who distinguished him/herself in a rencontres R” held in Bordeaux, France, in June 2012. science career. • M. Morales gave a plenary talk at the 10th Interna- • J. Garrido was the 2011–2012 recipient of the Dean’s tional Conference on Operations Research held in La Award for Academic Service in the Faculty of Science Habana, Cuba, in 2012. at Concordia University. • Y. Chaubey was cochair of both the Scientific Pro- • D. Haziza won a prestigious, university-wide “Prix gram Committee and the Local Organizing Committee d’enseignement” at the Université de Montréal for for the 5th Canadian Conference in Applied Statistics 2012. In 2011, he had already been awarded a similar held in Montréal, on July 1-4, 2011. He was also a mem- prize by the Faculté des arts et des sciences of the same ber of the Program Committee and an invited speaker university. at the 5th International Conference of the Institute for • The textbook entitled Le logiciel R, maîtriser le lan- Mathematics, Bioinformatics, Information Technology gage - effectuer des analyses statistiques (ISBN: 978-2- and Computer Science (IMBIC) held in Kolkota, India, 8178-0114-8) by the Laboratory member P. Lafaye de in December 2011. Micheaux and his coauthors (R. Drouilhet and B. Li- • D. Dupuis was appointed chair of the Program Com- quet) was the runner-up for the 2012 Prix Roberval, an mittee for the 41st Annual Meeting of the Statistical international award given yearly to a work (book, mul- Society of Canada, to be held in Edmonton, Alberta, timedia, etc.) written in the French language and aimed on May 26-29, 2013. at disseminating technology. • A. Murua was a member of the Program Committee Finally we list below some of the special addresses, ple- for an International Conference on Signal Processing nary talks, and publications by Laboratory members, and Multimedia Applications (SIGMAP) held in Seville as well as some of the major events organized by them. in 2011. He is serving in the same capacity for the 2012 • C. Genest gave the Gold Medal Address at the 40th meeting of SIGMAP in Rome. Annual Meeting of the Statistical Society of Canada in • The Laboratory was well represented at the 8th Guelph, Ontario, June 5, 2012. He was also the keynote World Congress in Probability and Statistics, held in speaker at an international workshop on “Copulas Istanbul, Turkey, on July 10-15, 2012. J. Nešlehová or- in Mathematical and Quantitative Finance” held in ganized an Invited Paper Session on Dependence Mod- Kraków, Poland, July 10-11, 2012, as well as plenary eling and L. Popovic and B. Rémillard were invited speaker at the 5th Canadian Conference in Applied speakers at two different sessions of the meeting. Statistics held in Montréal, July 1-4, 2011. • M. Asgharian organized an Invited Paper Session at • Y. Bengio gave an invited talk at the 49th Annual the 40th Annual Meeting of the Statistical Society of Meeting of the Association for Computational Linguis- Canada, held in Guelph (Ontario) last June. tics held in Portland, Oregon, in June 2011. He also • Y. Bengio was invited to give a tutorial on represen- gave an invited lecture at the 2012 Graduate Summer tation learning at the 2012 International Conference on School on Deep Learning organized by the Institute Machine Learning held in Edinburgh, Scotland, and an- for Pure and Applied Mathematics at the University of other tutorial on deep learning for neurolinguistic pro- California in Los Angeles. gramming at the 50th Annual Meeting of the Associa- • J. Garrido gave the keynote lecture at the 2nd tion for Computational Linguistics held on Jeju Island, Québec-Ontario Workshop on Insurance Mathemat- Korea, in July 2012. ics, held at the Fields Institute in Toronto, on February

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• D. Haziza gave a one-day workshop on the use of • UQAM M.Sc. student M. Dupont won the first prize auxiliary information through balanced sampling and in the category Statistical Genetics for a poster pre- calibration at the International Conference on Estab- sented at the Canadian Human and Statistical Genetics lished Surveys held in Montréal in June 2012. He was Meeting held at Niagara-on-the-Lake (April 29 to May also invited by the Société française de statistique to 2, 2012). give a two-day workshop on the treatment of non- • McGill (Biostatistics) Ph.D. student M. Schnitzer re- response in surveys at the Institut Pierre-et-Marie- ceived a Bourse de stage international from FRQNT to Curie in Paris, in December 2011. spend a term at the University of California (Berke- • C. Genest and J. Nešlehová gave a two-day workshop ley) in September 2011. She also received full fund- on dependence modelling at the Scottish Financial Risk ing to support her travel to Bristol, UK, to present Academy in Edinburgh, Scotland, in May 2012. her research at the workshop on “Time for Causality • In June 2012, A. Khalili gave an invited half-day - Causal Inference and Dynamic Decisions in Longitu- workshop on “Joint fixed and random effect selection dinal Studies.” in finite mixtures of linear mixed effect models” at In the course of the year 2011–2012 the Laboratory Tehran’s University of Medical Sciences, in Iran. welcomed several postdoctoral fellows (whose advi- • É. Marchand recently coedited (with D. Fourdrinier sors are listed within parentheses): E. Acar (C. Genest and A. Rukhin) a special volume entitled “Contem- and J. Nešlehová); W. Astle (A. Labbe and D. Stephens); porary Developments in Bayesian Analysis and Sta- A. Carabarin (C. Genest and B. Rémillard); O. Kortbi tistical Decision Theory: A Festschrift for William E. (É. Marchand); O. Saarela (E. Moodie and D. Stephens); Strawderman” (Inst. Math. Statist. Beachwood, OH, and R. Samb (S. Froda). Note that E. Acar became an As- USA, 256 pp.). sistant Professor of Statistics at the University of Man- • Four Laboratory members (C. Genest, D. Dupuis, itoba, effective July 1, 2012. J. Nešlehová, and B. Rémillard) and two others (J.-F. In the 2011–2012 academic year one undergraduate Plante from HEC Montréal; J.-F. Quessy from UQTR) student, 121 M.Sc. students, 88 Ph.D. students, and 13 coedited a special issue of the Journal of Multivari- postdoctoral fellows were supervised or cosupervised ate Analysis (vol. 110, 2012) on Copula Modeling and by members of the Statistics Laboratory. Dependence. This issue (188 pp.) features 12 papers presented during the workshop of the same name or- Seminars ganized for the Statistics Thematic Semester, in June 2011. The Laboratory members organize, and participate in, seven regular series of seminars. Students, postdoctoral fellows, and visitors (1) CRM–ISM–GERAD Statistics Colloquium: eight colloquia were held this year, namely on Friday The Statistics Laboratory is proud to report that38 September 9, October 14, November 11, and De- M.Sc. students and 15 Ph.D. students completed their cember 9, 2011, as well as on Friday January 13, degrees between August 1, 2011, and August 31, 2012. February 10, March 9, and April 13, 2012. The or- In addition there are several student success stories, ganizers were M. Bédard (Montréal), S. Guillotte described below. (UQAM), A. Khalili (McGill), J. Nešlehová (McGill), • Concordia M.Sc. student W. Liu received the best and L. Popovic (Concordia). Each colloquium was M.Sc. Thesis award at the IFM2 Mathematical Finance organized around a specific theme; it consisted of Days Conference in May 2012. two one-hour talks (one talk only in December and • Concordia M.Sc. student M. Wenger was awarded an January), with a 30-minute break in between and a NSERC CDSD3 Award in the 2012 Competition. reception at the end. There were between 40 and • UQAM M.Sc. student M.-H. Descary was awarded a 60 attendees on each occasion; Ph.D. position at the École polytechnique fédérale de (2) The McGill Statistics Seminar Series: this seminar Lausanne (these positions are rare and very well paid). was held at McGill on Friday afternoons in weeks She was also invited to give a talk at the Canadian Hu- where there was no colloquium. The organizer was man and Statistical Genetics Meeting held at Niagara- J. Nešlehová. Talks were 60 minutes in length, in- on-the-Lake (April 29 to May 2, 2012). cluding a question period (in two cases, two talks

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of one half-hour each by graduate students were Statistics Laboratory, attracted over 250 participants. scheduled on the same day). There were 23 speak- We refer the reader to the section Multidisciplinary ers during the year and the attendance varied be- and Industrial Program for a report on this event. tween 25 and 40 persons; Statistics 2011 Canada (3) The McGill Biostatistics Seminar Series: this sem- IMST 2011–FIM XX inar was organized by the McGill Department July 1–4, 2011, Concordia of Epidemiology, Biostatistics and Occupational Local Organizing Committee (Concordia): Yogen- Health and took place on Tuesday afternoons. The dra P. Chaubey (chair), Simon Bacon, Satyaveer organizer was J. Atherton and there were 24 speak- Chauhan, Patrice Gailliardetz, Jose Garrido, Nikolay ers during the year; Gospodinov, Cody Hyndman, Jochen Jaeger, Tak Mak, (4) The Université Laval Statistics Colloquium: this Danielle Morin, Fassil Nebebe (Co-chair), Lea Popovic, seminar was generally held at Université Laval on Arusharka Sen, Debaraj Sen, Mahesh Sharma, Murari Thursday afternoons in 2011–2012. Its organizers Singh, Wei Sun, Robert Weladji were T. Duchesne and L. Lakhal Chaïeb. There were 19 speakers during the year and the atten- An international workshop entitled “Perspectives on dance varied between 15 and 40 persons; high-dimensional data analysis II” was held at the CRM (5) The Université de Sherbrooke Statistics Seminar: in the Summer of 2012. It was the second workshop on this seminar series comprised 4 talks in the Fall this theme, following the HD-I conference held at the term and 6 in the Winter term. Its organizers were Fields Institute in 2011. The organizing committee con- É. Marchand and T. Bouezmarni. Talks were 50 sisted of three Laboratory members and three statisti- minutes in length, plus 10 minutes for questions. cians from Ontario. The reader will find a report on this The attendance varied between 10 and 20; event at the end of the section General Program. (6) The Montreal Seminar of Actuarial and Financial Mathematics: this series comprised 7 talks given in International Workshop the Winter of 2012. Five of them were given at Con- Perspectives on High-Dimensional Data Analysis II cordia; one talk was at the Université de Montréal May 30 – June 1, 2012, CRM and the other at UQAM. The seminar organizers Organizers: S. Ejaz Ahmed (Brock & Windsor) chair, were J. Garrido, M. Morales, J. Nešlehová, and J.-F. Abbas Khalili (McGill), David Stephens (McGill), Éric Renaud. Talks were 60 minutes in length, including Marchand (Sherbrooke), Peter X. K. Song (Michigan), a question period. The attendance varied between Ji Zhu (Michigan) 10 and 20 persons; Finally, the Second Graduate Student Workshop on Ac- (7) The CRM-ISM Probability Seminar: this new semi- tuarial and Financial Mathematics was held at Con- nar series was jointly initiated and organized by L. cordia University on December 9, 2011. The event Addario-Berry, L.-P. Arguin, and Laboratory mem- was organized by Laboratory members J. Garrido, M. ber L. Popovic. There were 9 talks in the Fall and Morales, and J.-F. Renaud, together with G. Léveillé 5 in the Winter. Partial funding for the event was from the Université Laval. It featured six 45-minute given by the ISM. The list of speakers and topics talks by graduate students in actuarial science at was very diverse, with 5 speakers from Europe, 3 Concordia, Laval, the Université de Montréal, and from the United States, one from China, and one UQAM. For additional details we refer the reader to from the Rest of Canada. the site http://www.dms.umontreal.ca/~morales/ GWorkshop/. Workshops, special sessions, and others Members of the Laboratory Every ten years since 1971, Concordia University orga- nizes a large Applied Statistics Conference whose first Regular members edition actually played a major role in the foundation of the Statistical Society of Canada. The 5th edition was Louis-Paul Rivest (Laval), Director held in July 2011, in conjunction with the 20th confer- Linear models, robustness, directional data, sampling, ence of the Forum for Interdisciplinary Mathematics. applications in finance The conference, which was generously funded bythe

