Annualreport 2012 2013

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C CENTRE R DERECHERCHES M MATHÉMATIQUES

AnnualReport 2012 2013

C CENTRE R DERECHERCHES M MATHÉMATIQUES

AnnualReport 2012 2013 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.

Presenting the Annual Report 2012–2013 1

Thematic Program 3 Thematic Program of the Year 2012–2013: “Moduli Spaces, Extremality and Global Invariants” and “Mathematics of Planet Earth 2013” ...... 4 Aisenstadt Chairholders in 2012–2013: Fedor Bogomolov, David Gabai, Helmut Hofer, and Gang Tian . 5 Activities of the Thematic Year ...... 7 Past Thematic Programs ...... 18

General Program 19 CRM activities ...... 20 Colloquium and Seminar Series ...... 35

Multidisciplinary and Industrial Program 37 Activities of the Multidisciplinary and Industrial Program ...... 38

CRM Prizes 40 CRM–Fields–PIMS Prize 2013 Awarded to Bruce Reed ...... 41 André-Aisenstadt Prize 2013 Awarded to Spyros Alexakis ...... 41 The CRM–SSC Prize 2013 Awarded to Derek Bingham ...... 42

The CRM Outreach Program 44 Mathematics of Planet Earth 2013 — CRM Public Lectures ...... 45 Mathematics of Planet Earth 2013 — Cross-Canada Series of Lectures ...... 48 Grandes Conférences du CRM ...... 49

CRM Partnerships 52 CRM Partners ...... 53 Joint Initiatives ...... 56

Mathematical Education 57 Institut des sciences mathématiques (ISM) ...... 58 Other Joint Initiatives ...... 60

Research Laboratories 61 Applied Mathematics ...... 62 CICMA — Centre Interuniversitaire en Calcul Mathématique Algébrique ...... 63 CIRGET — Centre Interuniversitaire de Recherches en Géométrie et Topologie ...... 64 GIREF — Groupe Interdisciplinaire de Recherche en Éléments Finis ...... 66 LaCIM — Laboratoire de Combinatoire et d’Informatique Mathématique ...... 67 Mathematical Analysis ...... 69 Mathematical Physics ...... 71 PhysNum ...... 73 Statistics ...... 74

Publications 76 Recent Titles ...... 77 Previous Titles ...... 77

Scientific Personnel 82 CRM Members in 2012–2013 ...... 83 Postdoctoral Fellows ...... 85

iii Centre de recherches mathématiqes

Visitors ...... 86

List of Students Having Graduated in 2012–2013 88 Ph.D. Students ...... 89 M.Sc. Students ...... 91

Governance and Scientific Guidance 95 Board of Directors ...... 96 Committee of Directors of Laboratories ...... 96 International Scientific Advisory Committee ...... 97

CRM Administrative and Support Staff 102 The Director’s Office ...... 103 Administration ...... 103 Scientific Activities ...... 103 Computer Services ...... 103 Publications ...... 103 Communications ...... 103

