Le BulletinCRM

C E N T R ED E R E C H E R C H E SM A T H É M A T I Q U E S

Printemps/Spring 2016 — Volume 22, No 1 — Le Centre de recherches mathématiques

Thematic Semester

Probabilistic Methods in Geometry,Topology and Spectral Theory

August—December 2016

Probabilistic methods have played an increasingly importantrole in many areas of mathematics, from the study of ran-dom groups and random simplicial complexes in topology, tothe theory of random Schrödinger operators in mathematicalphysics. The Centre de recherches mathématiques will orga-nize an intensive Thematic Program on Probabilistic Methodsin Geometry, Topology and Mathematical Physics during theperiod of August – December 2016. The program will be com-prised of five intensive week-long workshops, including a work-shop in honour of Barry Simon; the latter will be preceded bya Young Researchers Symposium held at the Fields Institute.In addition, there will be lecture series by three AisenstadtChair holders: Nalini Anantharaman, Yuval Peres, and Scott

Sheffield. The workshops will be preceded by preparatory lec-tures for advanced graduate students. Numerous long-termvisitors and postdoctoral researchers will participate in theprogram, hosted by the CRM Laboratories in Analysis andProbability.

The thematic program will cover a broad range of topics, in-cluding geometric analysis on manifolds of metrics and ap-plications to spectral theory and quantum chaos; geometryof random metrics and related problems in quantum gravity;applications of probabilistic techniques in PDE; eigenstate lo-calization in random domains; probabilistic results in num-ber theory; geometry of Teichmüller spaces; renormalization

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methods in dynamical systems; random variational problems;dynamical systems methods in PDE; random simplicial com-plexes and geometry of spaces of triangulations and connec-tions to geometric group theory, manifold learning, topo-logical statistics, and geometric probability; theory of ran-dom groups and their properties; probabilistic methods in 3-manifold theory; random growth problems and random ma-trices; random energy landscapes and their connections tostochastic PDEs and to integrable discrete models (such asTASEP); Bose – Einstein condensation; random matrices andrandom Schrödinger operators; dynamical systems and quasi-periodic operators; many-body quantum mechanics; orthogo-nal polynomials.

There will be an emphasis on interconnections and cross-fertilization of ideas between these topics, giving junior par-ticipants an excellent opportunity to learn from, and interactwith, experts in several different fields.

ORGANIZING COMMITTEE

Louigi Addario-Berry, Linan Chen, Dmitry Jakobson, VojkanJakšić, Mikaël Pichot, Piotr Przytycki, John Toth & DanielWise (McGill); Ilia Binder, Alexander Nabutovsky & BalintVirag (Toronto); Yaiza Canzani (Harvard); Matthew Kahle(Ohio State); Brian Rider (Temple); Igor Rivin (Temple/St Andrews); Armen Shirikyan (Cergy-Pontoise); Lior Silber-man (UBC)

INTERNATIONAL SCIENTIFIC COMMITTEE

Robert Adler (Technion); Walter Craig (McMaster); DmitryDolgopyat (Maryland); Konstantin Khanin, Alexander Nabu-tovsky & Balint Virag (Toronto); Svetlana Jitomirskaya (UCIrvine)

AISENSTADT CHAIRS

Nalini Anantharaman, Strasbourg (August 22 – 26, 2016); Yu-val Peres, Microsoft Research (September 1 – 7, 2016); ScottSheffield, MIT (September 1 – 7, 2016)

WORKSHOPS

Probabilistic Methods in Spectral Geometry and PDEAugust 22 – 26, 2016Organizers: Yaiza Canzani (Harvard); Linan Chen, DmitryJakobson & John Toth (McGill); Armen Shirikyan (Cergy-Pontoise); Lior Silberman (UBC)

Frontiers in Mathematical Physics—Conference in Honourof Barry Simon’s 70th BirthdayAugust 28 – September 1, 2016Organizers: Dmitry Jakobson & Vojkan Jakšić (McGill)Scientific Advisory Committee: Jonathan Breuer (Hebrew);Walter Craig (McMaster); Percy Deift (Courant Institute);George A. Hagedorn (Virginia Tech); Svetlana Jitomirskaya(UC Irvine); Andrei Martinez-Finkelshtein (Almeria)

This conference will be preceded by a five-day Young Re-searchers Symposium, to be held at Fields Institute, August22 – 26, 2016.

Random Growth Problems and Random MatricesSeptember 2 – 6, 2016Organizers: Louigi Addario-Berry (McGill); Ilia Binder &Balint Virag (Toronto); Brian Rider (Temple)

Probabilistic Methods in Dynamical Systems and Applica-tionsOctober 3 – 7, 2016Organizers: Dmitry Dolgopyat (Maryland); Dmitry Jakobson(McGill); Konstantin Khanin (Toronto)

Probabilistic Methods in TopologyNovember 14 – 18, 2016Organizers: Matthew Kahle (Ohio State); Alexander Nabu-tovsky (Toronto); Mikaël Pichot, Piotr Przytycki & DanielWise (McGill); Igor Rivin (Temple/St Andrews); Lior Silber-man (UBC)

FINANCIAL SUPPORT

Support is available for visitors, postdoctoral fellows andgraduate students wishing to attend the various events. Allrequests must be accompanied by a CV. Furthermore, grad-uate students are asked to send a letter of recommendationfrom their research supervisor.

Please apply online on the thematic semester website: www.crm.math.ca/Methods2016

SPONSORS

This thematic program is funded by the following organiza-tions: NSERC (Canada), FRQNT (Québec), Université deMontréal (where the CRM is located), McGill University,UQAM, Concordia University, Université Laval, Universityof Ottawa, Université de Sherbrooke.

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2016 CRM Nirenberg Lectures in Geometric AnalysisGunther Uhlmann (Washington & Hong Kong)

Pengfei Guan & Dmitry Jakobson (McGill); Iosif Polterovich (Montréal); Alina Stancu (Concordia)

Gunther Uhlmann

The annual lectureseries in geometricanalysis in honour ofLouis Nirenberg wasinaugurated by theCRM in 2014. The2016 CRM Niren-berg lectures weredelivered by Profes-sor Gunther Uhlmannover the periodMarch 18 – 22, 2016.Professor Uhlmannis the Walker FamilyEndowed Professor of

Mathematics at the University of Washington and IAS SiYuan Professor at the Hong Kong University of Science andTechnology. He is a world leader in the field of geometricanalysis, and is particularly well known for his fundamentalcontributions to the study of inverse problems. His outstand-ing research achievements include major breakthroughs onCalderón’s inverse problem, and the boundary rigidity prob-lem, as well as the mathematics of invisibility cloaking. Hehas received many awards and honours, such as the Guggen-heim fellowship in 2001, the 2011 Bôcher Memorial Prizeof the AMS and the 2011 Ralph E. Kleinman Prize of theSIAM. He is a member of the American Academy of Arts andSciences and the Finnish Academy of Science and Letters.The three lectures by Professor Uhlmann focussed on somerecent developments in the field of inverse problems. Thefirst lecture, with the intriguing title Harry Potter’s Cloak viaTransformation Optics, was delivered to a packed audience.As one could guess from the title, the topic was invisibilityand the mathematical foundations of cloaking. This subjectis closely related to Calderón’s inverse problem in electricalimpedance tomography (EIT) in which the conductivity ofa domain is inferred from the Dirichlet-to-Neumann map, orthe voltage-to-current map, on its boundary. The speaker de-scribed his breathtaking results with Greenleaf and Lassas onnonuniqueness for EIT and cloaking, illustrated by a beautifulexample of a “blow-up” of a point into a ball-shaped cloak.In a joint work with Greenleaf, Kurylev and Lassas, the ap-proach was extended to other types of cloaking, such as thecloaking for Maxwell’s equations and approximate quantumcloaking. Some exciting applications of these mathematicalideas were presented, notably, to optics, medical imaging andmetamaterials. The speaker has also indicated a number offurther applications that may become possible in the future.The second lecture took the audience on a Journey to theCenter of the Earth. Professor Uhlmann introduced an in-verse problem arising from global seismology: the question

is to determine the sound speed or index of refraction of amedium by measuring the travel times of waves going throughthe medium. It can be reformulated as a boundary rigidityproblem in geometric analysis. Examples indicate that certainconditions are needed for this type of rigidity to hold. Onepossible condition is that the Riemannian manifold is simple,that is, it has a strictly convex boundary and the exponen-tial map is a diffeomorphism at each point. It was conjec-tured by Michel in 1981 that simple manifolds are boundaryrigid, i.e. that the distance function between the points onthe boundary uniquely determines the Riemannian metric upto an isometry which is the identity on the boundary. Afterreviewing some earlier results, Professor Uhlmann presentedhis groundbreaking work with Pestov in which they provedthe conjecture in dimension two. In higher dimensions, theconjecture is known to be true for a generic set of simple met-rics, due to a result by Stefanov and Uhlmann. After a briefdiscussion of the lens rigidity problem, the speaker moved onto the boundary rigidity with partial data. He described someimportant recent developments on the subject, mainly due toStefanov, Vasy and himself. This has led to a discussion ofthe so-called “foliation condition,” which turned out to be anatural generalization of the classical condition for nonradialspeeds introduced by Herglotz and Wieckert-Zoeppritz. Theproofs of these results involved some novel ideas and power-ful techniques ranging from integral geometry to scatteringtheory.The final lecture was entitled Seeing Through Space-Time.Professor Uhlmann started by discussing the inverse prob-lems for scalar nonlinear hyperbolic equations. He explainedhow the nonlinear term could be of help, which is some-what counter-intuitive. After that, the speaker presentedthe inverse problems for the Einstein equation with a time-dependent metric on a 4-dimensional globally hyperbolicLorentzian manifold. He described some recent results oninverse problems in space-time in which the aim is to deter-mine the topology and the metric of the space-time usingpassive measurements (jointly with Kurylev and Lassas), aswell as inverse problems for nonlinear wave equations (jointlywith Kurylev and Lassas, and jointly with Lassas and Wang).The main idea of the proofs is to explore the singularitiesof solutions via a sophisticated study of the interaction be-tween waves. At the end of the lecture, Professor Uhlmanndescribed his most recent results on an inverse problem forthe Einstein scalar field equations, which are of importancein general relativity.The lecture series generated a lot of interest among the mem-bers of the Montréal mathematical community. In particular,many students and postdocs were present. As in the previ-ous years, we had the pleasure and honour to have ProfessorLouis Nirenberg in attendance.