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Belkacem Abdous (Laval) Brenda MacGibbon (UQAM) Biostatistics, health research methodology, construc- Mathematical statistics, decision theory, biostatistics tion and validation of measuring tools in the health Éric Marchand (Sherbrooke) sector Statistical inference, Bayesian statistics, multivariate Jean-François Angers (Montréal) analysis and probability Decision theory, Bayesian statistics, robustness with Alejandro Murua (Montréal) respect to prior information, function estimation Data mining, machine learning, object recognition, Masoud Asgharian (McGill) signal processing, and various applications of statistics Survival analysis, change-point problems, simulated and probability to bioinformatics and the social and annealing and its variants, optimization health sciences Yoshua Bengio (Montréal) François Perron (Montréal) Statistical learning algorithms, neural networks, nu- Decision theory, multidimensional data analysis, cleus models, probabilistic models, data mining, appli- Bayesian statistics cations in finance and statistical language modelling James Ramsay (McGill) Martin Bilodeau (Montréal) Functional data analysis, smoothing and nonparamet- Multivariate analysis, decision theory, asymptotic ric regression, curve registration methods Bruno Rémillard (HEC Montréal) Yogendra P. Chaubey (Concordia) Probability theory, empirical processes, time series, Sampling, linear models, resampling, survival analysis nonlinear filtering, applications in finance Pierre Duchesne (Montréal) Roch Roy (Montréal) Time series, sampling, multivariate analysis Time series analysis, predictive methods, applications Thierry Duchesne (Laval) in econometrics and epidemiology Survival analysis, longitudinal data analysis, missing Arusharka Sen (Concordia) data, modelling of losses, insurance of catastrophic Statistical inference of truncated data, nonparametric incidents, nonparametric inference, model selection, function estimation warranty Russell Steele (McGill) Debbie J. Dupuis (HEC Montréal) Bayesian approaches to mixing modelling, multiple Extreme values, robustness imputation Sorana Froda (UQAM) David Stephens (McGill) Nonparametric methods in function estimation, ap- Bayesian statistics, Markov Chain Monte Carlo and plications of stochastic modelling in biology and applications to bioinformatics, statistical genetics, and medicine time series analysis Christian Genest (McGill) Wei Sun (Concordia) Multidimensional data analysis, dependence measures, Nonlinear filtering and its applications, stochastic nonparametric statistics, decision theory, applications analysis, statistical inference, stochastic modelling in actuarial science, finance, and psychology David B. Wolfson (McGill) Nadia Ghazzali (Laval) Change-point problems, survival analysis, Bayesian Multidimensional data analysis, neural networks and statistics, optimal design, applications in medicine genetic algorithms, applications in astrophysics and biostatistics Associate members Aurélie Labbe (McGill) Juli Atherton (McGill) Biostatistics and statistical genetics Biostatistics, optimal Bayesian design, change-point Fabrice Larribe (UQAM) problems, survival analysis, applications to genetics Statistical genetics and biostatistics Mylène Bédard (Montréal) Christian Léger (Montréal) Optimal scaling, Metropolis-Hastings algorithms Resampling methods, adaptive estimation, model se- lection, robustness, applications in data mining

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Anne-Catherine Favre (Laval) Manuel Morales (Montréal) Statistical hydrology, analysis and modelling of time Mathematical finance, applied stochastic processes, series ruin theory, actuarial science, Lévy processes, math- José Garrido (Concordia) ematics of insurance Risk theory, insurance statistics Johanna Nešlehová (McGill) David Haziza (Montréal) Multivariate analysis, dependence modelling, non- Sampling theory, inference with missing data, robust parametric and asymptotic statistics, multivariate ex- inference treme value theory, empirical processes, applications to biostatistics, neuroscience, and risk management Lajmi Lakhal Chaïeb (Laval) Multidimensional analysis of survival data, analysis of Robert Platt (McGill) recurrent events, semi-parametric models and incom- Biostatistics and statistical methods for pediatric and plete data perinatal epidemiology. Geneviève Lefebvre (UQAM) Lea Popovic (Concordia) Bayesian and computational statistics, biostatistics Probability theory and its applications to evolutionary biology, population genetics, and cell biology Erica Moodie (McGill) Causal inference, optimal dynamic treatment regimes, longitudinal data, dose-response relationships

90 Publications Centre de recherches mathématiqes

he CRM publishes monographs, lecture notes, proceedings, software, videos, and research reports. Ithas T several collections. The in-house collection (Les Publications CRM) offers titles in both English andFrench. The CRM also has publishing agreements with the American Mathematical Society (AMS) and Springer. Since 1992, two collections, edited by the CRM, have been published and distributed by the AMS. They are the CRM Monograph Series and the CRM Proceedings and Lecture Notes. Springer publishes the CRM Series in Mathematical Physics. An asterisk preceding a publication indicates that its author is an Aisenstadt chairholder.

Recent Titles

The following list of recent titles contains books that Springer appeared in 2011–2012 or that will be published soon. CRM Series in Mathematical Physics

American Mathematical Society André D. Bandrauk & Misha Ivanov (eds.), Quantum CRM Monograph Series Dynamic Imaging, 2011. Joseph H. Silverman, Moduli Spaces and Arithmetic Dy- Séminaires de mathématiques supérieures namics, vol 30, 2012. Vašek Chvátal (ed.), Combinatorial Optimization: Meth- American Mathematical Society ods and Applications, NATO Science for Peace and Se- CRM Proceedings & Lecture Notes curity Series - D: Information and Communication Se- curity, vol. 31, IOS Press, 2011. Daniel Daigle, Richard Ganong & Mariusz Koras (eds.), Decio Levi, Peter Olver, Zora Thomova & Pavel Win- Affine Algebraic Geometry: The Russell Festschrift, ternitz (eds.), Symmetries and Integrability of Difference vol. 54, 2011. Equations, London Mathematical Society Lecture Note Bradd Hart, Thomas G. Kucera, Anand Pillay, Philip J. Series, vol. 381, Cambridge University Press, 2011 Scott & Robert A. G. Seely (eds.), Models, Logics, and Higher-Dimensional Categories, vol. 53, 2011.

Previous Titles

American Mathematical Society Prakash Panangaden & Franck van Breugel (eds.), CRM Monograph Series Mathematical Techniques for Analyzing Concurrent and Probabilistic Systems, vol. 23, 2004. Marcelo Aguiar & Swapneel Mahajan, Monoidal Cate- gories, Species and Hopf Algebras, vol 29, 2010. Montserrat Alsina & Pilar Bayer, Quaternion Orders, Quadratic Forms, and Shimura Curves, vol. 22, 2004. Saugata Ghosh, Skew-Orthogonal Polynomials and Ran- dom Matrix Theory, vol. 28, 2009. Andrei Tyurin, Quantization, Classical and Quantum Field Theory and Theta Functions, vol. 21, 2003. Jean Berstel, Aaron Lauve, Christophe Reutenauer & Franco V. Saliola, Combinatorics on Words: Christoffel Joel Feldman, Horst Knörrer & Eugene Trubowitz, Rie- Words and Repetitions in Words, vol. 27, 2008. mann Surfaces of Infinite Genus, vol. 20, 2003. Victor Guillemin & Reyer Sjamaar, Convexity Proper- *Laurent Lafforgue, Chirurgie des grassmanniennes, ties of Hamiltonian Group Actions, vol. 26, 2005. vol. 19, 2003. *Andrew J. Majda, Rafail V. Abramov & Marcus J. *George Lusztig, Hecke Algebras with Unequal Param- Grote, Information Theory and Stochastics for Multiscale eters, vol. 18, 2003. Nonlinear Systems, vol. 25, 2005. Michael Barr, Acyclic Models, vol. 17, 2002. Dana Schlomiuk, Andrei A. Bolibrukh, Sergei Yako- *Joel Feldman, Horst Knörrer & Eugene Trubowitz, venko, Vadim Kaloshin & Alexandru Buium, On Finite- Fermionic Functional Integrals and the Renormalization ness in Differential Equations and Diophantine Geome- Group, vol. 16, 2002. try, vol. 24, 2005.