Mandate of the CRM 104

iv Presenting the Annual Report 2012–2013 Centre de recherches mathématiqes

The 2012–2013 thematic program at the CRM wasa (André-Aisenstadt Prize 2013), and Derek Bingham perfect illustration of the breadth of its activities, since from Simon Fraser University (CRM–SSC Prize 2013). it included a Thematic Year on Moduli Spaces, Ex- The public lectures that took place at the CRM in2012– tremality and Global Invariants as well as the The- 2013 were especially brilliant. Four of these were re- matic Year “Mathematics of Planet Earth 2013”. Thus lated to the MPE 2013 Thematic Year. The lectures by both pure and interdisciplinary mathematics were fea- Ingrid Daubechies and Paul Embrechts were part of tured at the CRM this year. The Thematic Year on Mod- the MPE 2013 – CRM Public Lectures Series; the lec- uli Spaces, Extremality and Global Invariants was ded- ture by Professor Daubechies was actually sponsored icated to questions that lie at the heart of the cur- by the prestigious Simons Foundation. The lectures by rent research in geometry. It consisted of eight re- Nilima Nigam and Anthony Peirce were part of the search workshops (paired with mini-courses) and se- MPE 2013 – Cross-Canada Series of Public Lectures. ries of Aisenstadt lectures by Fedor Bogomolov, David The fifth public lecture was given by the French physi- Gabai, Helmut Hofer, and Gang Tian, respectively. I cist Alain Aspect and was part of the Grandes Con- would like to express my thanks to the members of the férences series. Thematic Year scientific committee: Vestislav Apos- tolov, Steven Boyer, Virginie Charette, Olivier Collin, An Unité Mixte Internationale (UMI) was established Octav Cornea, Jacques Hurtubise, François Lalonde, by the CNRS at the CRM in 2011 and has given Steven Lu, Frédéric Rochon, Peter Russell, and Jo- an impetus to the exchanges between the CRM and hannes Walcher. the French mathematical community: sixteen French mathematicians visited the CRM and three Montréal The Mathematics of Planet Earth program, launched researchers visited colleagues in France in 2012-2013 by Christiane Rousseau during her mandate as CRM thanks to the UMI. Also in 2012-2013, the relationship director, was enthusiastically adopted by our Cana- between the CRM and the French mathematical com- dian partners and many mathematics research insti- munity led to the organization of two colloquia within tutes across the globe. In particular the Mathematics of the Entretiens Jacques-Cartier (in Lyon): a colloquium Planet Earth 2013 (MPE 2013) program was a joint ini- on risk management and a colloquium on mathemati- tiative of Canadian institutions, with activities taking cal physics. place in many locations. The goal of this thematic program was to tackle pressing and emerging challenges The activities of the CRM are supported by the Gov- in population and ecosystem health, including the con- ernment of Canada through NSERC, the Government trol of major transmissible diseases, the optimization of Québec through FRQNT, the Government of the and monitoring of vaccination, the impact of climate United States through the National Science Foundation change on invasive species, the protection of biodiver- (NSF), the Mprime network, and its partner university, and the sustainable management of ecosystems. sities: the Université de Montréal, McGill University, The MPE 2013 year featured three summer schools for the Université du Québec à Montréal, Concordia Uni- graduate students and postdoctoral fellows as well as versity, the Université Laval, the Université de Sher- workshops that took place at the CRM, the Fields In- brooke, and the University of Ottawa. The Society for stitute (in Toronto), the PIMS (in Edmonton), St. John’s Mathematical Biology (SMB) provided support to stu- (under the auspices of AARMS), and BIRS. The sci- dents and young (particularly pre-tenure) investiga- entific committee of the Canadian program included tors participating in the MPE 2013 program. On behalf Jacques Bélair, Mark Lewis, Frithjof Lutscher, James of the CRM I extend my sincere thanks to all our part- Watmough, and Jianhong Wu. ners, who help the CRM develop its activities within a world-class research program in the mathematical sci- The CRM is also proud of the outstanding re- ences. searchers who were awarded its prizes this year: Bruce Reed from McGill University (CRM–Fields–PIMS Prize Luc Vinet, Director 2013), Spyros Alexakis from the University of Toronto Centre de recherches mathématiques (CRM)