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Nikita Nekrasov (Stony Brook University), Aisenstadt ChairSeptember 14 – 18, 2015

Alexander Maloney, McGill University

Nikita Nekrasov

Nikita Nekrasov visited the CRMfrom September 14 – 18, 2015, togive four lectures as part of the2015 Aisenstadt Chair lecture se-ries. Nekrasov was one of twoAisenstadt Chair holders hosted aspart of the thematic semester onAdS/CFT, Holography and Inte-grability.

A professor at the Simons Centerfor Geometry and Physics at theStony Brook University, Nekrasovis regarded as one of the leadingexperts on mathematical aspects

of quantum field theory. Nekrasov received his Ph.D. in 1996from Princeton University, where he studied under the super-vision of David Gross. He then joined the society of fellowsat Harvard University as a junior fellow, after which he spenttwo years as a Dicke fellow at Princeton University. Nekrasovjoined the faculty of the Institut des Hautes Études Scien-tifiques in Bures-sur-Yvette, France, before moving in 2013 tohis current position at the Simons Center. Nekrasov’s workhas been honoured by several awards, including the JacquesHerbrand Prize, the Herman Weyl Prize and the CompositioPrize.

Nekrasov’s work has centred on the theory of supersymmet-ric gauge theories; these theories share many of the importantfeatures of the quantum field theories that describe the fun-damental interactions of matter, yet possess enough symme-try that exact computations are possible. A typical quantumfield theory computation can be performed only perturba-tively, in a regime where the theory possesses a coupling con-stant which can be tuned to be small; corrections can thenbe computed either using Feynmann diagrams or instantontechniques. Nekrasov’s signature contributions have often in-volved the computation of quantum field theory observablesprecisely at all values of the coupling constant. In particu-lar, in defining a quantum field theory one can in principleformulate the dynamics in terms of a functional integral overa continuous space of field variables. Nekrasov has shownthat in many cases these function integrals can be computedprecisely, using a technique known as localisation where thea-priori infinite-dimensional integral is reduced to a finite-dimensional matrix integral.

Nekrasov’s primary interest lies in Yang – Mills theories withN = 2 supersymmetry, where the dynamics at low ener-gies can be captured by the Seiberg – Witten prepotential.Among other things, Nekrasov has clarified the mathematical

structure contained within the Seiberg – Witten prepotential,which is related to the Donaldson invariants of four-manifoldsas well as to Gromov – Witten theory. Nekrasov has pioneeredthe use of various deformations of quantum gauge theories asa tool for solvability. For example, by putting the theory ina noncommutative space, where the algebra of functions ismodified so that coordinates do not commute:

[xi, xj ] = iθij ,

the theory can be rendered solvable. Similarly, Nekrasov haspioneered the use of the Ω deformation, where the theory isconsidered on a particular curved background and deformedin such a way that the supersymmetry is preserved. No-table in Nekrasov’s work is the relationship between theseYang – Mills invariants and integrability and combinatorics,where — for example — Yang – Mills partition functions arerelated to statistical ensembles of random partitions.

Nekrasov gave a general lecture, Gauge Theories and Inte-grable Systems, which introduced the general notion of in-tegrability in Yang – Mills theory and described several ex-amples. This was accompanied by a set of four technical lec-tures entitled the BPS/CFT Correspondence I – IV which out-lined Nekrasov’s recent work relating the quantum field the-ories in four dimensions to two-dimensional conformal fieldtheories. In particular, topological invariants of instantonmoduli spaces in four dimensions are related to the spaceof conformal blocks in two-dimensional conformal field the-ories. Nekrasov’s “BPS/CFT” programme unifies observa-tions which have been made by various authors over the pastdecade — including the celebrated AGT conjecture — and de-velops new techniques for the computation of field theory par-tition functions.

In memoriamFedor Soloviev

Fedor Soloviev

It is with great sadness that weannounce the passing of Dr. FedorSoloviev on March 24, 2016, after abattle with cancer since 2012.

Dr. Soloviev was a Fields – CRMpostdoctoral fellow at the FieldsInstitute and at the CRM since2013. He was also a postdoctoralfellow, lecturer, and seminar orga-nizer at the University of Torontosince receiving his Ph.D. (Mathe-

matics) from New York University in May 2010. His areaof research was classical integrable systems.

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Bertrand Eynard (CEA Saclay), Aisenstadt ChairSeptember 28 –November 6, 2015

John Harnad (Concordia)

Bertrand Eynard

A key part of the 2015CRM Thematic semesteron AdS/CFT, Hologra-phy and Integrability,was the Aisenstadt Chairlecture series given byBertrand Eynard (IPhT,CEA Saclay). This con-sisted of three lectures,the first relating to the

general theme of “Topological Recursion,” an area in whichhe has been a leading pioneer, the second and the third onthe general theme of “CFT Amplitudes and Hitchin Sys-tems.” These were supplemented by two intensive series ofminicourses developing the same topics in greater detail.

Bertrand Eynard is a member of the Institut de PhysiqueThéorique, CEA Saclay. A leading innovator in a numberof currently active fields of mathematical physics, includingrandom matrices, conformal field theory, quantum gravity,string theory, graphical enumeration and combinatorics, ran-dom geometry and integrable systems, he has become knownover the past decade as the driving force behind the excitingunifying development that goes under the name “TopologicalRecursion.” This forms one of the two main topics of his 2015Aisenstadt Chair lecture series.

He is recognized worldwide for his contributions and is a fre-quent invited speaker at major international meetings, includ-ing an invited talk at the 2014 ICM in Seoul, South Korea andinvited plenary talks at the series of biannual String-Mathconferences (most recently, in Edmonton, 2014) and the Stat-Phys24 conference (Cairns, Australia, 2010).

Since the founding of the CRM’s Mathematical Physics Lab-oratory (PhysMath), Bertrand Eynard has been a valuablelong-term visiting member (2001 – 2003), subsequently an ex-ternal member, and a frequent collaborator with several ofits regular members (M. Bertola, J. Harnad, J. Hurtubise,D. Korotkin). Throughout this time he also has been a keymember of the joint FQRNT research team on Random Ma-trices, Moduli Spaces and Integrable Systems.

Topological recursion is an ubiquitous and universal recursiverelationship between various enumerative/geometric/topolog-ical invariants associated with Riemann surfaces and theirmoduli, links, knots and other basic low dimensional topo-logical invariants of current interest. Numerous applicationsare known in various domains of mathematics and physics,including: volumes of moduli spaces, coefficients of asymp-totic expansions in random matrix theory, Hurwitz numbers,

Jones polynomials, Gromov – Witten invariants, and manyother combinatorial objects, all mysteriously satisfying thesame recursion relations. Moreover, these relations are ef-fective: they allow an actual computation of the invariantsinvolved. The theory has by now been axiomatized into adefinition of “new invariants” of curves. The first AisenstadtChair lecture, entitled Topological recursion (Oct. 2, 2015)introduced the notion of topological recursion, listed its prop-erties and illustrated it with several beautiful examples. Thesubsequent two lectures, CFT amplitudes and Hitchin systems(Oct. 9 & 23, 2015) introduced a systematic construction ofCFT amplitudes from an arbitrary Hitchin system, and ex-plained the relationship between CFT conformal blocks andtau functions of integrable systems, as well as showing howthe Liouville theory 4-point function is related to Painlevé VItau function.

These Aisenstadt Chair lectureswere supplemented by two inten-sive series of minicourses furtherelaborating on the topics involved.The first (Sept. 29 – Oct. 15, 2015)gave a detailed introduction totopological recursion, treating nu-merous examples and explainingthe general formalism. The ma-terial presented forms the basisof a monograph Counting Surfacespublished by Springer.

The first lecture dealt with twomain introductory examples: Hur-

witz numbers and Mirzakhani’s recursion. The next gavean introduction to the general theory underlying the notionof topological recursion, introducing the associated spectralcurves, both classical and quantum, and recalling some ba-sic algebraic geometry of plane curves. The third detailedthe main features of the diagrammatic computation, and in-troduced the notions of symplectic invariance, modular in-variance, singular limits and form-cycle duality. The fourthintroduced tau functions, Baker – Akhiezer functions and theSato relations, connecting them to topological recursion. Thefinal lecture tied together the previous constructs, relating thetau function to generating functions for the various enumera-tive and topological invariants associated to Riemann surfacesand their moduli spaces.

The second minicourse (Oct. 21 – Nov. 3, 2015) Integrable Sys-tems, Random Matrices, Hitchin Systems and CFTs placed

(continued on page 6)

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Moduli Spaces, Integrable Systems, and Topological RecursionsJanuary 9 – 13, 2016

Organizers: Dmitry Korotkin (Concordia University), Jacques Hurtubise (McGill University)

The computation and enumeration of invariants of modulispaces took a sudden turn with the conjecture of Wittenthat they could be combined into a formal series that solvedthe KdV hierarchy. This conjecture, subsequently provenby Kontsevich, was motivated by considerations of quantumgravity. It was followed by a series of developments in thesame direction, notably in the computation of invariants forHurwitz spaces and for Gromov – Witten invariants, for ex-ample in the work of Okounkov and Pandharipande, tyingGromov – Witten theory to the 2-Toda hierarchy. Kontse-vich’s proof involved a detour through the theory of randommatrices, and subsequently Eynard and Orantin proposed avast generalization of the technique, with a wide variety ofimplications. The questions have physical motivations, andthe subject has advanced with the rapid mixture of calcula-tion and heuristic reasoning which characterizes theoreticalphysics; mathematicians have in many but not all cases pro-vided proof, and, it is hoped, some understanding.Thus a first piece of the puzzle is the theory of moduli spaces.The moduli spaces of interest are mainly associated withcomplex algebraic curves: moduli spaces of (pointed) curves,moduli spaces of meromorphic functions on curves (Hurwitzspaces and spaces of admissible covers) and, more generally,moduli spaces of stable maps. A second part of the puz-zle, brought to the fore by Chekhov, Eynard and Orantin,has its origin in the theory of random matrices; invariantsare combined into generating series from which can be com-puted directly a single spectral curve, by what has come tobe known as the topological or Eynard – Orantin recursion. Athird theme comes with the theory of Frobenius manifolds,which were introduced around 1990 by Dubrovin as a ge-ometrization of quantum cohomology that originated fromWitten – Dijkgraaf – Verlinde – Verlinde (WDVV) associativ-ity equation in topological field theories. The quantities as-sociated to the Frobenius manifolds are computable in termsof the topological recursion.The theory of integrable systems seems to lie at the heart ofthe subject, providing a thematic link. It is fair to say, though,that the way in which it happens is still ill-understood. In-deed, so far, it is more the tools, computational devices, andactual functions that appear, rather than flows and conservedquantities.The workshop covered all these themes, and contributedgreatly to completing the picture. Thus, Hurwitz numbersof many sorts are now seen to have a computation in termsof a family of spectral curves; the same goes for the Gro-mov – Witten invariants of toric Calabi – Yau manifolds, wherethe spectral curve is in effect the mirror. The theme oftopological recursion is extending its remit to knot invari-ants and Chern – Simons theories. Likewise, one now has aclear idea of which spectral curves correspond to Frobenius

manifolds. From the integrable systems side, the ties betweenthe topological recursion and WKB approximations for eitherSchrödinger operators or Hitchin systems are gradually be-coming clearer. The workshop was a veritable hotbed of ideasand discussions, with lively scientific discussion not only dur-ing the talks but also between them and well into the eveningafterwards. The CRM staff was in its usual efficient and pleas-ant form, and helped make the event a scientific success forits participants.