92 Publications

Jose I. Burgos, The Regulators of Beilinson and Borel, Miguel Abreu, François Lalonde & Leonid Poltero- vol. 15, 2002. vich (eds.), New Perspectives and Challenges in Symplec- Eyal Z. Goren, Lectures on Hilbert Modular Varieties and tic Field Theory, vol. 49, 2009. Modular Forms, vol. 14, 2002. David Avis, David Bremner & Antoine Deza (eds.), Michael Baake & Robert V. Moody (eds.), Directions in Polyhedral Computation, vol. 48, 2009. Mathematical Quasicrystals, vol. 13, 2000. John Harnad & Pavel Winternitz (eds.), Groups and Masayoshi Miyanishi, Open Algebraic Surfaces, vol. 12, Symmetries: From Neolithic Scots to John McKay, 2001. vol. 47, 2009. Spencer J. Bloch, Higher Regulators, Algebraic K- Jean-Marie De Koninck, Andrew Granville & Florian Theory, and Zeta Functions of Elliptic Curves, vol. 11, Luca (eds.), Anatomy of Integers, vol. 46, 2008. 2000. Panos M. Pardalos & Pierre Hansen (eds.), Data Mining James D. Lewis, A Survey of the Hodge Conjecture, 2nd and Mathematical Programming, vol. 45, 2008. edition, vol. 10, 1999 (with an appendix from B. Brent Stanley Alama, Lia Bronsard & Peter Sternberg (eds.), Gordon). Singularities in PDE and the Calculus of Variations, *Yves Meyer, Wavelets, Vibrations and Scaling, vol. 9, vol. 44, 2007. 1997. Andrew Granville, Melvyn B. Nathanson & Jozsef *Ioannis Karatzas, Lectures on Mathematics of Finance, Solymosi (eds.), Additive Combinatorics, vol. 43, 2007. vol. 8, 1996. Donald A. Dawson, Vojkan Jakšić & Boris Vain- John Milton, Dynamics of Small Neural Populations, berg (eds.), Probability and Mathematical Physics: A vol. 7, 1996. Volume in Honor of Stanislav Molchanov, vol. 42, 2007. *Eugene B. Dynkin, An Introduction to Branching André Bandrauk, Michel C. Delfour & Claude Measure-Valued Processes, vol. 6, 1994. Le Bris (eds.), High-Dimensional Partial Differential Equations in Science and Engineering, vol. 41, 2007. Andrew M. Bruckner, Differentiation of Real Functions, vol. 5, 1994. Vestislav Apostolov, Andrew Dancer, Nigel Hitchin & McKenzie Wang (eds.), Perspectives in Comparison, *David Ruelle, Dynamical Zeta Functions for Piecewise Generalized and Special Geometry, vol. 40, 2006. Monotone Maps of the Interval, vol. 4, 1994. Pavel Winternitz, David Gomez-Ullate, Arieh Iserles, V. Kumar Murty, Introduction to Abelian Varieties, Decio Levi, Peter J. Olver, Reinout Quispel & Piergiulio vol. 3, 1993. Tempesta (eds.), Group Theory and Numerical Analysis, Maximilian Ya. Antimirov, Andrei A. Kolyshkin & vol. 39, 2005. Rémi Vaillancourt, Applied Integral Transforms, vol. 2, Jacques Hurtubise & Eyal Markman (eds.), Algebraic 1993. Structures and Moduli Spaces, vol. 38, 2004. *Dan V. Voiculescu, Kenneth J. Dykema & Alexandru Piergiulio Tempesta, Pavel Winternitz, John Harnad, Nica, Free Random Variables, vol. 1, 1992. Willard Miller Jr., George Pogosyan & Miguel A. Ro- American Mathematical Society driguez (eds.), Superintegrability in Classical and Quan- CRM Proceedings & Lecture Notes tum Systems, vol. 37, 2004. Hershy Kisilevsky & Eyal Z. Goren (eds.), Number The- Dmitry Jakobson, Stéphane Nonnenmacher & Iosif ory, vol. 36, 2004. Polterovich (eds.), Spectrum and Dynamics, vol. 52, H. E. A. Eddy Campbell & David L. Wehlau (eds.), In- 2010. variant Theory in All Characteristics, vol. 35, 2004. Javad Mashreghi, Thomas Ransford & Kristian Pavel Winternitz, John Harnad, C. S. Lam & Jiří Pat- Siep (eds.), Hilbert Spaces of Analytic Functions, vol. 51, era (eds.), Symmetry in Physics, vol. 34, 2004. 2010. André D. Bandrauk, Michel C. Delfour & Claude P. Robert Kotiuga (ed.), A Celebration of the Mathemat- Le Bris (eds.), Quantum Control: Mathematical and Nu- ical Legacy of Raoul Bott, vol. 50, 2009. merical Challenges, vol. 33, 2003.

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Vadim B. Kuznetsov (ed.), The Kowalevski Property, Peter G. Greiner, Victor Ivrii, Luis A. Seco & Catherine vol. 32, 2002. Sulem (eds.), Partial Differential Equations and their John Harnad & Alexander R. Its (eds.), Isomonodromic Applications, vol. 12, 1997. Deformations and Applications in Physics, vol. 31, 2002. Luc Vinet (ed.), Advances in Mathematical Sciences: John McKay & Abdellah Sebbar (eds.), Proceedings on CRM’s 25 Years, vol. 11, 1997. Moonshine and Related Topics, vol. 30, 2001. Donald E. Knuth, Stable Marriage and Its Relation to Alan Coley, Decio Levi, Robert Milson, Colin Rogers & Other Combinatorial Problems, vol. 10, 1996. Pavel Winternitz (eds.), Bäcklund and Darboux Trans- Decio Levi, Luc Vinet & Pavel Winternitz (eds.), Sym- formations, vol. 29, 2001. metries and Integrability of Difference Equations, vol. 9, John C. Taylor (ed.), Topics in Probability and Lie 1995. Groups: Boundary Theory, vol. 28, 2001. Joel S. Feldman, Richard Froese & Lon M. Rosen (eds.), Israel M. Sigal & Catherine Sulem (eds.), Nonlinear Dy- Mathematical Quantum Theory II: Schrödinger Opera- namics and Renormalization Group, vol. 27, 2001. tor, vol. 8, 1995. John Harnad, Gert Sabidussi & Pavel Winternitz (eds.), Joel S. Feldman, Richard Froese & Lon M. Rosen (eds.), Integrable Systems: From Classical to Quantum, vol. 26, Mathematical Quantum Theory I: Field Theory and 2000. Many-Body Theory, vol. 7, 1994. Decio Levi & Orlando Ragnisco (eds.), SIDE III— Guido Mislin (ed.), The Hilton Symposium 1993, vol. 6, Symmetry and Integrability of Difference Equations, 1994. vol. 25, 2000. Donald A. Dawson (ed.), Measure-Valued Processes, B. Brent Gordon, James D. Lewis, Stefan Müller-Stach, Stochastic Partial Differential Equations and Interacting Shuji Saito & Noriko Yui (eds.), The Arithmetic and Ge- Systems, vol. 5, 1994. ometry of Algebraic Cycles, vol. 24, 2000. Hershy Kisilevsky & M. Ram Murty (eds.), Elliptic Pierre Hansen & Odile Marcotte (eds.), Graph Colour- Curves and Related Topics, vol. 4, 1994. ing and Applications, vol. 23, 1999. Andrei L. Smirnov & Rémi Vaillancourt (eds.), Asymp- Jan Felipe van Diejen & Luc Vinet (eds.), Algebraic totic Methods in Mechanics, vol. 3, 1993. Methods and q-Special Functions, vol. 22, 1999. Philip D. Loewen, Optimal Control via Nonsmooth Michel Fortin (ed.), Plates and Shells, vol. 21, 1999. Analysis, vol. 2, 1993. Katie Coughlin (ed.), Semi-Analytic Methods for the M. Ram Murty (ed.), Theta Functions, vol. 1, 1993. Navier–Stokes Equations, vol. 20, 1999. Springer Rajiv Gupta & Kenneth S. Williams (eds.), Number The- CRM Series in Mathematical Physics ory, vol. 19, 1999. Serge Dubuc & Gilles Deslauriers (eds.), Spline Func- John Harnad (ed.), Random Matrices, Random Processes tions and the Theory of Wavelets, vol. 18, 1999. and Integrable Systems, 2011. Olga Kharlampovich (ed.), Summer School in Group Marc Thiriet, Biology and Mechanics of Blood Flows, Theory in Banff, 1996, vol. 17, 1998. 2008 (2 volumes). Alain Vincent (ed.), Numerical Methods in Fluid Me- David Sénéchal, André-Marie Tremblay & Claude chanics, vol. 16, 1998. Bourbonnais (eds.), Theoretical Methods for Strongly Correlated Electrons, 2003. François Lalonde (ed.), Geometry, Topology and Dy- namics, vol. 15, 1998. *Roman Jackiw, Lectures on Fluid Dynamics, 2002. John Harnad & Alex Kasman (eds.), The Bispectral Prob- Yvan Saint-Aubin & Luc Vinet (eds.), Theoretical lem, vol. 14, 1998. Physics at the End of the Twentieth Century, 2001. Michel Delfour (ed.), Boundaries, Interfaces and Transi- Yvan Saint-Aubin & Luc Vinet (eds.), Algebraic Meth- tions, vol. 13, 1998. ods in Physics, 2000. Jan Felipe van Diejen & Luc Vinet (eds.), Calogero– Moser–Sutherland Models, 1999.