2 Thematic Program Centre de recherches mathématiqes

Thematic Programs of the Year 2012–2013 “Moduli Spaces, Extremality and Global Invariants” and “Mathematics of Planet Earth 2013” Moduli Spaces, Extremality and Global ometry that had, until then, stagnated since its infancy Invariants almost two centuries ago. Moduli spaces are present everywhere: the spaces of Geometry in the large sense, and especially the ge- metrics, be they Kähler or almost Kähler, the space ometry of the most natural and simple structures on of almost complex structures, the space of represen- manifolds, is going through a golden age. More than tations of the fundamental group of surfaces or 3- ever, we are close to a satisfactory understanding of the folds in suitable Lie groups and the so-called higher basic blocks that constitute the most intricate spaces, Teichmüller spaces, the Hamiltonian diffeomorphism be they Riemannian, complex, algebraic, symplectic or group over which the Hofer norm is given, the space dynamical. Contemplating this development, one sees of configurations of the so-called clusters, a sort of the ubiquitous role played by extremality and stabil- dual to the Fukaya A-structure, the space of pseudo- ity understood in various contexts: the proof of the algebraic functions on algebraic curves that are myste- Poincaré conjecture and the parabolic methods that riously connected to integrable systems, random ma- reach minimality in low-dimensional manifolds place trices, Gromov–Witten-invariants, all of these spaces us roughly at the point where mathematicians were at are currently attracting the attention of the mathemat- the end of the nineteenth century when one had to ical community more than ever before, with an inter- invent, beyond the analytical method of uniformiza- disciplinary perspective that is now, clearly, essential. tion, a full topological theory needed to achieve a satisfactory classification. Minimality and extremality are The theme year on “Moduli Spaces, Extremality and also present in higher dimensions, both in the Kähler– Global Invariants” was a hub dedicated to the study Einstein case and in the constant scalar curvature Käh- of these questions, which lie at the heart of the cur- ler case, where Aubin, Yau, Tian and Donaldson estab- rent developments in geometry. The program con- lished basic existence theorems. sisted of eight research workshops paired with minicourses and several series of Aisenstadt lectures, all co- Extremality is also behind the recent spectacular proof ordinated to maximize constructive interactions. The by Taubes of the full Weinstein conjecture on the exis- program also supported a number of research visi- tence of closed orbits of the Reeb flow on contact man- tors and postdoctoral fellows so that they could work ifolds. Although his proof relies on a subtle interplay at CIRGET, the geometry-topology research labora- between the contravariant Seiberg–Witten theory and tory of the CRM. The scientific committee ofthe the covariant embedded contact homology, the conjec- year included the following researchers: Vestislav ture itself and ultimately the idea of its proof rely on Apostolov (UQAM), Steven Boyer (UQAM), Virginie the minimality of an action associated to some closed Charette (Sherbrooke), Olivier Collin (UQAM), Oc- trajectory that can also be computed as a capacity. In tav Cornea (Montréal), Jacques Hurtubise (McGill), symplectic topology and geometry, the progress over François Lalonde (Montréal), Steven Lu (UQAM), the last decade is remarkable on almost all important Frédéric Rochon (UQAM & ANU), Peter Russell questions: while relative symplectic field theory, con- (McGill), Johannes Walcher (McGill). The organizers of sidered by some mathematicians to be the ultimate the- the semester are very grateful to the National Science ory of classical and quantum mechanics, is developing Foundation for its financial support. quickly with tools coming from several parts of mathematics (analytical foundations, algebraic formalism, Mathematics of Planet Earth 2013 geometric intuition and setting), advances on all aspects of the ubiquitous Floer theory are now percolat- As part of the Mathematics of Planet Earth 2013 ing in 3 and 4-dimensional manifolds. Almost indepen- (MPE 2013) initiative, a series of workshops and sum- dently, the theory of J-holomorphic curves has been mer schools was organized in 2013, consisting of activi- used to derive real enumerative invariants, opening for ties taking place across Canada. The challenges that we the first time the field of enumerative real algebraic ge- face on our planet are becoming increasingly complex

4 Thematic Program since ecological, economic and social systems are large change and stimulating cross-disciplinary research be- intertwined networks governed by dynamic processes tween all scientific areas involved. Three summer and feedback loops. Mathematical models are indis- schools introduced graduate students and postdoctoral pensable in understanding and managing such sys- fellows to the art of modelling living systems and to the tems because they provide insight into governing pro- latest tools and techniques for analyzing these mod- cesses; they help predict future behaviour; and they al- els. These activities took place not only at the CRMin low for risk-free evaluation of possible interventions. Montréal, but also at the Fields Institute in Toronto, at The goal of this thematic program was to tackle press- the PIMS in Edmonton, at St. John’s under the auspices ing and emerging challenges in population and ecosys- of AARMS, and at BIRS. The scientific committee ofthe tem health, including the understanding and control- Canadian program included Jacques Bélair (Univer- ling of major transmissible diseases, the optimizing sité de Montréal), Mark Lewis (University of Alberta), and monitoring of vaccination, the prediction of the Frithjof Lutscher (University of Ottawa), James Wat- impacts of climate change on invasive species, the pro- mough (University of New Brunswick), and Jianhong tection of biodiversity, and the sustainable manage- Wu (York University). The National Science Founda- ment of ecosystems. tion (NSF) and the Society for Mathematical Biology This pan-Canadian program brought together the in- (SMB) provided funding in order to support students ternational community of researchers who work on and young (particularly pre-tenure) investigators par- these topics in a series of workshops fostering ex- ticipating in this program.

Aisenstadt Chairholders in 2012–2013 Fedor Bogomolov, David Gabai, Helmut Hofer, and Gang Tian