Bertrand Eynard(continued from page 5)

the study of conformal field amplitudes in the context of inte-grable systems, most notably, Hitchin systems, and the spec-tral theory of random matrices.The first lecture introduced the Lax formalism, isospectralsystems, algebro-geometric solutions, and Baker – Akhiezerfunctions, expressed in terms of prime forms and thetafunctions corresponding to the associated invariant spectralcurves. The next lecture focused on partition functions forrandom matrices, spectral correlation functions and orthog-onal polynomials as illustrations of solutions to integrablehierarchies. The ODEs and recursion relations satisfied bythe corresponding orthogonal polynomials were shown to beisospectral or isomonodromic systems for an associated Laxmatrix and meromorphic covariant derivative. The partitionfunction and various spectral correlators were interpreted astau functions of the associated integrable hierarchy. The lasttwo lectures of the series dealt in greater detail with the Liou-ville theory 4-point function and its relation to the Painlevé VItau function.In January, Prof. Eynard returned to the CRM to givethe opening talk of the last workshop of the thematicsemester, Moduli Spaces, Integrable Systems, and TopologicalRecursions.

PrixJean-Marie De Koninck

Jean-Marie De Koninck

Jean-Marie De Koninck (Laval)a reçu le prix commémoratifMargaret Sinclair pour 2016 enreconnaissance de son travail depromotion des mathématiques.

Le prix commémoratif MargaretSinclair souligne l’innovation etl’excellence dans l’enseignementdes mathématiques au niveauélémentaire, secondaire, collégialet universitaire.

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2014 CAP–CRM Prize in Mathematical PhysicsLecture by Mark Van Raamsdonk (UBC)

Gravity and EntanglementRobert Brandenberger (McGill)

Mark Van Raamsdonk

Professor Mark VanRaamsdonk is the2014 winner of theCAP – CRM Prize inMathematical Physicsfor his highly original,influential contribu-tions to several areasof theoretical physics,including string the-ory, quantum fieldtheory, and quantumgravity.

Mark Van Raamsdonk is a theoretical physicist whose work,as the CAP – CRM citation states, lies in the field of stringtheory and quantum gravity. Through his work, he attemptsto answer some of the grandest open question, in theoreticalphysics: What is space? What is time? How did our uni-verse begin? How will it end? What is inside a black hole?Throughout his career, he has made many novel contributionsapplying string theory to other areas of physics, from nuclearmatter at high densities to properties of black holes.

Mark received his B.Sc. degree from the University of BritishColumbia in 1995. For his graduate work he moved to Prince-ton University where he obtained his Ph.D. in 2000 under thesupervision of Professor Washington Taylor. After two post-doctoral years at Stanford University he joined the faculty ofUBC in 2002, where he has rapidly risen to the rank of FullProfessor.

Already as a Ph.D. student Mark co-authored papers whichwere to become classics in the field. In particular, in his mosthighly cited paper he and his co-authors discovered an intrigu-ing mixing of high energy and low energy effects in a classof noncommutative quantum field theories. Other pioneer-ing and highly cited work which Mark did while still a Ph.D.student involved the study of multiple D-branes (nonpertur-bative objects which arise in superstring theory) in weaklycurved background space-times.

As a postdoctoral fellow at Stanford Mark turned to othertopics in quantum field theory and string theory. He wrotemany influential papers on M-theory, a candidate for nonper-turbative superstring theory. Maybe the most impressive con-tribution from Mark’s postdoctoral years is the proof of con-finement in a class of four-dimensional quantum field theories.

After taking up his faculty position at UBC, Mark has contin-ued to produce outstanding research. He has a steady streamof highly cited papers on string theory and quantum field the-

ory, including applications to condensed matter physics andcosmology. He has established productive collaborations withleading international researchers in string theory in the UnitedStates, England and India, he has written papers with facultycolleagues at UBC, he has attracted excellent postdoctoralfellows to UBC, and he has successfully trained a number ofgood Ph.D. students. He has helped make UBC one of theleading centres of research in formal quantum field theory andstring theory in North America. He has organized workshopson forefront topics at UBC which participants rave about.

In recent years, Mark’s attention has turned to the connec-tions between quantum entanglement and gravitation. With apaper entitled Building up spacetime with quantum entangle-ment, he won first prize in the Gravity Research Foundationessay award competition of 2010. In this paper, Mark arguesthat the emergence of classically connected space-times is in-timately related to the quantum entanglement of degrees offreedom in a nonperturbative description of quantum gravity.This essay is based on a single author paper which Mark putout a year earlier, and has spawned a huge amount of interestin the field.

Mark’s Prize lecture at the CRM on March 27, 2015 was abeautiful description of this work. Mark’s work on gravityand entanglement is very deep and touches on some of themost important unsolved problems in fundamental physics.Our classical description of space-time appears to be in con-flict with the need for quantum mechanics to describe thenongravitational forces of nature. This is the driving forcebehind our search for a quantum theory of gravity. Tradi-tional ways to quantize gravity have run into road blocks ortechnical difficulties. Since the pioneering work of Maldacenain 1999, the hope has arisen that certain gravitational the-ories are dual to nongravitational theories which live in onelower space-time dimension. Since the dual nongravitationaltheories can be quantized, it is thus possible to study certainquantum aspects of gravity. In his recent work, Mark goesone important step forwards and presents a framework forthe emergence of a classical space-time from quantum build-ing blocks.

Mark’s research excellence has been recognized by a SloanFoundation Research Fellowship and by a Canada ResearchChair. He is also one of the principal investigators on a largeSimons Foundation team research project involving leadingexperts on string theory and quantum information from acrossthe world. We wish to congratulate Mark on his researchachievements and on winning the 2014 CAP – CRM Prize forMathematical Physics.

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Grande Conférence publique du CRM

Systèmes et contrôle : enjeux et réussitesEnrique Zuazua (Universidad Autónoma de Madrid)

Christiane Rousseau (Montréal)

Enrique Zuazua

Le 29 janvier der-nier, le CRM recevaitEnrique Zuazua dela Universidad Autó-noma de Madrid. Cedernier a relevé avecbrio le défi de donnerune grande conférencepublique en françaissur le thème Systèmeset contrôle : enjeux etréussites.

Selon le conférencier,qui a cité Aristote, le désir d’automatisation remonte à trèsloin : « Si les navettes tissaient toutes seules ; si l’archet jouaittout seul de la cithare, les employeurs se passeraient d’ouvrierset les maîtres, d’esclaves. » Le premier exemple de contrôleprésenté, celui de la réduction du bruit, a permis de montrerla différence entre le contrôle passif et les boucles de rétro-action.

La conférence a ensuite fait un détour vers le calcul des varia-tions avec, comme motivation, la quête par Leonhard Eulerde principes d’optimisation pour expliquer les lois de l’uni-vers. Des exemples ont illustré le propos : le problème isopé-rimétrique de la reine Dido, les géodésiques sur une surface,les bulles de savon et le problème de Plateau, le principe deFermat en optique, ainsi que le transport optimal. Commenttrouver numériquement un minimum : le conférencier a pré-senté deux méthodes d’esprit tout à fait différent : la méthodedu gradient est efficace lorsque la fonction ou fonctionnelle àminimiser est suffisamment régulière, alors qu’on préfère uneméthode de Montecarlo quand la structure de la fonctionnelleest très complexe.

Le cœur de la conférence a porté sur la contrôlabilité : c’estla cybernétique introduite par Ampère au xixe siècle et queNorbert Wiener décrit comme the science of control and com-munication in animals and machines, anticipant que, dans lefutur, on voudrait que les machines imitent les humains. Lepropos a été illustré par l’exemple d’un bras de robot, n’ayantque 3 doigts en opposition au pouce, parce que chaque doigtadditionnel ajoute énormément à la complexité de la concep-tion. Peut-on contrôler l’état de n composantes avec seule-ment m contrôles, lorsque n m ? Le théorème de Kálmán(1958) donne des conditions nécessaires et suffisantes pourque ce soit le cas. Ainsi, dans une auto, on a 4 degrés de li-berté, soit la position de son centre de gravité, son orientation

et l’orientation des roues motrices. Pourtant, deux contrôlessuffisent, soit le volant et le mouvement d’avancer, commel’ont illustré plusieurs vidéos de chauffeurs particulièrementdoués.

Enrique Zuazua est ensuite passé à la description des mathé-matiques impliquées dans la conception optimale d’un avion,soit la mécanique des fluides pour simuler l’écoulement de l’airle long d’un avion, et l’optimisation de la forme par itérationssuccessives en minimisant la fonctionnelle coût. Il a expliquédans les équations de Navier – Stokes l’importance du termede viscosité qui permet aux oiseaux de voler et les grands défisque posent la solution de ces équations aux mathématiciens.