94 Publications

Robert Conte (ed.), The Painlevé Property, 1999. Rémi Vaillancourt, Compléments de mathématiques Richard MacKenzie, Manu B. Paranjape & Woj- pour ingénieurs, 1993. ciech J. M. Zakrzewski (eds.), Solitons, 1999. Robert P. Langlands & Dinakar Ramakrishnan (eds.), Luc Vinet & Gordon Semenoff (eds.), Particles and The Zeta Functions of Picard Modular Surfaces, 1992. Fields, 1998. Florin N. Diacu, Singularities of the N-Body Problem, 1992. Springer Jacques Gauvin, Théorie de la programmation mathé- Lecture Notes in Statistics (subseries CRM) matique non convexe, 1992. Marc Moore (ed.), Spatial Statistics: Methodological As- Pierre Ferland, Claude Tricot & Axel van de Walle, pects and Applications, vol. 159, 2001. Analyse fractale, 1992 (software and user guide). S. Ejaz Ahmed & Nancy Reid (eds.), Empirical Bayes Stéphane Baldo, Introduction à la topologie des en- and Likelihood Inference, vol. 148, 2001. sembles fractals, 1991. Robert Bédard, Groupes linéaires algébriques, 1991. Les Publications CRM Rudolf Beran & Gilles R. Ducharme, Asymptotic Theory Laurent Guieu & Claude Roger, L’Algèbre et le Groupe for Bootstrap Methods in Statistics, 1991. de Virasoro, 2007. James D. Lewis, A Survey of the Hodge Conjecture, 1991. Luc Lapointe, Ge Mo-Lin, Yvan Saint-Aubin & Luc David W. Rand & Tatiana Patera, Concorder, 1991 (soft- Vinet, Proceedings of the Canada–China Meeting on ware and user guide). Theoretical Physics, 2003. David W. Rand & Tatiana Patera, Le Concordeur, 1991 Armel Mercier, Fonctions de plusieurs variables : Diffé- (software and user guide). rentiation, 2002. Véronique Hussin (ed.), Lie Theory, Differential Equa- Nadia El-Mabrouk, Thomas Lengauer & David tions and Representation Theory, 1990. Sankoff (eds.), Currents in Computational Molecular John Harnad & Jerrold E. Marsden (eds.), Hamiltonian Biology, 2001. Systems, Transformation Groups and Spectral Trans- James G. Huard & Kenneth S. Williams (eds.), The Col- form Methods, 1990. lected Papers of Sarvadaman Chowla. Volume I: 1925– M. Ram Murty (ed.), Automorphic Forms and Analytic 1935; Volume II: 1936–1961; Volume III: 1962–1986, Number Theory, 1990. 2000. Wendy G. McKay, Jiří Patera & David W. Rand, Tables Michael Barr & Charles Wells, Category Theory for of Representations of Simple Lie Algebras. Volume I: Ex- Computing Science, 1999. ceptional Simple Lie Algebras, 1990. Maximilian Ya. Antimirov, Andrei A. Kolyshkin & Anthony W. Knapp, Representations of Real Reductive Rémi Vaillancourt, Mathematical Models for Eddy Cur- Groups, 1990. rent Testing, 1998. Wendy G. McKay, Jiří Patera & David W. Rand, Sim- Xavier Fernique, Fonctions aléatoires gaussiennes, vec- pLie, 1990 (software and user guide). teurs aléatoires gaussiens, 1997. Francis H. Clarke, Optimization and Nonsmooth Anal- Faqir Khanna & Luc Vinet (eds.), Field Theory, Inte- ysis, Montréal, 1989. grable Systems and Symmetries, 1997. Samuel Zaidman, Une Introduction à la théorie des équa- Paul Koosis, Leçons sur le théorème de Beurling et Mal- tions aux dérivées partielles, 1989. liavin, 1996. *Yuri I. Manin, Quantum Groups and Noncommutative David W. Rand, Concorder Version Three, 1996 (soft- Geometry, 1988. ware and user guide). Lucien Le Cam, Notes on Asymptotic Methods in Statis- Jacques Gauvin, Theory of Nonconvex Programming, tical Decision Theory, 1974. 1994. Decio Levi, Curtis R. Menyuk & Pavel Winter- nitz (eds.), Self-Similarity in Stimulated Raman Scatter- ing, 1994.

95 Centre de recherches mathématiqes

Les Presses de l’Université de Montréal Constance van Eeden, Lecture Notes–Monograph Se- Chaire Aisenstadt ries, vol. 42, 2003 (a collaboration with the Institute of Mathematical Statistics). *Laurent Schwartz, Semimartingales and their Stochas- tic Calculus on Manifolds, 1984. Duong H. Phong, Luc Vinet & Shing-Tung Yau (eds.), Mirror Manifolds and Geometry, AMS/IP Studies in Ad- *Yuval Ne′eman, Symétries, jauges et variétés de groupe, vanced Mathematics, vol. 10, 1998 (a collaboration with 1979. the AMS and International Press). *R. Tyrrell Rockafellar, La théorie des sous-gradients et Pierre Ferland, Claude Tricot & Axel van de Walle, ses applications à l’optimisation, fonctions convexes et Fractal Analysis User’s Guide, 1994 (a collaboration non convexes, 1979. with the AMS). *Jacques-Louis Lions, Sur quelques questions d’analyse, Hedy Attouch, Jean-Pierre Aubin, Francis Clarke & de mécanique et de contrôle optimal, 1976. Ivar Ekeland (eds.), Analyse non linéaire, 1989 (a col- *Donald E. Knuth, Mariages stables et leurs relations laboration with Gauthier-Villars). avec d’autres problèmes combinatoires, 1976. *Robert Hermann, Physical Aspects of Lie Group Theory, Videos 1974. Efim Zelmanov, Abstract Algebra in the 20th Century, *Mark Kac, Quelques problèmes mathématiques en phy- 1997. sique statistique, 1974. Serge Lang, Les grands courants, 1991. *Sybreen de Groot, La transformation de Weyl et la Robert Bédard, Brouiller les cartes, 1991. fonction de Wigner : une forme alternative de la méca- nique quantique, 1974. Serge Lang, Les équations diophantiennes, 1991. Laurent Schwartz, Le mouvement brownien, 1990. Other Collaborations with Publishers Laurent Schwartz, Une vie de mathématicien, 1989. Marc Moore, Sorana Froda & Christian Léger (eds.), Mathematical Statistics and Applications: Festschrift for

96 Scientific Personnel Centre de recherches mathématiqes

CRM Members in 2011–2012

In contrast with most other mathematics institutes around the world, the CRM can count on the solid foundation of regular, associate, and invited members. Each regular member is also a professor at one of the partner insti- tutions: Montréal, Concordia, McGill, UQAM, Laval, Sherbrooke, and Ottawa. Other members are researchers affiliated with the CRM in 2011–2012 as part of exchange agreements with neighbouring universities andindus- try or are long-term visitors from Canadian and foreign institutions. The presence at the CRM of such an active group of researchers has brought many benefits to the Centre. In particular, the CRM’s national program isgreatly facilitated by having on hand a large reserve of willing organizers, who even contribute financially to the organi- zation of activities. The largest partnership is with the Université de Montréal, which grants the equivalent offive full-time teaching positions in release time to the CRM. Release agreements with the other Montréal area univer- sities afford the equivalent of two more full-time positions to the CRM. Facilities are also provided toresearchers affiliated with junior colleges. Several members are affiliated to the CRM through industrial agreements.

Regular members Henri Darmon, McGill Syed Twareque Ali, Concordia Chantal David, Concordia Jean-François Angers, Montréal Jean-Marie De Koninck, Laval Vestislav Apostolov, UQAM Michel C. Delfour, Montréal Ibrahim Assem, Sherbrooke Maxime Descoteaux, Sherbrooke André D. Bandrauk, Sherbrooke Eusebius J. Doedel, Concordia Line Baribeau, Laval Pierre Duchesne, Montréal Peter Bartello, McGill Thierry Duchesne, Laval Robert Bédard, UQAM Nadia El-Mabrouk, Montréal Jacques Bélair, Montréal André Fortin, Laval Habib Benali, UPMC & Inserm Richard Fournier, Dawson; Montréal Yoshua Bengio, Montréal Marlène Frigon, Montréal François Bergeron, UQAM André Garon, Polytechnique Montréal Marco Bertola, Concordia Paul M. Gauthier, Montréal Yves Bourgault, Ottawa Christian Genest, McGill Anne Bourlioux, Montréal Eyal Z. Goren, McGill Steven P. Boyer, UQAM Andrew Granville, Montréal Gilles Brassard, Montréal Christophe Grova, McGill Srečko Brlek, UQAM Alfred Michel Grundland, UQTR Thomas Brüstle, Sherbrooke & Bishop’s Pengfei Guan, McGill Virginie Charette, Sherbrooke Geňa Hahn, Montréal Cédric Chauve, Simon Fraser Richard L. Hall, Concordia Vašek Chvátal, Concordia Sylvie Hamel, Montréal Francis H. Clarke, Lyon 1 John Harnad, Concordia Olivier Collin, UQAM Tony R. Humphries, McGill Octav Cornea, Montréal Jacques Hurtubise, McGill Miklós Csűrös, Montréal Véronique Hussin, Montréal Chris J. Cummins, Concordia Adrian Iovita, Concordia Galia Dafni, Concordia Dmitry Jakobson, McGill