La conférence s’est terminée sur les perspectives et nom-breuses applications de la théorie du contrôle en mécanique,médecine, électronique, chimie, économie et finance. Les ré-seaux qui nous entourent sont de plus en plus complexes etdistribués, posant ainsi de nouveaux défis aux mathémati-ciens. De nouveaux outils sont nécessaires : la combinatoireet la théorie des graphes, le forage de données et le Big data,l’apprentissage statistique, tandis que des algorithmes com-putationnels de plus en plus raffinés voient le jour. Le publica quitté la salle, charmé, tout autant que l’organisatrice.

PrixDaniel T. Wise

Daniel T. Wise

Daniel T. Wise (McGill) est lelauréat 2016 des prix CRM –Fields – PIMS et Jeffrey – Williams.M. Wise est généralement reconnucomme l’un des meilleurs théo-riciens des groupes géométriquesdans le monde, et le meilleur desa génération. Ses travaux ont desrépercussions profondes non seule-ment en théorie des groupes géomé-triques, mais aussi en raison de leur

rôle clé dans la résolution de problèmes jamais encore ré-solus en théorie des variétés à 3 dimensions.

Le prix CRM – Fields – PIMS souligne des réalisations ex-ceptionnelles en sciences mathématiques.

Le prix Jeffery – Williams de la SMC rend hommage auxmathématiciens qui se sont distingués par l’excellence deleur contribution à la recherche mathématique.

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In memoriamS. Twareque Ali (1942 – 2016)

S. Twareque Ali

A Book of Verses underneath the Bough,A Jug of Wine, a Loaf of Bread – and ThouBeside me singing in the Wilderness –Oh, Wilderness were Paradise enow!(The Rubáyát of Omar Khayyám, Quatrain XII,English transl. E. FitzGerald, 5th ed., 1889)

It is with great sorrow that we communicate the passing ofSyed Twareque Ali, a long-time member of the CRM, Profes-sor at Concordia University, eminent researcher in mathemat-ical physics, good friend and valued colleague. The followingis a collection of personal recollections by some of his closestfriends and collaborators, who had the privilege of sharingthoughts and experiences with him over many years, and anoverview of his career and his scientific contributions.

Personal recollectionsJean-Pierre Antoine (Louvain-la-Neuve)

I started to collaborate with Twareque in 1989, on the topicof coherent states. He was originally referred to me because ofdifficulties encountered in the decomposition of a phase spacerepresentation of the Poincaré group. The solution to thiswas quickly found, just replacing a bounded Hilbert spaceoperator by an unbounded one, and this began a wonderfulcollaboration that continued till the sadly unexpected, prema-ture end of his life. In the following year, Jean-Pierre Gazeaujoined us and thus started our triangular collaboration thatled to eleven joint papers and two joint books.Twareque travelled a lot; we kept meeting each other all overthe world, until the most recent times. We often attended thesame meetings, in addition to visiting each other at our homeuniversities, including being respective invited professors. Toname a few of the places we travelled together, there wereQuébec, Germany (Clausthal), Poland (Białowieża), Cuba,France, Italy, Bangladesh (Dhaka), China (Tianjin), India(Bangalore), and many others.Working with Twareque was always a rewarding experience.Even if his papers were sometimes dense and compact, hisclean, polished mathematical style was always a pleasure toread, and all his papers have a luminous clarity. His nonscien-tific writings have the same quality, including his poetry; I re-member a memorable poem composed by him in Białowieża!His talks were always extremely clear and pedagogically wellthought out, and his ideas were often thought-provoking.Altogether I feel fortunate to have been able to work with himfor so long, and so surely do all his other collaborators. Every-one will remember his characteristic whole-hearted laughter,inviting everyone to share his great and subtle sense of hu-mour, and enjoyment of the moment, and of life.

Jean-Pierre Gazeau (Paris-Diderot)

I met Twareque through Jean-Pierre Antoine at the end ofthe 1980s, and we started a long and fruitful collaboration,which continued to the last. It was always extremely pleas-ant to work with him because of his intelligence and extremetolerance for the ideas advanced by others. Open minded-ness was one of his great qualities. We still had new projectsplanned, and I had planned to come to Montréal this May todevelop one of these with his recent Master’s student Das. Ibelieve it was my mention of Twareque’s name to Anatol Odz-ijewicz in ’91 that led to his subsequent strong and constantinvolvement in the organization of the Białowieża series, withso many excellent remembrances.

Gerald Goldin (Rutgers)

Twareque Ali and I met in Clausthal, Germany during the1980s, invited by Heinz-Dietrich Doebner to the Arnold Som-merfeld Institute. Each summer from 1992 to 2015, nearlywithout exception, we would see each other at the Work-shop on Geometric Methods in Physics in Białowieża, Poland.With our spouses we toured Beijing and visited the GreatWall of China after the Group Theory Colloquium in Tian-jin in 2012 (where he was honoured on the occasion of his70th birthday). We shared family weddings and other events.Twareque was not only a colleague and collaborator, but aclose personal friend, an intimate confidant. He was someonewith whom one could discuss the meaning of life’s joys anddisappointments without self-consciousness.With his serious expression, his black hair and beard onlylately streaked with grey, he looked thoughtful and wise — buthis eyes twinkled, and he loved to laugh. He knew how to livelife, to find humour in its seriousness. He would quote po-etry extensively from memory, in Bengali, Italian, German,

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and of course English. He loved Omar Khayyam’s Rubáyát,in the Edward FitzGerald translations. And his laughter al-ways restored balance. He was especially fond of the novelSmall World by David Lodge, which satirizes the sometimespretentious academic scene we both knew so well. We imag-ined we could recognize Lodge’s characters in people we knew,including (of course) ourselves.And Twareque was a deep thinker. He believed deeply inpeace, and gave generously of himself to the less-privilegedin the world. For him, the truths of science were part of theever-unattainable beauty for which he yearned, for which allof us yearn. He sought scientific truths through mathemat-ics, especially an understanding of the mysteries of quantummechanics. Influenced deeply by his teacher Gérard Emch, hein turn inspired numerous students and colleagues. ThoughTwareque has gone now, his inspiration, gentleness, and hu-manity will live on for many generations.

John Harnad (Concordia)

Twareque was a cherished friend, a unique and wonderful hu-man being, a highly esteemed researcher and valued colleague.We shared many things over nearly four decades of friendship.All who knew Twareque could appreciate his abundance ofwisdom, humour, generosity, kindness, tolerance, and endur-ing, simple goodness of nature.Science and friendship were both very important to him. Hehad a large network of colleagues and friends around the globewith whom he kept in touch in his many travels, and sharedhis enjoyment of life, and his fascination with the variety andrichness of all he encountered. He saw something positive ev-erywhere, and had a genuine love of different cultures, person-alities and environments, finding something of value to enjoyand celebrate everywhere he went and in all things he did.It was characteristic of Twareque to be constantly on themove, travelling around the world, visiting friends and fam-ily, attending scientific conferences, sharing his thoughts andexperiences generously with others, while always further aug-menting his vast store of knowledge, his awareness of thingsof beauty, and the poetry and richness of life.Sharing his laughter, good humour and enjoyment of the di-verse environments he relished and the friendships he formedhelped lift everyone’s spirits. The wide scope of his knowl-edge, not only of science, but the broad range of human ex-perience, things of learning and of beauty, poetry, art, diversecultures and languages, together with the benefits of humour,combined to give him a unique perspective on life. We allbenefitted from his positive spirit, his learning, and his ap-preciation of the variety and richness of life.In addition to his scientific work, he worked relentlessly, dis-cretely, unobtrusively, in helping others in need; this was sim-ply second nature to him, an essential ingredient in his life.Whether those who came to Canada to continue their lives, orremained in his home country of Bangladesh, or in Cuba, orelsewhere, where circumstances made their lives much moredifficult than here, he was always helping those facing the

challenges of life. He made it his ongoing mission to assiststudents, colleagues and others in overcoming the obstaclesthey faced and making possible the fullest use of their abili-ties. Throughout the many crises that occurred in his countryof origin, he remained a lifelong, devoted, generous source ofhelp to those who needed it.I had the good fortune of sharing and enjoying his friendship,his company and good nature for many years, occasionally ontravels, at various events and places around the world, as wellas at home. It was both uplifting and cheering to be with him.I greatly benefitted from the generous gift of his friendship,his wisdom, his kindness and his enjoyment and celebrationof life. Twareque was a unique, kind and good human being,an irreplaceable friend and highly valued colleague. He willbe sorely missed.

Mourad Ismail (Central Florida)I first met Twareque Ali when we both arrived in Toronto inthe fall of 1975 to start a one-year postdoctoral fellowship. Weshared an office and taught two different sections of a calculusclass concurrently. Twareque had such a nice personality thatwe became friends very quickly and this led eventually to alifelong friendship.In those early days, it seemed that our research interests werefar apart, but later Twareque and I met at various confer-ences and exchanged ideas about our work. Fast forwardingthirty-five years, when I visited Montréal in the summer of2011, Twareque told me about coherent states and proposeda very interesting question involving orthogonal polynomials.We then began a very enjoyable and fruitful working collabo-ration on this problem. He also invited me to give a talk at aspecial session he was organizing at a meeting on Group The-oretical methods in Physics in Tianjin, China. At first, I washesitant, but Twareque insisted that it would be worthwhileto attend. In the end, it turned out to be one of the mostproductive meetings I ever attended. Thanks to Twareque,working on this topic led to a goldmine of new research resultsrelating our overlapping interests in orthogonal polynomialsand coherent states, including two joint papers on the subject.Twareque will live in my memory for the rest of my life, as afriend, collaborator, and a very caring and wonderful humanbeing.

Anna Krasowska (Vanier College) and Renata Deptula (JohnAbbott College)

Twareque Ali was our Ph.D. supervisor at Concordia Univer-sity; we came to know him as “Dr. Ali.” He will forever remainin our hearts as Dr. Ali, and this is the way we remember him,a fatherly figure. He had a far deeper impact in our lives thanthe role of supervisor.He was always a very patient, encouraging teacher and sogenerous with his time. He understood so well all the needsand challenges of students in a foreign land, undoubtedly be-cause this had been his experience more than once in his ownlife. Our meetings, while mostly filled with discussions about

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wavelets or Wigner functions, always had time reserved totalk about our new experiences in Montréal. If anything inour lives became too complicated it was a clear sign we neededto talk to Dr. Ali. Every meeting with him provided a bigdose of encouragement and new energy, never accompaniedwith any criticism or judgment.All his students knew how fond he was of visiting new places,meeting new people, establishing new friendships. And as itwas with everything else, whatever he cherished, he shared:whether we travelled to Cuba, Mexico or Germany we feltpart of a big family, because we were students of Dr. Ali.It has been a great privilege to have known Dr. Ali. He willalways be an inspiration to us as a wonderful teacher and avirtuous person.