98 Scientific Personnel

Vojkan Jakšić, McGill Christiane Rousseau, Montréal Tomasz Kaczynski, Sherbrooke Damien Roy, Ottawa Niky Kamran, McGill Peter Russell, McGill Olga Kharlampovich, McGill Yvan Saint-Aubin, Montréal Hershy Kisilevsky, Concordia David Sankoff, Ottawa Paul Koosis, McGill Dana Schlomiuk, Montréal Dmitry Korotkin, Concordia Robert Seiringer, McGill Gilbert Labelle, UQAM Alexander Shnirelman, Concordia John Labute, McGill Vasilisa Shramchenko, Sherbrooke François Lalonde, Montréal Alina Stancu, Concordia Benoît Larose, Champlain St-Lambert & Concordia Ron J. Stern, Concordia Christian Léger, Montréal Alain Tapp, Montréal Frédéric Lesage, Polytechnique Montréal Francisco Thaine, Concordia Sabin Lessard, Montréal John A. Toth, McGill Claude Levesque, Laval Lennaert van Veen, UOIT Jean-Marc Lina, ÉTS Roger Villemaire, UQAM Shiping Liu, Sherbrooke Luc Vinet, Montréal Steven Lu, UQAM Johannes Walcher, McGill Brenda MacGibbon, UQAM Timothy R. S. Walsh, UQAM Michael C. Mackey, McGill Thomas P. Wihler, Bern Vladimir Makarenkov, UQAM Pavel Winternitz, Montréal Michael Makkai, McGill Daniel T. Wise, McGill Javad Mashreghi, Laval Xiaowen Zhou, Concordia Sherwin A. Maslowe, McGill Associate members Pierre Mathieu, Laval John McKay, Concordia Nantel Bergeron, York Manuel Morales, Montréal Robert Conte, CEA/Saclay M. Ram Murty, Queen’s Stéphane Durand, Édouard-Montpetit Fahima Nekka, Montréal Bertrand Eynard, CEA/Saclay Robert G. Owens, Montréal Martin J. Gander, Genève Manu Paranjape, Montréal Pierre Ille, CNRS & Aix-Marseille Jiří Patera, Montréal Marc Laforest, Polytechnique Montréal François Perron, Montréal Decio Levi, Roma Tre Iosif Polterovich, Montréal Jun Li, Pharsight Lea Popovic, Concordia Emmanuel Lorin de la Grandmaison, Carleton James O. Ramsay, McGill Yiannis N. Petridis, Univ. Coll. London Thomas J. Ransford, Laval Elisa Shahbazian, OODA Technologies Bruno Rémillard, HEC Montréal Marc Thiriet, CNRS, UPMC & INRIA Rocquencourt Christophe Reutenauer, UQAM Pierre Valin, Defence R&D Canada Louis-Paul Rivest, Laval Carolyne M. Van Vliet, Montréal & Miami Ivo G. Rosenberg, Montréal Jean-Paul Zolésio, INRIA Sophia Antipolis

99 Centre de recherches mathématiqes

Invited members Pierre Lafaye de Micheaux, Montréal Mylène Bédard, Montréal Alejandro Murua, Montréal Laurent Habsieger, CNRS & Lyon 1 Yuanli Zhang David Haziza, Montréal

Postdoctoral Fellows

Each year the CRM plays host to a large number of postdoctoral fellows. Their funding is provided through the NSERC and FRQNT postdoctoral programs, a NATO international program administered by NSERC, the CRM (usually in collaboration with the ISM), the CRM’s research laboratories, and individual research grants from CRM members. The list below includes postdoctoral fellows in residence at the CRM and those cofunded bythe CRM. Some of the fellows were in residence at the CRM for only part of the year. The affiliation given isthe institution where the doctorate was obtained.

Elif Fidan Acar, Toronto Alexander E. Hoffnung, UC Riverside Shabnam Akhtari, UBC Nabil Kahouadji, Paris Diderot Ferenc Balogh, Concordia Caroline Kalla, Bourgogne Alexander Bihlo, Wien Abdoulaye Kane, Laval Winton Brown, Dartmouth Coll. Leila Kheibarshekan, Gent Mattia Cafasso, SISSA Dimitris Koukoulopoulos, UI Urbana-Champaign Renato Calleja, UT Austin Antonio Lei, Cambridge Vorrapan Chandee, Stanford Alok Kumar Maharana, Tata Inst. Nikolai Dimitrov, Cornell Guyslain Naves, Joseph Fourier Tiago Dinis da Fonseca, UPMC Sarah Post, Minnesota Fabrizio Donzelli, Miami Danilo Riglioni, Roma Tre Grégoire Dupont, Lyon 1 Vivien Ripoll, Paris Diderot Abdelkrim El Basraoui, Ottawa Brian Seguin, Carnegie Mellon Suresh Eswarathasan, Rochester Ethan C. Smith, Clemson François Fillion-Gourdeau, McGill Christian Stump, Wien Ke Gong, Henan Marzena Szajewska, Bialystok Igor Gorelyshev, RAS Matthias Westrich, Aarhus Philip Grech, ETH Zürich Mark Wilde, Southern California Melita Hadzagic, McGill Driss Yacoubi, UPMC Mariah E. Hamel, UBC Guofu Yu, Shanghai Jiao Tong Eric Harper, Miami

Visitors

Each year the CRM hosts a large number of visitors. The majority come to the Centre to participate in scientific activities organized or co-organized by the CRM. In 2011–2012 there were 13 activities in the thematic program and 821 researchers took part in these activities, 10 of which were held at the CRM itself. There were also 13 activities in the general program, 7 of which were held at the CRM; altogether 665 participants took part in these activities. Finally the multidisciplinary and industrial program featured 3 activities, one of which took place at Concordia University and two at the CRM; 101 researchers participated in the two activities held at the CRM.

100 Scientific Personnel

Long-term visitors Short-term visitors

The following list only includes visitors who werein The following visitors were in residence for less than residence for at least four weeks. four weeks. Maia Angelova, Northumbria Jeffrey A. Achter, Colorado State Pierre Cagne, ÉNS Michael Aizenman, Princeton Yi-Fu Cai, Arizona State Alain Arnéodo, CNRS & ÉNS Lyon Leonid Chekhov, Steklov Inst. Joan Carles Artés, UA Barcelona Patrick Desrosiers, Talca Yosi Avron, Technion Eduardo Dubuc, Buenos Aires Sven Bachmann, UC Davis Semen Dyatlov, UC Berkeley Thomas Ballesteros, Cergy-Pontoise Victor Enolskii, NAS Ukraine Jean-Marie Barbaroux, Toulon Corneille Auxence Eyallo, Tver SU Jean-François Barraud, Paul Sabatier Piotr P. Goldstein, Sołtan Inst. Eva Bayer, EPFL Philip Grech, ETH Zürich Valérie Berthé, Montpellier 2 Mark Haiman, UC Berkeley Paul Biran, ETH Zürich Christian Hainzl, Tübingen Guillaume Blin, Marne-la-Vallée Bernard R. Hodgson, Laval Laurent Bruneau, Cergy-Pontoise Vojkan Jakšic, McGill Alina Bucur, UC San Diego Zdenek Kabat, TU Prague Philip Candelas, Oxford Israel Klich, Virginia Goce Chadzitaskos, Doppler Inst. Mathieu Lewin, Cergy-Pontoise Horia Cornean, Aalborg Keivan Mallahi Karai, Jacobs Stephan De Bièvre, Lille 1 Tomáš Mikolov, Brno UT Clelia De Felice, Salerno Aïda Ouangraoua, Simon Fraser Xenia de la Ossa, Oxford Annalisa Panati, Toulon Maksym Derevyagin, TU Berlin Petr Paramonov, Moscow SU Jan Derezinski, Warsaw Lucas Pastor, Savoie Bernard Derrida, ÉNS Claude-Alain Pillet, Toulon Charles Doran, Alberta Pedro Real, Sevilla Vladimir Dorodnitsyn, Keldysh Inst. Michael Rubinstein, Waterloo Vladimir Dragovic, MI SANU Robert Seiringer, McGill Konstantin Fedorovskiy, Moscow STU Ramesh Sreekantan, ISI Bangalore Brooke Feigon, East Anglia Michael Sullivan, UMass Amherst Oleksandr Filipov, NAS Ukraine Sumati Surya, Raman RI Kevin Ford, UI Urbana-Champaign David Taj, Toulon Dominique Fourdrinier, Rouen Marc Thiriet, CNRS & UPMC Grigorios Fournodavlos, Toronto Nicolae Vulpe, IMI Moldova Alexander Fribergh,NYU Eduardo Santillan Zeron, Cinvestav Jixiang Fu, Fudan Oleksiy Zhedanov, Donetsk IPE Samuele Giraudo, Marne-la-Vallée Peter Zograf, Steklov Inst. Cameron Gordon, UT Austin

101 Centre de recherches mathématiqes

Matthew Greenberg, Calgary Patrick Peter, CNRS & IAP F. Alberto Grünbaum, UC Berkeley Stephen C. Preston, CU-Boulder Martin Guest, Tokyo MU Rachel Pries, Colorado State Mo Hendon, Georgia Maksym Radziwill, Stanford Jiří Hrivnák, TU Prague Jorgen Rasmussen, Melbourne Duc Khiem Huynh, Rutgers David Ridout, ANU Clément Hyvrier, Uppsala Danilo Riglioni, Roma Tre Pierre Ille, CNRS & Aix-Marseille Miguel A. Rodríguez, Complutense Sarah Iveson, UC Berkeley Victor Rotger, UPC Damien Jamet, Henri Poincaré David P. Ruelle, IHÉS Alain Joye, Joseph Fourier Mary-Beth Ruskai, Tufts Camell Kachour, Macquarie Yoshitaka Sasaki, Kinki Nicola Kistler, Bonn Helena Sedivakova, TU Prague Gerasim Kokarev, München Ruedi Seiler, TU Berlin Flora Koukiou, Cergy-Pontoise Armen Shirikyan, Cergy-Pontoise Decio Levi, Roma Tre Libor Šnobl, TU Prague Michael Levitin, Reading Domingo Tarzia, Austral Elliott H. Lieb, Princeton Agnieszka Tereszkiewicz, Bialystok Chang-Shou Lin, NCCU Lawrence E. Thomas, Virginia Roberto Livi, Firenze Zora Thomova, SUNY IT David Loeffler, Warwick Satoshi Tsujimoto, Kyoto Jérôme Martin, IAP Alexander Turbiner, UNAM Hiroshi Miki, Kyoto Pedro Vieira, Perimeter Inst. Jacob Schach Møller, Aarhus Matthias Westrich, Aarhus Damien Mondragon, UC Berkeley Jakob Yngvason, Wien Bruno Nachtergaele, UC Davis Valentin Zagrebnov, Aix-Marseille Vasileios Nestoridis, Athens Sarah Zerbes, Exeter Leonid Parnovski, Univ. Coll. London Jean-Paul Zolésio, INRIA Sophia Antipolis

102 List of Students Having Graduated in 2011–2012 Centre de recherches mathématiqes

he CRM members supervise a large number of graduate students. In this section we give information on the T students supervised by CRM members who graduated in 2011–2012. The name of the student is followed by the name of his or her supervisor (or names of his or her supervisors), his or her institution, and his or her program. Some names may be missing from this list, because we have only included those that have been brought to our attention.

Ph.D. Students

Blache Paul Akpoué Myriam Fillion Jean-François Angers Fabrice Larribe Université de Montréal Université du Québec à Montréal Statistics Environmental Sciences Raluca Apostu Daniel Fiorilli Michael C. Mackey Andrew Granville McGill University Université de Montréal Physiology Mathematics (pure mathematics option) Hirbod Assa Mark Hagen Bruno Rémillard and Manuel Morales Daniel T. Wise and Dmitry Jakobson Université de Montréal McGill University Mathematics (applied mathematics option) Mathematics James Bergstra Othmane Kortbi Yoshua Bengio Éric Marchand Université de Montréal Université de Sherbrooke Computer Science Mathematics Rebecca J. Danos Jun Li Robert Brandenberger Yogendra P. Chaubey McGill University Concordia University Physics Mathematics Michel Dieme Li Ma Roger Pierre and A. Séné Wei Sun Université Laval Concordia University Mathematics Mathematics Matthew Doyle Felicia Magpantay Yves Bourgault Anthony R. Humphries University of Ottawa McGill University Engineering Mathematics Nicolas Dutil Romuald H. Momeya Ouabo Claude Crépeau Manuel Morales and Louis G. Doray McGill University Université de Montréal Computer Science Statistics Layan Ahmad El-Hajj Ramin Okhrati John A. Toth José Garrido McGill University Concordia University Mathematics Mathematics Ashkan Ertefaie Murray Patterson David A. Stephens and Masoud Asgharian Cédric Chauve McGill University Simon Fraser University Mathematics Bioinformatics

104 List of Students Having Graduated in 2011–2012

Myriam Rioux Marzena Szajewska Yves Bourgault and Youssef Belhamadia Zbigniew Pasternak-Winiarski and Jiří Patera University of Ottawa University of Bialystok and Université de Montréal Mathematics Mathematics Patrice Rivard Jie Zhang Line Baribeau Thomas Brüstle Université Laval Université de Sherbrooke Mathematics Mathematics Joël Sango Xiangwen Zhang Pierre Duchesne Pengfei Guan Université de Montréal McGill University Statistics Mathematics Marius Serban Jun Zhou Jiří Patera José Garrido Université de Montréal Concordia University Mathematics (pure mathematics option) Mathematics

M.Sc. Students

Yassine Ajjaouj Audrey Béliveau Lajmi Lakhal Chaieb David Haziza Université Laval Université de Montréal Statistics Statistics Shervin Asgari Jonathan Belletête Arusharka Sen Manu B. Paranjape Concordia University Université de Montréal Mathematics Physics Tigran Atoyan Michaël Bernier David A. Stephens Maxime Descoteaux McGill University Université de Sherbrooke Statistics Mathematics Edward Baraghis Alexandre Bérubé-Beaulne Frédéric Lesage Bruno Rémillard École Polytechnique de Montréal HEC Montréal Electrical Engineering Financial Engineering Justine C. Barolet Mélanie Boisvert Michel C. Delfour Virginie Charette and Ibrahim Assem Université de Montréal Université de Sherbrooke Mathematics (applied mathematics option) Mathematics Mouloud-Beallah Belbahri Clément Bonnery David Haziza Frédéric Lesage Université de Montréal École Polytechnique de Montréal Statistics Electrical Engineering Alexandre Beaulne Arnaud Boré Bruno Rémillard and Pierre Laroche Maxime Descoteaux HEC Montréal Université de Sherbrooke Financial Engineering Mathematics

105 Centre de recherches mathématiqes

Audrey Champagne-Paradis Mohamad Elmasri Ivo G. Rosenberg Arusharka Sen Université de Montréal Concordia University Mathematics (pure mathematics option) Statistics Alexandre Couët Andrea Ferraguti André Fortin Adrian Iovita Université Laval Concordia University Mathematics Mathematics Jean-François Cyr Vincent Genest Richard Duncan Yvan Saint-Aubin Université de Montréal Université de Montréal Mathematics Physics Gaël David Charles-Édouard Giguère Virginie Charrette Martin Bilodeau and Jean Séguin Université de Sherbrooke Université de Montréal Mathematics Statistics Victoria De Quehen Esteban Herrera-Cordero Eyal Z. Goren and Peter Russell François Lalonde McGill University Université de Montréal Mathematics Mathematics (pure mathematics option) Mouhamed El Moctar Diop Niamh Higgins Bruno Rémillard Erica E. M. Moodie HEC Montréal McGill University Financial Engineering Epidemiology Philippe Dompierre Lennart Hilbert Ibrahim Assem Michael C. Mackey Université de Sherbrooke McGill University Mathematics Physiology Andrea Doroftei Audrey Juhasz Nadia El-Mabrouk Ron J. Stern Université de Montréal Concordia University Computer Science Mathematics Katherine Edwards Loredana Kis Bruce Shepherd Jean-François Angers McGill University Université de Montréal Mathematics Statistics Walid El Maksoud Marc-André Lacasse Thierry Duchesne Andrew Granville Université Laval Université de Montréal Statistics Mathematics Yara Elias Ruomeng Lan Andrew Granville Alexander Shnirelman Université de Montréal Concordia University Mathematics Mathematics

106 List of Students Having Graduated in 2011–2012

Julie Langlois Claudiu Mircea Motoc Jérémie Rostand Geneviève Lefebvre Université Laval Université du Québec à Montréal Mathematics Statistics Alexandre Laurin Jungbae Nam Chris J. Cummins Hershy Kisilevsky Concordia University Concordia University Mathematics Mathematics Guillaume Lavoie Nicolas Paquin Iosif Polterovich Gilbert Labelle and Robert Bédard Université de Montréal Université du Québec à Montréal Mathematics (pure mathematics option) Mathematics Elena Lavrova Larissa Paulo Iosif Polterovich Louis-Paul Rivest Université de Montréal Université Laval Mathematics (pure mathematics option) Statistics Martin Leclerc Michèle Picard-Flibotte Lajmi Lakhal Chaieb Thierry Duchesne and Christian Genest Université Laval Université Laval Statistics Statistics Philippe Lemieux-Mellouki Antoine Poirier Hugo Chapdelaine and Claude Levesque Andrew Granville Université Laval Université de Montréal Mathematics Mathematics (pure mathematics option) Arnaud Lepage-Jutier Iuliana Adriana Popper Alexander Maloney Pavel Winternitz McGill University Université de Montréal Physics Mathematics (pure mathematics option) Ahmad Mahmoody Mireille Prevost Cédric Chauve Vojkan Jaksic and Robert Seiringer Simon Fraser University McGill University Bioinformatics Mathematics Matei Mireuta Oscar Alberto Quijano Xacur Mylène Bédard José Garrido Université de Montréal Concordia University Statistics Mathematics Abdelkarim Mohammedi Yasmine Raad Louis-Paul Rivest Alina Stancu Université Laval Concordia University Statistics Mathematics Jonathan Moscovici Ashok Rajaraman Alain C. Vandal and Roland Grad Cédric Chauve McGill University Simon Fraser University Statistics Bioinformatics

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Gerasimos Rassias Joel Tousignant-Barnes Bruno Rémillard Dmitry Jakobson and John A. Toth HEC Montréal McGill University Financial Engineering Mathematics Santiago Ravassi Pierre-Olivier Vallerand-Beaudry Lea Popovic and Galia Dafni Tomasz Kaczynski and Virginie Charette Concordia University Université de Sherbrooke Mathematics Mathematics Sudipta Saduhkhan Vasile Vanciu David A. Stephens Sorana Froda and René Ferland McGill University Université du Québec à Montréal Statistics Statistics Robinson Saint-Frard Richard Vermette Pierre Duchesne Thierry Duchesne and Christian Genest Université de Montréal Université Laval Statistics Statistics Alexis Selezneff Jing Wang Thomas J. Ransford Christian Léger Université Laval Université de Montréal Mathematics Statistics Mikhail Misha Smilovic Matthieu Willems Daniel T. Wise, Jacques Hurtubise and Vladimir Makarenkov Dmitry Jakobson Université du Québec à Montréal McGill University Computer Science Mathematics Karim Zerouali Mengjue Tang Frédéric Lesage Yogendra P. Chaubey École Polytechnique de Montréal Concordia University Electrical Engineering Mathematics Quan Zhou Alexandre Tomberg David A. Stephens Vojkan Jakšić and Robert Seiringer McGill University McGill University Statistics Mathematics Petr Zorin Artour Tomberg Richard L. Hall Jacques Hurtubise and Robert Seiringer Concordia University McGill University Mathematics Mathematics

108 Governance and Scientific Guidance Centre de recherches mathématiqes

he CRM structure consists of a Board of Directors, an Assembly of Members, an International Scientific Ad- T visory Committee, a Local Scientific Committee, an Executive Committee, and a Committee ofDirectors Laboratories. In 2011-2012, the members of the Local Scientific Committee were Steven P. Boyer (Université du Québec à Montréal), Gilles Brassard (Université de Montréal), André Fortin (Université Laval), Andrew Granville (Université de Montréal), Dmitry Jakobson (McGill University), and François Lalonde (Université de Montréal; Director of the CRM). The Executive Committee consists of the CRM Director and the Deputy Directors. For more information, the reader may consult the web site crm.math.ca/apropos/CRM_structure_an.shtml.