Reinaldo Rodriguez Ramos (Havana)Twareque Ali’s contributions to the scientific development ofthe Faculty of Mathematics and Computer Science at theUniversity of Havana went well beyond the co-organizationof conference series. Since 1998, he began collaborating withthe faculty, encouraging the participation of teachers in re-search and in the development of the research on wavelets and

its various applications. He provided further ongoing help tothe University and the Fac-ulty of Mathematics andComputer Science by or-ganizing donations of com-puter equipment and bring-ing international experts todeliver specialized coursesand share their knowledgeand experience with theCuban community of mathe-maticians. In 2009, the Uni-versity of Havana honouredhim with the special awardof Invited Professor of theUniversity of Havana.He was a man of great hu-man sensitivity, and a deepthinker who could often come up with the best solution to anyproblem. He was also a cherished special friend of my family.We regret the loss of a great friend and a great man of science.

Overview of Twareque Ali’s scientific contributions and career

Nitya kaaler utshab tabaBishyer-i-dipaalikaAami shudhu tar-i-mateer pradeepJaalao tahaar shikhaa (Tagore)(English transl.: “Thine is an eternal celebration. . . A cosmicFestival of Lights!. . . Therein I am a mere flicker of a wickerlamp. . . O kindle its flame, (my Master!).”)

Twareque Ali’s life and career included a range of contrastingexperiences. Born a citizen of the British Empire, he acquireda succession of three further nationalities: Pakistani in 1947,Bangladeshi in 1971, and finally Canadian.

After completing his M.Sc. in Dhaka, Bangladesh in 1966,and a Ph.D. in 1973 in Rochester, USA under the supervi-sion of G. Emch, he occupied positions successively at ICTP(Trieste, Italy), Univ. of Toronto, Univ. of Prince Edward Is-land, and TU Clausthal (Germany), before settling down, in1981, in Montréal, first as Assistant Professor (1981 – 1983)in the Department of Mathematics and Statistics, ConcordiaUniversity, then Associate Professor (1983 – 1990) and finallyFull Professor (as of 1990).

Twareque Ali was a world-recognized leader in at least threedomains of current research in mathematical physics: quan-tization methods, coherent states and wavelet analysis; hemanaged to build important bridges between these, as well aspublishing a large number of ground breaking research articlesand widely appreciated monographs on these subjects.

He was a member of the Mathematical Physics Laboratory ofthe Centre de recherches mathématiques since its inception in2001, and contributed actively to its range of scientific activ-ities. He was also Concordia’s representative to the ISM formany years, before becoming ISM Director in 2003. Over theyears, he was an invited professor at many foreign universi-ties throughout the world and was in constant demand as aninvited speaker at international conferences.

His main scientific interests can be aptly summarized bythe key words that represent his favourite topics: phasespace, quantization, positive operator valued measures, re-producing kernels, coherent states. He began a close andfruitful collaboration in the late 1980s with two of hisprincipal co-authors — Jean-Pierre Antoine and Jean-PierreGazeau — that continued throughout his lifetime. As de-scribed in the personal recollections above, it is on the last ofthese topics that they collaborated for the first time and thiscontinued up to the present day. Along the way, eleven paperswere jointly written (plus four with JPA alone and ten withJPG), three books edited (the Białowieża conference proceed-ings), two research monographs [2, 3] were co-authored, anda recent special volume co-edited, together with F. Bagarello[1]. Throughout these years, Twareque relentlessly soughtto instill mathematical rigour in the field of coherent states,something he felt was needed, but too often missing in someof the published literature on quantum optics.

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More specifically, in the 1970s and 1980s, he devoted muchof his attention to measurement problems in (fuzzy) phasespace and stochastic, Galilean and Einsteinian; quantum me-chanics. This was partly in joint work with E. Prugovecki inToronto (which led to a memorable and lasting dispute withGerald Kaiser), G. Emch in Rochester and H.-D. Doebnerin Clausthal. His 1984 Stochastic Localization, Quantum Me-chanics on Phase Space and Quantum Space-Time was a ped-agogical landmark for the domain. He then gradually focusedon coherent states for the Galilei and the Poincaré groupsand other semi-direct product groups. One of his first worksin this direction was with S. De Bièvre. A notable result of [2]was the extension of square integrability of group representa-tions to homogeneous spaces and the introduction of contin-uous frames in Hilbert spaces, the key to many applications,including wavelets.

One of his best known joint papers with Antoine and Gazeauwas the 1993 Annals of Physics Continuous frames in Hilbertspace. Twareque subsequently began to be interested in quan-tization methods, mostly Berezin or coherent states quanti-zation, and in the mathematics of signal processing. In thelast few years, his focus of interest included noncommutativequantum mechanics, quaternionic Hilbert spaces and complexorthogonal polynomials, on which a further productive collab-oration began with his old friend from Toronto days, MouradIsmail. (See M. I.’s personal recollections above.)

Travelling widely and frequently in his professional life, healways managed to combine these travels with a keen appre-ciation for the cultural and human milieu in which he foundhimself.

Another important part of Twareque’s working life was the or-ganization of scientific meetings on topics generally related tohis research interests. Two series of conferences are notable.First, the Białowieża Workshops on Geometric Methods inPhysics, spearheaded by their charismatic founder and chieforganizer, Anatol Odzijewicz. These take place annually in aregion of Poland bordering on Belarus that is famous for itslocal culture and natural beauty, the wild forests, bison, andlocal artisanal crafts. The workshops are characterized alsoby the abundance of good food (as well as vodka), good spiritsand active participation of several Russian mathematicians ofthe highest caliber. From the XIth meeting, in 1992, onward,Twareque was instrumental in transforming what was earliera small local workshop into a full-fledged international event,which is still going strong. (The last edition was Nr. XXXIV,in June, 2015.)

A further remarkable achievement was the series of workshopsin Havana, Cuba, organized jointly by Concordia Universityand the Universidad de La Habana, in which the leading spiritwas Twareque’s longtime friend Reinaldo Rodriguez Ramos.As member of the Organizing Committee and founder of the

Workshops I – XII held in the Faculty of Mathematics andComputer Science at La Habana from 1998 to date, Twarequewas one of the driving forces of the meetings. He succeededin attracting a number of distinguished participants of inter-national standing to those beautiful surroundings and almostsingle-handedly arranged for the publication of the proceed-ings. Through the Department of Mathematics and Statisticsand the Center for International Academic Cooperation atConcordia University, he contributed valuably to the develop-ment of international cooperation and scientific collaborationwith the Universidad de La Habana.

More recently Twareque also became a faithful participantand contributor at the school and workshops on mathemat-ical physics (COPROMAPH) organized in Cotonou, Bénin,by Norbert Hounkonnou.

Throughout his career Twareque was deeply devoted to theteaching and supervision of students, both undergraduate andgraduate, and was greatly appreciated by all his students forhis patience, insight and generous help. Chairman of the grad-uate studies committee at Concordia’s Department of Math-ematics and Statistics for many years, nine Doctoral degreeswere completed under his supervision or co-supervision andan equal number of Master’s degrees. He was also, from 2003till 2006, Director of the Institut des sciences mathématiques(ISM), the inter-university consortium responsible for coor-dinating graduate studies at Québec universities. During histerm as Director, he contributed much to the enhancementof both the quality of graduate education in mathematics atQuébec universities and the level of its support. He helpedenhance the ISM outreach to schools and CEGEPs, as wellas to improve and advance the rationalization of pedagogicalresources, the level of cooperation between different univer-sity groups, and the recruitment of high quality students fromoverseas.

All his scientific colleagues and collaborators would agree thatTwareque had a very deep and subtle understanding of Quan-tum Physics, both in its foundations and its working mathe-matical tools. It was extremely pleasant to interact and workwith him, not just because of his intelligence, original insightsand innovative contributions, but also his modesty, consider-ation and generous interest in the ideas advanced by others.Open-mindedness was one of his greatest qualities.

[1] S.T. Ali, J.-P. Antoine, F. Bagarello, and J.-P. Gazeau, eds.J. Phys. A: Math. Theor. 45.24 (2012): Special Issue on Co-herent States: Mathematical and Physical Aspects.

[2] S.T. Ali, J.-P. Antoine, and J.-P. Gazeau. Coherent States,Wavelets and Their Generalizations. 2nd ed. Theoretical andMathematical Physics, volume. New York: Springer, 2014.

[3] J.-P. Antoine, R. Murenzi, P. Vandergheynst, and S.T. Ali.Two-Dimensional Wavelets and their Relatives. Cambridge:Cambridge Univ. Press, 2004.