Board of Directors The Board of Directors is composed of: • The Director (ex officio); • A member of the Executive Committee nominated • The Vice-Principal, Research, of each of the main by the Board for a two-year mandate; partner universities of the CRM, or his representa- • Two regular members nominated by the Assembly tive; for three-year mandates, normally renewable once; • A Vice-Principal, Research, of one of the other part- • A Laboratory Director, nominated by the Committee ner universities of the CRM, chosen by these univer- of Directors of Laboratories for a two-year mandate, sities on a rotating basis for a two-year mandate. normally renewable once; Here are the members of the Board of Directors for 2011–2012. Jacques Beauvais, Vice-Rector (Research) Joseph Hubert, Vice-Rector (Research) Université de Sherbrooke Université de Montréal (until December 31, 2011) Graham Carr, Vice-President (Research) François Lalonde, Director of the CRM Concordia University (from January 1, 2012) Université de Montréal Olivier Collin Odile Marcotte, Deputy Director of the CRM Université du Québec à Montréal Université du Québec à Montréal Louise Dandurand, Vice-President (Research) Yves Mauffette, Vice-Rector (Research) Concordia University (until December 31, 2011) Université du Québec à Montréal Rose Goldstein, Vice-Principal (Research) Christiane Rousseau McGill University Université de Montréal John Harnad Geneviève Tanguay, Vice-Rector (Research) Concordia University Université de Montréal (from January 1, 2012)

Chantal David (Concordia University) and Octav Cornea (Université de Montréal), Deputy Directors of the CRM, were invited members.

Committee of Directors of Laboratories

The Committee of Directors of Laboratories is composed of the Director, the Directors of the ten CRM Laboratories and the Deputy Directors of the Centre. It meets at least once a year to discuss any question that concerns the laboratories. The Directors of the laboratories are:

Steven P. Boyer (UQAM) Henri Darmon (McGill University) CIRGET — Geometry and Topology CICMA — Number Theory and Algebra François Bergeron (UQAM) André Fortin (Université Laval) LaCIM — Combinatorics and Theoretical Computer GIREF — Modelling and Numerical Simulation Science

110 Governance and Scientific Guidance

Eliot Fried (McGill University) Jean-Marc Lina (École de technologie supérieure) Applied Mathematics PhysNum — Medical Imaging and Pharmacometrics John Harnad (Concordia University) Louis-Paul Rivest (Université Laval) Mathematical Physics Statistics Dmitry Jakobson (McGill University) Mathematical Analysis

International Scientific Advisory Committee

The International Scientific Advisory Committee consists of distinguished researchers from Canada andabroad. Its members are either mathematicians or scientists with close ties to the mathematical sciences. The Advisory Committee is kept informed regularly of the activities of the Centre through the Director. The Committeemakes recommendations about the general scientific orientations of the CRM and gives advice about proposed scientific activities.

Martin Barlow received his Allan Borodin received undergraduate degree from the his B.A. in Mathematics in University of Cambridge in 1975 1963 (from Rutgers Univer- and completed his doctoral de- sity), his M.Sc. in Electri- gree with David Williams at the cal Engineering and Com- University College of Swansea puter Science in 1966 (from in Wales (1978). Since then he Stevens Institute of Tech- has been a leading researcher in nology), and his Ph.D. in probability theory, in particular diffusion in fractals Computer Science in 1969 (from Cornell University). and other disordered media. He held a Royal Soci- He was a systems programmer at Bell Laboratories in ety University Research Fellowship at the University New Jersey from 1963 to 1966 and a Research Fellow of Cambridge from 1985 to 1992, when he joined the at Cornell from 1966 to 1969. Since 1969, he has been Mathematics Department at the University of British a professor in the Department of Computer Science Columbia. He is currently Professor of Mathematics at at the University of Toronto, where he became a full UBC. He has held a number of visiting professorships professor in 1977. He was department chair from 1980 at leading universities. Martin Barlow gave an invited to 1985. Professor Borodin is a world leader in the lecture at the 1990 ICM in Kyoto and was an invited mathematical foundations of computer science and lecturer at the prestigious Saint-Flour Summer School has made fundamental contributions to many areas, in 1995. In 2008 he received the Jeffery-Williams Prize including algebraic computations, resource tradeoffs, of the Canadian Mathematical Society and in 2009 the routing in interconnection networks, parallel algo- CRM –Fields–PIMS Prize. Other distinctions include rithms, on-line algorithms, and adversarial queuing the Rollo Davidson Prize from the University of Cam- theory. Professor Borodin has been the editor of many bridge and the Junior Whitehead Prize from the Lon- journals, including the SIAM Journal on Computing. don Mathematical Society. He has been a leader of He has held positions on, or been active in, dozens of the international probability community as a lead or- committees and organizations, both inside and outside ganizer of numerous conferences, Associate Editor of the University, and has held several visiting professor- all the top probability journals, and Editor-in-Chief of ships internationally. In 1991 Professor Borodin was the Electronic Communications in Probability. He has elected a Fellow of the Royal Society of Canada and in been a Fellow of the Institute of Mathematical Statis- 2008 he received the CRM –Fields–PIMS Prize. tics since 1995 and of the Royal Society of Canada since 1998. In 2006 he was elected Fellow of the Royal Soci- ety (London).

111 Centre de recherches mathématiqes

Stephen E. Fienberg is Mau- Their Applications of the National Academies. She has rice Falk University Professor also been involved continuously in the organization of Statistics and Social Science of conferences and workshops; in particular she was at Carnegie Mellon University. a member of the AMS-Shanghai Joint Meeting Pro- He is the Carnegie Mellon codi- gram Committee. She has served on numerous AMS rector of the Living Analytics editorial boards and university committees. She has Research Centre. Fienberg re- been honoured with several academic awards, includ- ceived his hon. B.Sc. in Mathe- ing the Institut Henri-Poincaré Medal, the Gauthier- matics and Statistics from the University of Toronto Villars Prize for Nonlinear Analysis, and the Univer- (1964) and his A.M. and Ph.D. degrees in Statistics from sity of Illinois Scholar Award (in 2003). Over the years, Harvard University (1965, 1968). she has been a frequent invited lecturer in the United Professor Fienberg has served as Dean of the College States and around the world of Humanities and Social Sciences at Carnegie Mellon Mark Goresky has been a mem- and as Vice President for Academic Affairs at York Uni- ber of the Institute for Advanced versity, in Toronto, as well as on the faculties of the Study in Princeton since 1994. He University of Chicago and the University of Minnesota. received his B.Sc. from the Univer- He has been a founding editor of a number of statistical sity of British Columbia in 1971 journals. He has been Vice President of the American and a Ph.D. from Brown Univer- Statistical Association and President of the Institute of sity in 1976. In 1986 he was elected Mathematical Statistics and the International Society to the Royal Society of Canada. He for Bayesian Analysis. was awarded the Jeffery-Williams Prize of the Cana- Fienberg’s research includes the development of statis- dian Mathematical Society in 1996 and the Steele Prize tical methods, especially tools for categorical data anal- of the American Mathematical Society in 2002 (jointly ysis and the analysis of network data, algebraic statis- with R. MacPherson). He was a member of the editorial tics, causal inference, statistics and the law, machine board of the Canadian Journal of Mathematics from learning, and the history of statistics. 1997 to 2000 and is currently a member of the edito- rial board of the Bulletin of the American Mathemat- Fienberg is a member of the U.S. National Academy of ical Society. He is a world expert in geometric repre- Sciences, and a fellow of the Royal Society of Canada, sentation theory. the American Academy of Arts and Sciences, and the American Academy of Political and Social Science, as Mark L. Green has been a pro- well as a fellow of the American Association for the fessor in the UCLA Department Advancement of Science, the American Statistical As- of Mathematics since 1982. He re- sociation, the Institute of Mathematical Statistics, and ceived his Ph.D. from Princeton an elected member of the International Statistical In- University in 1972 and was Direc- stitute. tor of the Institute for Pure and Applied Mathematics from 2001 to Susan Friedlander is cur- 2008. Mark Green has received nu- rently Director of the Center merous honours during his career. In particular, he for Applied Mathematical Sci- was an invited speaker at the International Congress ences and Professor of Math- of Mathematicians in Berlin in 1998. He was a plenary ematics at the University of speaker at the Abel Centennial held in Oslo in 2002 Southern California. She ob- and the Hodge Centennial held in Edinburgh in 2003. tained her Doctoral degree at Professor Green’s services to the mathematical com- Princeton University in 1972. munity are extensive. He was a member of the Board She has published extensively in the areas of differen- of Trustees at the Claremont Center for the Mathemat- tial equations and fluid mechanics. She has been very ical Sciences and a member of the Board of Directors active on numerous committees and evaluation panels, of the Center for Mathematics and Teaching. Profes- including the Council of the American Mathematical sor Green also served on the NSERC Major Resources Society and the Board on Mathematical Sciences and Support Committee and was the editor of the Journal