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Grande Conférence publique du CRMThe Art and Science of Systems Involving Too Many Unknowns

Emmanuel Candès (Stanford University)

Christian Genest and David A. Stephens (McGill)

Emmanuel Candès

On October 29, 2015,a public lecture onThe Art and Scienceof Systems Involv-ing Too Many Un-knowns was given atthe CRM by Profes-sor Emmanuel Can-dès, holder of the Bar-num – Simons Chairin Mathematics andStatistics at Stanford

University. Born in Paris, France, where he received most ofhis education, Professor Candès has consistently earned highacclaim for his groundbreaking contributions to compressedsensing, an area of research and emerging technology thatlargely grew out of his joint work with Justin Romberg andTerence Tao over the past 15 years [1–3].Compressed sensing [4] is a signal processing technique for effi-ciently acquiring and reconstructing a signal by solving under-determined linear systems of equations. In his hour-long pre-sentation, Professor Candès motivated and illustrated some ofhis research on the subject by drawing mainly from diagnosticmedicine, with an emphasis on medical magnetic resonanceimaging, where the need for rapid and yet high-quality im-age reconstruction is paramount. He stressed, however, thatcompressed sensing finds applications in many other areas, in-cluding circuit design, optics, photography, holography, andfacial recognition. As a further illustration of this generalmethodology, he discussed the 2006 – 2009 Netflix Prize opencompetition, whose ultimate goal was to predict user ratingsfor films as accurately as possible, based only on previous rat-ings without any other information about the users or films.Compressed sensing is based on the principle that, throughoptimization, the sparsity of a signal can be exploited to re-cover it from far fewer observations than prescribed by thefamous Nyquist – Shannon theorem. In the canonical two-dimensional imaging example, measurements y are made atvarious locations (k1, k2) in the spectral domain, the requiredimage f lies in the spatial domain, and the two objects arerelated through the identity

y(k1, k2) =

∫∫f(x1, x2)K(k1, k2, x1, x2) dx1 dx2,

where K stands for a Fourier kernel. The main challenge isto reconstruct f at as high a resolution as possible when onlya sketch of the Fourier transform is available, i.e. on the basisof a few observations from the spectrum. Minimizing datacollection in the spectral domain is practically relevant, e.g.in the context of magnetic resonance imaging where taking

measurements is potentially time consuming and invasive orunpleasant for the patient.Professor Candès explained that under a discrete approxima-tion, the problem of reconstructing an image f from indirectmeasurements y ∈ Rm reduces, for a known m × n matrixA, to the solution x ∈ Rn of a linear system of equationsy = Ax given by the discrete (inverse) Fourier transform ofthe observed data. This system is underdetermined whenm < n, i.e. when data collection has low resolution. How-ever, a unique solution can be found by imposing that x hasas many zero entries as possible, provided that the measure-ment matrix A satisfies minimal conditions, in particular if itcontains a sufficient amount of “randomness” and “incoher-ence.”In practice, the search for the sparse (or compressed) solutionis computationally intractable, as it is an NP-hard problem.Luckily, it turns out that under broad and realistic condi-tions, equivalent sparse solutions can be obtained by insteadimposing 1 constraints, thereby converting the optimizationproblem into a convex programming issue. As Professor Can-dès showed, the resulting sparse reconstruction is extremelyeffective.In the last third of his talk, Professor Candès went on todemonstrate how these principles could be generalized toother forms of underdetermined systems using alternativeconstrained solutions and low-rank decompositions. The uni-fying theme was again the framing of a mathematically andcomputationally intractable problem in a tractable, convexoptimization setting.The “Grande Conférence” by Professor Candès attracted alarge audience and aroused much interest among mathemati-cians, statisticians, and the general public alike. It was a priv-ilege to have him visit Montréal and the CRM for a few days.A video of his talk (in French) can be found at www.crm.math.ca/Candes/, and a related lecture (in English) given byProfessor Candès at the 2014 International Congress of Math-ematicians in Seoul, South Korea, is available on YouTube(www.youtube.com/watch?v=W-b4aDGsbJk). See also [5]for a popular introduction to compressed sensing.

[1] E.J. Candès and J.K. Romberg. “Sparsity and incoherencein compressive sampling”. Inverse Problems 23:3 (2007), 969–985.

[2] E.J. Candès, J.K. Romberg, and T. Tao. “Stable signal recov-ery from incomplete and inaccurate measurements”. Comm.Pure Appl. Math. 59:8 (2006), 1207–1223.

(continued on page 14)

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Prix CRM–SSCMatías Salibián-Barrera (UBC)

La détection de courbes aberrantesÉric Marchand (Sherbrooke)

Matías Salibián-Barrera, professeur titulaire de l’Universitéde la Colombie-Britannique et 17e lauréat du prix CRM – SSC,était à Montréal le 11 février dernier pour présenter des tra-vaux de recherche récents. C’est en reconnaissance de sescontributions fondamentales à la statistique robuste et à desalgorithmes innovants que Matías s’est vu décerner ce prixprestigieux.

L’exposé du professeur Salibián-Barrera (disponible sur le siteWEB du CRM) a brillamment abordé des perspectives aussidiverses que les défis de la modélisation en statistique et del’identification de données aberrantes, l’analyse de donnéesfonctionnelles (ADF) traitant de l’analyse d’échantillons decourbes et de surfaces, l’analyse en composantes principalesen ADF et l’utilisation de méthodes robustes pour estimer cescomposantes principales. Le tout fut illustré par une analysede courbes (journalières) de concentration d’ozone à Rich-mond (C.B.) pour les mois d’août de 2004 à 2012.

L’évolution de la statistique robuste émane du souci que lesmodèles avec lesquels on travaille sous-estiment la variabilitésous-jacente ou encore la complexité des données. Elle chercheà développer des méthodes d’inférence moins sensibles à desdonnées atypiques ou non représentatives du modèle. MatíasSalibián-Barrera a aussi relevé la pertinence accrue d’aborderde telles méthodes robustes, ainsi que des distributions de mé-lange, dans des contextes actuels où les données deviennentd’une part plus faciles à obtenir et plus volumineuses, maisd’autre part sont assujetties à des sources de plus en plushétérogènes.

En analyse de données fonctionnelles (voir par exemple l’ou-vrage de Jim Ramsay et de Bernard Silverman), chaque ob-servation — dont la concentration d’ozone sur une période de24 heures — est une courbe ou une surface. L’identificationde données aberrantes ou atypiques est alors plus complexeque pour le cas de données vectorielles car l’évaluation de laproximité de deux courbes par une distance usuelle telle ladistance L2 ne tient pas compte d’une différence de forme.

Et de telles différences peuvent être très significatives pour descourbes. Matías Salibián-Barrera a abordé de telles difficultéset a passé en revue la notion de profondeur pour des donnéesvectorielles (due à John Tukey), ainsi que de telles mesurespour des données fonctionnelles et permettant d’identifier descourbes atypiques.

L’exposé s’est alors tourné vers l’analyse en composantesprincipales (ACP) en ADF et la recherche d’une bonne ap-proximation pour des données fonctionnelles (typiquement en

Matías Salibián-Barrera

dimension infinie) par des objets en plus basse dimension. Unetechnique pour contourner cette difficulté fait intervenir la re-présentation de Karhunen – Loève en termes d’éléments de labase orthonormale associée aux valeurs propres d’un opéra-teur induit par la fonction d’autocovariance. Par contre, cetteapproche requiert l’existence de seconds moments et des mé-thodes alternatives robustes sont alors d’intérêt.

Abordant des aspects de modélisation probabiliste, MatíasSalibián-Barrera a introduit la notion de courbes elliptiqueset d’une représentation-clé faisant intervenir des mélanges delois normales, telles que présentées dans un article conjointavec Graciela Boente et David Tyler (Journal of MultivariateAnalysis, 2014). Matías a alors enchaîné avec la présentationd’une nouvelle méthode (G. Boente et M. Salibián-Barrera,Journal of the American Statistical Association, 2015) robustepour l’analyse en composantes principales de données fonc-tionnelles. Il a présenté des propriétés d’optimalité, dont laconvergence, il a exposé des défis au niveau de la mise enœuvre de l’algorithme et il a conclu par une évaluation etune illustration de la méthode proposée sur les données deconcentration.

Emmanuel Candès(continued from page 13)[3] E.J. Candès and T. Tao. “The power of convex relaxation:

Near-optimal matrix completion”. IEEE Trans. Inform. The-ory 56:5 (2010), 2053–2080.

[4] D.L. Donoho. “Compressed sensing”. IEEE Trans. Inform.Theory 52:4 (2006), 1289–1306.

[5] D. Mackenzie. “Compressed sensing makes every pixel count”.What’s Happening in the Mathematical Sciences, Volume 7.Providence, RI: Amer. Math. Soc., 2009, 114–127.

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2015 CRM–Fields – PIMS PrizeLecture by Kai Behrend (UBC)

Algebraic Stacks and the Inertia OperatorJacques Hurtubise (McGill)

What does the space of all curves look like? How about thespace of all algebraic subvarieties of projective space? Thequestion of how to describe and classify such objects has pre-occupied algebraic geometers for more than a century, andhas seen a variety of approaches. Tied to this question is ofcourse that of deciding which objects in our category are thesame; one is typically quotienting out some group of equiv-alences. In the late nineteenth century, a lot of effort wentinto describing invariant theory — one looks for functions on aset of objects invariant under the action of the group. Mum-ford, in the 1960s, gave more geometric meaning to this bydescribing which geometric objects were actually described bythe invariants — the so-called stable ones.

Kai Behrend

It turns out, however, than in a few crucial applications, thesestable objects are not enough — the function theory missessome objects, and has trouble handling families. This broughton, already in the 1960s, the theory of stacks. In some sense,stacks are tautological — one simply takes all families, and allequivalences and maps between families, and tries not to getlost in all the arrows. The difficulty, of course, is in describingthe actual properties of such a creature; for example, what isits cohomology?

There are applications: for example, the theory of Gro-mov – Witten classes of a complex manifold. One considersthe set of maps of curves into a complex manifold, and in-tegrates certain naturally defined forms over this set, to getnumbers, which should be invariants. But are they? Howdoes one integrate them? And the Gromov – Witten are onlysome of the invariants, many inspired by ideas from theoret-

ical physics, that have appeared over the last few years, andinvolve similar basic issues of definition.

Kai Behrend’s work has given us many answers to these typesof questions, for example in developing the fundamental cycleover which one performs the integrals. He has, along with hiscollaborators, built up the theory of these stacks and otherrelated objects, not only in the algebraic category, but alsoin the related area of symplectic geometry, where similar in-variants can be found, easy to posit, but hard to define in arigorous fashion. His work has been fundamental in under-standing these invariants, and for this he was quite rightlyawarded the 2015 CRM – Fields – PIMS Prize.

It was therefore with great pleasure that the Montréal math-ematical community went to hear him lecture on some of thebasic ideas underlying stacks, illustrated by a very simple ex-ample, that of families of triangles in the plane. In essence,while equivalence classes of triangles are well known, one canalready see some of the subtleties which occur when consid-ering families. In the end, this justifies, if not for triangles atleast for the more elaborate cases involved in defining invari-ants, the development of a remarkable and elaborate machine.And more, a machine which gives answers.

PrixLouigi Addario-Berry

Louigi Addario-Berry

Le directeur adjoint aux pro-grammes scientifiques du CRM,Louigi Addario-Berry (McGill) estle lauréat 2016 du prix Coxe-ter – James pour sa contribution ex-ceptionnelle à la recherche mathé-matique. Louigi Addario-Berry s’in-téresse aux interconnexions entre laprobabilité et la combinatoire. « Leprofesseur Addario-Berry s’est tailléune place comme leader de sa géné-ration dans le domaine des probabilités discrètes », a com-menté un évaluateur.

Le prix Coxeter – James de la SMC a été créé en 1978 afinde souligner la contribution exceptionnelle de jeunes ma-thématiciens qui se sont démarqués dans le domaine de larecherche en mathématique.

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Appel à propositionsLe CRM émet un appel à propositions concernant desactivités scientifiques de haut niveau en sciences mathé-matiques. Lors du choix de notre programme scientifique,notre priorité est de soutenir des activités de grande qua-lité scientifique qui présentent de passionnantes nouvellesdirections de recherche à la communauté du CRM toutentière.

Programmes thématiques

Ils sont le fondement des activités du CRM. Généralementles programmes thématiques sont d’une durée allant de 4mois à un an. Ils englobent des ateliers, des conférences,des mini-cours ou des écoles, ainsi que des séjours prolon-gés au CRM, de chercheurs venant d’ailleurs.

Programme général

Le CRM appuie également des activités de courte duréequi ne sont pas associées au programme thématique. Ellescomprennent des ateliers, des conférences, des groupes derecherche, et des activités de formation telles que les écolesou les mini-cours soutenues par des chercheurs invités.

Calendrier

Programmes thématiques

Nous sollicitons présentement des lettres d’intention en vuedes programmes thématiques qui se tiendront au cours dela période de juillet 2019 à juin 2020. Les lettres d’intentiondevraient inclure l’information suivante :

– Le titre du programme.– Le nom et les coordonnées des organisateurs.– Une description scientifique de l’événement, incluant les

principales activités de recherche et de formation.– Une liste provisoire des principaux participants invités

et leur rôle éventuel dans le cadre du programme.

– Un calendrier des activités proposées.

Les lettres d’intention devraient être transmises au plustard le 1er octobre 2016.

Programme général

Nous sollicitons présentement les propositions pour des ac-tivités de courte durée qui auront lieu au cours de la pé-riode commençant en juillet 2017 et se terminant en juin2018. La date limite pour soumettre des propositions d’ac-tivités qui se tiendront en 2017 est le 1er octobre 2016.La date limite pour soumettre des propositions d’activitésqui se tiendront en 2018 est le 1er avril 2017.

Conditions

Toutes les activités doivent être d’un intérêt scientifiquemanifeste et pertinentes pour les domaines de recherchesdu CRM. L’argumentaire doit être détaillé dans la propo-sition.

Le CRM reconnaît la sous-représentation systématique degroupes dans la communauté de chercheurs en sciencesmathématiques et compte sur les organisateurs pour abor-der cette question, à la fois dans la proposition et dans laplanification.

Généralement, le CRM ne finance pas les événements quise répètent. Il est notamment peu probable que les confé-rences récurrentes reçoivent un appui.

Pour de plus amples informations

De l’information supplémentaire sur les conditions des pro-positions est disponible à crm.math.ca/Propositions.

Les propositions doivent être envoyées au CRM par cour-riel à projet@crm.umontreal.ca.

Simons FellowsAdrian Iovita et Adam Oberman

Adrian Iovita

Deux membres du CRM, Adrian Iovita(Concordia) et Adam Oberman (McGill)viennent d’être nommés « Simons Fel-lows » en mathématiques par la SimonsFoundation. Les 37 fellows choisis enmathématiques pour 2016 (dont trois pro-venant d’universités canadiennes) sontd’éminents mathématiciens à différentsstades de leurs carrières respectives.

Adam Oberman

Les fellows reçoivent des fonds leur as-surant, pendant quelques mois ou un se-mestre, une tâche réduite d’enseignementet de services à la collectivité. Cette ré-duction de tâche stimule la créativité et laproductivité des professeurs qui reçoiventcet honneur.

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Call for Proposals

The CRM invites proposals for scientific activities of highcalibre in the mathematical sciences. When choosing ourscientific programming, our priority is to support activitiesof top scientific quality and which introduce exciting newresearch directions to the entire CRM community.

Thematic programs

These are a cornerstone of the CRM activities. Thematicprograms typically have a duration of between four monthsand one year. They include workshops, conferences, shortcourses or schools, and extended visits to the CRM byresearchers from other locations.

General program

The CRM also supports shorter activities not associatedwith a thematic program. These include workshops, con-ferences, research in groups, and training activities such asschools or short courses by visiting scholars.

Timeframe

Thematic programs

We are currently inviting letters of intent (LOIs)for thematic programs to take place in the periodJuly 2019 – June 2020. LOIs should include the followinginformation:

• The title of the program.• Names and contact information for the organizers.• A scientific description of the event, including the major

research and training activities.• A tentative list of the principal invited participants and

their proposed role within the thematic program.

• A proposed timeline of activities.

LOIs should be received by October 1, 2016.

General program

We are currently inviting proposals for shorter activitiesto take place in the period July 2017 – June 2018. For ac-tivities taking place in 2017, the deadline for proposals isOctober 1, 2016. For activities taking place in 2018, thedeadline for proposals is April 1, 2017.

Requirements

All activities should be of clear scientific interest and rele-vance to the research areas of the CRM. The case for thisshould be explicitly made in the proposal.

The CRM recognizes that there are systematically under-represented groups within the mathematical sciences re-search community, and expects organizers to actively ad-dress this fact, both in their proposal and throughout theplanning process.

The CRM typically does not fund repeat events. In partic-ular, recurring conferences are unlikely to be offered sup-port.

Further information

Additional information on requirements for proposals canbe found at crm.math.ca/Proposals.

Proposals should be sent to the CRM by email atproposal@crm.umontreal.ca.

AMS–CRM Publications

This volume contains papers from the ShortThematic Program on Rational Points, Ra-tional Curves, and Entire HolomorphicCurves and Algebraic Varieties, held fromJune 3 – 28, 2013, at the CRM.

The program was dedicated to the studyof subtle interconnections between geomet-ric and arithmetic properties of higher-dimensional algebraic varieties. The mainareas of the program were, among others,

proving density of rational points in Zariski or analytic topology onspecial varieties, understanding global geometric properties of ra-tionally connected varieties, as well as connections between geom-etry and algebraic dynamics exploring new geometric techniquesin Diophantine approximation.

M. Ram Murty has had a profound im-pact on the development of number theorythroughout the world. To honour his math-ematical legacy, a conference focusing onnew research directions in number theory in-spired by his most significant achievementswas held from October 15 – 17, 2013, at theCRM.

This proceedings volume is representative ofthe broad spectrum of topics that were ad-

dressed at the conference, such as elliptic curves, function fieldarithmetic, Galois representations, L-functions, modular forms andautomorphic forms, sieve methods, and transcendental numbertheory.

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Positive Grassmannians: Applications to IntegrableSystems and Super Yang–Mills Scattering Amplitudes

July 27—31, 2015

Organizers: Marco Bertola (Concordia and SISSA), Michael Gekhtman (Notre-Dame), John Harnad (Concordia)The workshop was organized within the framework of the the-matic semester “AdS/CFT, Holography, Integrability.” Thetheory of Grassmannians and their positive substructures hasbeen developed by mathematicians without a particular appli-cation to physics in mind; on the other hand, in the past years,theoretical physicists have recognized that certain computa-tions they performed laboriously by hand can be framed inthat theory. The encounter is thus one of those serendipitoussituations in science, like the development of non-Euclideangeometries (a purely mathematical topic, at the time of theirinvention without any “real” application) and later on generalrelativity.

The main goal of the workshop was therefore bringing to-gether mathematicians and theoretical physicists who havebeen lately discovering that the tools developed in the studyof positive Grassmannians prove useful in seemingly unrelatedfields such as computation of scattering amplitudes, soliton in-teractions, discovery of new discrete integrable models, mirrorsymmetry, parameterizations of rings of invariants, etc.

Each session of the workshop was loosely tied to a unifyingtheme, although none of these topics were isolated within ageneral flow of the workshop. These included

• Integrable maps generated by cluster mutations (Glick,Pylyavskyy, Shapiro, Kenyon)

• Combinatorics of positive Grassmannians with applica-tions to geometry and analysis (Farber, Muller, Neitzke,H. Williams, L. Williams)

• Scattering amplitudes, on-shell diagrams and the ampli-tuhedron (Arkani-Hamed, Franco, Thomas, Trnka)

• Cluster structures in Poisson geometry and invariant the-ory (Fomin, Gekhtman)

• Solitons and positive Grassmannians (Abenda, Kodama)• Conformal field theory and quantum cluster algebras

(Di Francesco, Kedem, Marshakov)• Twistor theory (Mason)• Cluster combinatorics (Garver, Musiker)

The scope of presentations ranged from analyzing a particularillustrative example, to reporting on progress on a long-termresearch program, to providing a broad overview of futuredirections of research. For example, Shapiro and Kenyon pre-sented two different approaches to the construction of discreteintegrable systems associated with toric quivers — one relyingon rational boundary measurement matrices arising from di-rected networks on a cylinder, another based on dimer con-figurations constructed from Newton polytopes of algebraiccurves. These talks were complemented by Glick’s report ona new rich family of discrete maps that can be analyzed via

either of these approaches and by Pylyavskyy’s account ofconjectures on integrability of certain compositions of clustermutations associated with bipartite quivers, complete withsupporting examples.

Similarly, lectures of Arkani-Hamed and Thomas presentedcomplementary perspectives on the definition and propertiesof the amplituhedron, one motivated by theoretical physics,another geometric and combinatorial in nature. Franco andTrnka provided a fascinating array of concrete examples andconjectures arising in the study of the amplituhedron.

New exciting applications of the combinatorics of plabicnetworks in a disc — to the mirror duality and to Legen-drian knots — were outlined in talks by L. Williams andH. Williams, while Fomin described how more complicatednetworks (possibly on higher genus surfaces) provide novelinsights into the classical theory of invariants. He concludedwith a list of concrete conjectures that will be certain to at-tract a lot of interest.

The success of the goal of bridging together, developing acommon language and striking interactions between the ab-stract mathematical community on the one hand, and the the-oretical physics community on the other, was evident. Withsixty registered participants, the talks were well attended andwere followed by active discussions during breaks between thetalks, and in the afternoon. We list these examples as evidenceof the successful and scientifically significant event that theworkshop proved to be.