112 Governance and Scientific Guidance of Algebraic Geometry. His research interests are in A mathematician and physicist by commutative algebra, algebraic geometry, and applied training, François Lalonde holds mathematics. a Doctorat d’État (1985) from the Jacques Hurtubise obtained a B.Sc. Université Paris-Sud in the field of in mathematics in 1978 from the Uni- differential topology. His fields of versité de Montréal and a Ph.D. in interest include symplectic topol- mathematics in 1982 from the Univer- ogy, Hamiltonian dynamics and the sity of Oxford, where he was a Rhodes study of infinite-dimensional groups scholar. From 1982 to 1988 he was a of transformations. He has been a member of the Royal professor at UQAM. Since 1988 he has Society of Canada since 1997 and was a Killam Re- been a professor in the Department search Fellowship recipient in 2000–2002. He holds of Mathematics and Statistics of McGill University (of the Canada Research Chair in the field of Symplectic which he has been the chairman since 2009). His re- Geometry and Topology at the Department of Math- search interests are in gauge theory, algebraic geome- ematics and Statistics of the Université de Montréal. try, integrable systems, and mathematical physics. He François Lalonde was a plenary speaker at the First was a Fellow of the Institute for Advanced Study at Canada–China congress in 1997; part of his work in Princeton in 1987–1988 and a Centennial Fellow of the collaboration with Dusa McDuff was presented in her American Mathematical Society in 1993–1994. In 1993 plenary address at the ICM 1998 in Berlin. He was also Jacques Hurtubise was awarded the Coxeter–James an invited speaker at the ICM 2006 in Madrid. Prize by the Canadian Mathematical Society. In 2004 Claude Le Bris obtained his doc- he became a Fellow of the Royal Society of Canada. torate from the École Polytech- From 2010 to 2012 he was the President of the Cana- nique in France and his accredi- dian Mathematical Society. Jacques Hurtubise was or is tation to supervise research from a member of numerous committees of NSERC, FRQNT, the Université Paris Dauphine in and the Council of Canadian Academies. 1997. His research interests include Barbara Lee Keyfitz has been a mathematical analysis and numer- professor at the Ohio State Univer- ical methods for partial differen- sity since January 2009. She served tial equations and their applications to molecular sim- as Director of the Fields Institute ulation, multiscale problems, materials science, and for Research in Mathematical Sci- continuum mechanics. He is a world-renowned ex- ences from 2004 to 2008. From 2000 pert in the mathematics of quantum chemistry and to 2008, she was John and Rebecca the computation of the electronic structure in quan- Moores Professor of Mathematics tum physics. Claude Le Bris received the Blaise Pascal at the University of Houston, which she joined in 1987, Prize from the Académie des Sciences in 1999, the “CS following appointments at Columbia, Princeton, and 2002 Prize in Scientific Computing,” and the Giovanni Arizona State University. She studied at the University Sacchi-Landriani Prize from the Istituto Lombardo in of Toronto and obtained her Ph.D. at the Courant In- 2002. He was Civil Engineer-in-Chief and Research stitute (NYU). Barbara Keyfitz is a Fellow of the Amer- Scientist at the École Nationale des Ponts et Chaussées ican Association for the Advancement of Science and and scientific leader of the MICMAC project at INRIA. the recipient of the 2005 Krieger–Nelson Prize of the Claude Le Bris has been a member of several program Canadian Mathematical Society. She serves as Trea- committees of international conferences and thematic surer of the International Council of Industrial and Ap- years organized by research centres. He was co-editor plied Mathematics and has been a member of several of Mathematical Modelling and Numerical Analysis and editorial boards. Her research interests are in the field editor of the Applied Mathematics Research eXpress. He of nonlinear partial differential equations. has supervised 12 Ph.D. students and authored five books, 80 articles published in international journals, and 20 articles included into books or conference pro- ceedings. He has given 90 invited lectures at interna-

113 Centre de recherches mathématiqes tional conferences and a series of Aisenstadt lectures derforschungsbereich: Collaborative Research Centre) at the CRM (in the fall of 2009). in Germany in the area of representation theory. Claus Michael Ringel received Akshay Venkatesh has been a the Diplom (1968) and Ph.D. in professor at Stanford University Mathematics from the Goethe- since September 2008. He obtained Universität Frankfurt am Main in his Ph.D. from Princeton Univer- 1969 and the Habilitation from sity in 2002, was C.L.E. Moore In- the Eberhard Karls Universität Tü- structor at MIT from 2002 to 2004, bingen in 1972. He taught briefly and a professor at the Courant In- at Carleton University in Ottawa stitute (NYU) from 2004 to 2008. (1970–1972). From 1978 to 2010 he was Professor of Akshay Venkatesh has received many prizes and fel- Mathematics at the Universität Bielefeld in Germany, lowships since the beginning of his career, in particu- where he is now Professor Emeritus. He is in addi- lar the Sloan Foundation Fellowship (2007), the Salem tion Visiting Chair Professor at Shanghai Jiao Tong Prize (2007), the David and Lucile Packard Foundation University in China. Claus Ringel’s research is in Rep- Fellowship (2007–2012), and the SASTRA Ramanujan resentation Theory, the study of concrete realizations Prize (2008). In 2010 he was Aisenstadt Chair lecturer of abstract algebraic structures. His work has been at the CRM, within the framework of the thematic profoundly influential in the development of the the- semester on Number Theory as Experimental and Ap- ory of representations of finite-dimensional algebras, plied Science. His research interests are in number the- in particular quivers, hereditary algebras, Ringel–Hall ory and automorphic forms, including representation algebras, and quantum groups. He has had, and con- theory, dynamics on homogeneous spaces, and arith- tinues to have, a leading role in a number of SFB (Son- metic algebraic geometry.

Geneviève Tanguay, Vice-Rector (Research), Université de Montréal, is an ex-officio member of the International Scientific Advisory Committee. Chantal David (Concordia University), Octav Cornea (Université de Montréal), and Odile Marcotte (Université du Québec à Montréal), all Deputy Directors of the CRM, are invited members of the Committee.

114 CRM Administrative and Support Staff Centre de recherches mathématiqes

The Director’s Office

François Lalonde Chantal David Director Deputy Director, Le Bulletin du CRM and joint publi- Octav Cornea cations with the AMS and Springer Deputy Director, CRM Prizes Odile Marcotte Deputy Director, Annual Report and Coordination with Related Fields

Administration

Vincent Masciotra Guillermo Martinez-Zalce Head of Administration Research Laboratories Administrative Coordinator Muriel Pasqualetti Diane Brulé-De Filippis Administrative Assistant Administrative Assistant Julie Labbé Secretary

Scientific Activities

Louis Pelletier Sakina Benhima Scientific Activities Coordinator Project Manager Louise Letendre Administrative Assistant

Computer Services

Daniel Ouimet André Montpetit Systems Administrator Office Systems Manager (half-time)

Publications

André Montpetit TEX Expert (half-time)

Communications

Suzette Paradis Communications Officer and Webmaster

116 Mandate of the CRM Centre de recherches mathématiqes

he Centre de recherches mathématiques (CRM) is tional achievement in theoretical and mathemati- T one of the first and foremost institutes of mathe- cal physics, and the CRM–SSC Prize for exceptional matical research in the world. Indeed it was the first in- contributions to statistics in early career, ternational institute to introduce the famous thematic • it publishes technical reports and books (some of its programs (in 1984, at the same time as the MSRI). These collections are published jointly with the AMS or programs were created independently by the two in- Springer), stitutes and were an inspiration for the tens of insti- • it has an extensive postdoctoral fellowship program, tutes that were created in Europe and Asia after 1984. with more than thirty postdoctoral fellows on site, This model turned out to be the most creative and funded in partnership with other organizations and efficient means of fostering research and its applica- researchers, tions to state-of-the-art technology. Although the ini- • it informs the community of its activities through its tial programs were concentrated in pure and applied newsletter, Le Bulletin du CRM, and its web site at mathematics, they are now much broader and include http://crm.math.ca/, all the fields that use sophisticated mathematical meth- • it participates, with the other two Canadian insti- ods: theoretical physics, classical and quantum infor- tutes, in groundbreaking national initiatives, for in- mation, medical imaging, statistics, probabilistic meth- stance the Mprime network (formerly Mathemat- ods on large-scale networks, etc. ics of Information Technology and Complex Sys- The CRM was created in 1969 by the Université de tems). The institutes sponsor the Annual Meetings Montréal through a special grant from the National of the Mathematical Sciences Societies (CMS, SSC, Research Council of Canada. It became an NSERC na- CAIMS), the development of the mathematical sci- tional research centre in 1984. It is currently funded ences in the Atlantic provinces through AARMS, by NSERC (Natural Sciences and Engineering Research and other activities organized outside the three insti- Council of Canada), by the Government of Québec tutes. They also participate in the National Institute through the FRQNT (Fonds de recherche du Québec – for Complex Data Structures jointly with the Cana- Nature et technologies), by the Université de Montréal, dian statistical community. as well as McGill University, the Université du Qué- This national mandate is complemented by, and indeed bec à Montréal, Concordia University, the University supported by, a long-standing vocation of promoting of Ottawa, the Université Laval, the Université de Sher- research in the mathematical sciences in Québec. For brooke, and by private donations. The mission of the instance, CRM is to support research in mathematics and closely • the CRM supports research through its ten research related disciplines and to provide leadership in the de- laboratories spanning most of the important areas of velopment of the mathematical sciences in Canada. the mathematical sciences, • it supports, through partnership agreements, a The CRM carries on its mission and national mandate group of local researchers chosen mainly from de- in several ways: partments of mathematics and statistics, but also • it organizes each year a series of scientific events on computer science, physics, economics, engineering, a specific theme (high-profile lectures, workshops, etc., summer schools, etc.), • it organizes series of regular seminars and lecture • its general program and its multidisciplinary and in- courses on different areas of the mathematical sci- dustrial program provide funding for conferences ences, and special events at the CRM and across the coun- • it sponsors joint activities with the Institut des try, sciences mathématiques (ISM), including the CRM • each year it invites, through the Aisenstadt Chair, –ISM colloquia, graduate courses offered by distin- one or more distinguished mathematicians to give guished visitors, and a program of postdoctoral fel- advanced courses as part of its thematic program, lowships, • it awards four prizes yearly: the CRM–Fields–PIMS • it works actively at developing contacts with indus- Prize recognizing major contributions to mathe- try, especially through the Montreal Industrial Prob- matics, the André-Aisenstadt Prize given for out- lem Solving Workshops. standing work carried out by a young Canadian The CRM fulfils its national mission by involving the mathematician, the CAP–CRM Prize for excep- largest possible number of Canadian mathematicians

118 Mandate of the CRM in its scientific programs, both as participants and as attend lectures given by outstanding international sci- organizers. It also supports many events taking place entists. outside Montréal and the Province of Québec. The The director of the CRM is assisted by two managerial CRM is reaching out to the general public through two structures: the Board of Directors and the International ongoing programs: the Accromαth magazine, which Scientific Advisory Committee. The Advisory Commit- was created jointly by the CRM and the ISM and has tee is a group of internationally renowned mathemati- won many international prizes and the Prix spécial de cians from Canada and abroad, who approve scientific la Ministre de l’Éducation (in 2008), and the Grandes programs and thematic years, choose recipients of the Conférences du CRM, which allow a broad public to André-Aisenstadt Prize, and suggest new scientific av- enues to explore.

119