Particularly enlightening was the panel discussion: a panelof experts (Gekhtman, Harnad, Kodama, Mason, Trnka,L. Williams), representing the main themes of the workshop,invited the audience to a discussion of questions and problemsinspired by workshop, often striving at creating an effectivetranslation dictionary between the two communities.

The organizers are investigating the possibility of publishingproceedings of the workshop in a special issue of Journal ofPhysics A: Mathematical and General.

ABONNEMENT/DÉSABONNEMENT auBulletin.Veuillez compléter un bref formulaire à la page web :www.crm.math.ca/bulletin/abonnement.

SUBSCRIBE/UNSUBCRIBE to the Bulletin.Please fill a short form at:www.crm.math.ca/bulletin/abonnement.

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Le Bulletin du CRMVolume 22, No 1Printemps 2016

Le Bulletin du CRM est une lettred’information à contenu scientifique,faisant le point sur les actualités duCentre de recherches mathématiques(CRM).

ISSN 1492-7659Le Centre de recherches mathémati-ques a vu le jour en 1969. Actuelle-ment dirigé par Luc Vinet, il a pourobjectif de servir de centre natio-nal pour la recherche fondamentaleen mathématiques et leurs applica-tions. Le personnel scientifique duCRM regroupe plus d’une centainede membres réguliers et de boursierspostdoctoraux. De plus, le CRM ac-cueille chaque année entre mille etmille cinq cents chercheurs du mondeentier.Le CRM coordonne des cours decycles supérieurs et joue un rôleprépondérant (en collaboration avecl’ISM) dans la formation de jeuneschercheurs. On retrouve partoutdans le monde de nombreux cher-cheurs ayant eu l’occasion de parfaireleur formation en recherche au CRM.Le Centre est un lieu privilégié derencontres où tous les membres béné-ficient de nombreux échanges et col-laborations scientifiques.Le CRM tient à remercier ses diverspartenaires pour leur appui financierà sa mission : le Conseil de recherchesen sciences naturelles et en génie duCanada, le Fonds de recherche duQuébec – Nature et technologies, laNational Science Foundation, l’Uni-versité de Montréal, l’Université duQuébec à Montréal, l’Université Mc-Gill, l’Université Concordia, l’Uni-versité Laval, l’Université d’Ottawa,l’Université de Sherbrooke, le réseauMitacs, ainsi que les fonds de dota-tion André-Aisenstadt et Serge-Bis-sonnette.Directeur : Luc VinetDirectrice d’édition : Galia DafniConception : André MontpetitCentre de recherches mathématiquesUniversité de MontréalC.P. 6128, succ. Centre-villeMontréal, QC H3C 3J7

Téléphone : 514.343.7501Courriel : CRM@CRM.UMontréal.CA

Le Bulletin est disponible à :crm.math.ca/docs/docBul_fr.shtml.

Séminaires Universitaires enMathématiques à Montréal

Alexis Langlois-Rémillard, président de l’édition 2016 des SUMM

Ce sont près de 130 étudiantes et étu-diants en mathématiques, en physique,en statistique et en informatique duQuébec et de l’Ontario qui se sont ras-semblés en janvier dernier à l’occasion dela septième édition des Séminaires Uni-versitaires en Mathématiques à Mont-réal. Grâce à l’accueil généreux du dé-partement de mathématiques de l’Uni-versité du Québec à Montréal et del’ISM, les participants et participantesdu colloque ont échangé pendant unefin de semaine des idées, communiquédes problèmes mathématiques et pré-senté leurs résultats de recherche, le toutdans une atmosphère conviviale. Ce futl’occasion pour plusieurs de rencontrerou de revoir leurs collègues provenantde diverses universités de la métropoleet de l’étranger. De constater autant decohésion au sein de la communauté ma-thématique étudiante est pour nous fortréjouissant.

Dix-neuf conférences étudiantes sur unepalette variée de sujets ont ainsi été don-nées en anglais et en français, en plusdes traditionnelles conférences plénières.Cette année, ce sont les professeurs

Christian Genest de McGill, FrancoSaliola de l’UQAM, Dimiter Dryanovde Concordia ainsi que la professeureMarlène Frigon de l’Université de Mont-réal qui ont eu la parole lors de la fin desemaine.

Conférence étudiante Photo : Gida Hussani

Cette année, l’événement était subven-tionné et soutenu par les départementsde mathématiques et de statistique desuniversités montréalaises, par le ser-vice à la vie étudiante et la facultédes sciences de l’UQAM, par l’ISM, leSTUDC, Waterloo Maplesoft ainsi queles nombreuses associations étudiantesde mathématiques et de statistique dela métropole.

CRM Summer School on Spectral Theory and ApplicationsUniversité Laval, July 4 – 14, 2016

The goal of the 2016 CRM SummerSchool in Quebec City is to preparestudents for research involving spec-tral theory. The school will givean overview of a selection of topicsfrom spectral theory, interpreted ina broad sense. It will cover topicsfrom pure and applied mathematics,each of which will be presented in a 5-hour mini-course by a leading expert.These lectures will be complementedby supervised computer labs and exer-cise sessions. At the end of the school,invited speakers will give specializedtalks. This rich subject intertwinesseveral sub-disciplines of mathemat-ics, and it will be especially beneficial

to students. The subject is also verytimely, as spectral theory is witness-ing major progress both in its math-ematical sub-disciplines and in its ap-plications to technology and science ingeneral.

The school is intended for ad-vanced undergraduate and begin-ning graduate students. As such,the prerequisites will be kept at a min-imum. Students will be housed oncampus in the university dormitories.

For more information, or to submit anapplication, please see the webpage ofthe summer school: www.crm.math.ca/2016/Quebec16/

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Mot du directeurMerci ! Thank you!

We never say that enough. If you are reading these lines itis because you have an interest in the CRM, and you may besure that we appreciate it. Thank you.

Si vous avez des textes à lire dans ce Bulletin, c’est que descollègues ont pris du temps pour les écrire, c’est qu’il y a eudes événements scientifiques excitants, des chercheurs qui sontvenus de partout pour y participer, des organisateurs qui ontconçu et réalisé ces activités, des membres de comités béné-voles qui ont apporté leur assistance, etc. Je les en remercietous. Merci aussi au grand public qui participe aux grandesconférences que l’on organise pour lui.

If the Bulletin offers interesting reading material, it is due toindustrial partners teaming up with our researchers, lab direc-tors orchestrating our 13 research units, and the presence intheir midst of fantastic graduate students, postdocs and fac-ulty that keep making scientific advances. We applaude all ofthem. This Bulletin is in front of you also because the CRMhas a creative executive team and above all a remarkable staffcomposed of dedicated and professional people who are mak-ing it all happen. This is not taken for granted. Nothingwould occur of course without the financial support from ourfunding agencies, our partner universities and the tax payers.We are very grateful.

From January onward, the CRM has transitioned from anextremely successful ensemble of activities organized aroundthe AdS/CFT correspondance to a programming focusingon computational mathematics in emerging applications. Asusual the diversity of events past or future is inspiring. I hopeyou will enjoy learning about these many facets of the CRMin the various articles of this Bulletin. J’espère que cela aurapour effet de soutenir votre intérêt et de vous encourager àmaintenir votre implication dans cet institut qui est le vôtre.

Le CRM est une grande famille accueillante et « tricotéeserré » qui cherche toujours à s’agrandir et à intégrer d’autresmembres. Comme toute famille, le CRM partage les joies etles succès des uns mais aussi les peines que la vie amène. Nousnous réjouissons énormément de la reconnaissance dont plu-sieurs membres du CRM ont été l’objet récemment, mention-nons le prix Coxeter – James de la SMC à Louigi Addario-Berry, les prix CRM – Fields – PIMS et Jeffrey – Williams àDani Wise et les Simons fellowships à Adrian Iovita et AdamOberman. Si besoin était, cela témoigne de l’immense talentdes chercheurs que le CRM regroupe.

The CRM was much saddened however by the recent loss ofthree members who were all intimately part of the fabrics ofthe CRM: Jacques St-Pierre who was the first Director of theCRM, Twareque Ali, our much esteemed colleague from theMathematical Physics Lab, and Fedor Soloviev, a postdoc-toral fellow in that same lab. We mourn them and will have

them in mind as we move forward, always celebrating the hu-man spirit. Merci Jacques, thank you Twareque, thank youFedor. Ils sont le CRM et vous l’êtes aussi.

Luc Vinet

In memoriamJacques St-Pierre

Jacques St-Pierre

M. Jacques St-Pierre, premier di-recteur du Centre de recherchesmathématiques, s’est éteint le 29mars 2016 à l’âge de 95 ans.

À la fin des années 60, Ro-ger Gaudry, Maurice L’Abbé etJacques St-Pierre jetaient lesbases du CRM pour créer le pro-totype du modèle qui est au-

jourd’hui prévalent. On ne peut que s’émerveiller de laforce visionnaire de ces fondateurs. Jacques St-Pierre auraété le premier directeur du CRM ; c’est à lui que l’on doitla mise en place des structures administratives qui ont sibien servi le centre.

Springer –CRM PublicationsCRM Short Courses

The CRM is happy to announce the recent launch of a newseries of publications with Springer.

The volumes in the CRM Short Courses series have a pri-marily instructional aim, focusing on presenting topics ofcurrent interest to readers ranging from graduate studentsto experienced researchers in the mathematical sciences.Each text is aimed at bringing the reader to the forefrontof research in a particular area or field, and can consist ofone or several courses with a unified theme. The inclusionof exercises, while welcome, is not strictly required. Pub-lications are largely but not exclusively, based on schools,instructional workshops and lecture series hosted by, oraffiliated with, the Centre de recherches mathématiques(CRM). Special emphasis is given to the quality of expo-sition and pedagogical value of each text.

Editorial Board: Mireille Bousquet-Mélou (CNRS, LaBRI,Bordeaux); Antonio Córdoba Barba (ICMAT, UAM);Svetlana Jitomirskaya (UC Irvine); V. Kumar Murty(Toronto); Leonid Polterovich (Tel Aviv)

Series Editor: Galia Dafni (CRM, Concordia University)

http://www.springer.com/series/15360

http://www.crm.umontreal.ca/pub/pub_fr.shtml

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