Fedor Bogomolov Professor David Gabai of Princeton University gave a series of four lectures during the events surround- Professor Fedor Bogomolov is an outstanding mathe- ing the workshop The Topology of 3-dimensional man- matician renowned for his work in algebraic geometry ifolds. Professor Gabai is a world leader in the topol- and number theory. He graduated from the Faculty of ogy and geometry of low-dimensional manifolds, with Mechanics and Mathematics of the Moscow State Uni- many outstanding research contributions throughout versity and earned his doctorate at the Steklov Institute a career in which he has solved major problems and de- in 1973. F. Bogomolov obtained his habilitation in 1983 veloped powerful techniques that have had a profound and became a full professor at the Courant Institute impact in the field. These include proofs of the Seifert in 1994. He has conducted seminal work on the geom- fiber space conjecture (1992), the rigidity of homotopy etry of Kähler manifolds, Calabi–Yau manifolds, mir- hyperbolic 3-manifolds (1994), the Smale Conjecture ror symmetry, holomorphic vector bundles, and the for hyperbolic 3-manifolds (2001), and Marden’s Tame- approach of diophantine equations through the geom- ness Conjecture (2006). He was awarded the Oswald etry of hyperbolic manifolds and dynamical systems. Veblen Prize in Geometry by the American Mathemat- We refer the reader to the Spring 2013 edition of the ical Society in 2004, and was made a member of the Bulletin du CRM for a description of Bogomolov’s lec- American National Academy of Sciences in 2012. tures, respectively entitled Professor Gabai’s first two lectures were expository in • External and Internal Symmetries and their Role in nature. The first provided an overview of Poincaré’s Mathematics and Nature; many contributions to topology, remarkable for their • Universal Spaces in Birational Algebraic Geometry; foundational and seminal nature as well as their im- and pact on subsequent research. The second surveyed the • Several Aspects of Infinite Transitivity. still mysterious field of the volumes of hyperbolic 3- manifolds from W. Thurston’s 1970s proof that the set David Gabai of such positive real numbers is closed and well or- by Steven Boyer (UQAM) dered, to Professor Gabai’s 2009 theorem with Robert Meyerhoff and Nathaniel Thurston that the Weeks

5 Centre de recherches mathématiqes manifold is the unique manifold to realize the mini- The topic of Hofer’s talks was Hamiltonian Dynamics mal possible volume among closed orientable hyper- and Symplectic Rigidity. Hamiltonian systems, which bolic 3-manifolds. He described the three decades of occur frequently in physics, are also of great interest effort by many mathematicians, using a wide vari- in many branches of mathematics. Symplectic geome- ety of techniques, that bridged these results, includ- try allows us to formulate certain dynamical questions ing the use of Ricci flow by Ian Agol and Nathan Dun- into geometric and, sometimes, even algebraic prob- field to obtain strong volume estimates. The talk con- lems. This is based on the properties of the moduli cluded with a discussion of open problems and an ap- spaces of (perturbed) J-holomorphic curves that nat- proach for addressing the Thurston, Weeks, Matveev– urally arise in relation to a given Hamiltonian sys- Fomenko conjecture that complete low-volume hyper- tem, once the appropriate action functional is defined. bolic 3-manifolds are of low topological complexity. Assuming that these moduli spaces are well-behaved, Professor Gabai’s last two Aisenstadt Chair lectures fo- they are amenable to combinatorial assembly and the cused on the topology of the ending lamination space output is presented as certain homological type in- associated to a finite type hyperbolic surface S. He set variants such as Gromov–Witten invariants, Floer ho- the stage by describing its connections with the space mology, and others. Understanding of these invariants of projective measured laminations of S, the Gromov sheds light on the dynamical properties of the initial boundary of the curve complex of S, and the set of dou- Hamiltonian system. In the last twenty years the sym- bly degenerate hyperbolic structures on S × R. Most plectic machinery that follows this general scheme has of his time was devoted, though, to explaining his re- developed tremendously. Hofer’s talks reviewed part cent results in the area. For instance, if S has genus g of these developments, and emphasized that the time and p punctures, then its ending lamination space is has come for a renewed exploration of questions origi- both (n − 1)-connected and (n − 1)-locally-connected nating in celestial mechanics and space transportation where 2n + 1 = 6g + 2p − 7. Further, when g is zero, by using all the sophisticated tools at our disposal to- its ending lamination space is the Nöbeling space of day. points in R2m+1 with at most m rational coordinates. Gang Tian Helmut Hofer by Vestislav Apostolov (UQAM) by Octav Cornea (Université de Montréal) Professor Gang Tian, who is Eugene Higgins Profes- Helmut Hofer obtained his Ph.D. at the University of sor at Princeton and the director of the Beijing Inter- Zürich in 1981 and is currently a permanent member of national Centre for Mathematical Research (BICMR), the Institute for Advanced Study in Princeton. Among gave a series of three Aisenstadt lectures during the other prestigious distinctions, he is a member of the workshop Extremal Kähler metrics. In global analysis National Academy of Sciences and was twice an in- and geometry over the last 25 years, Professor Gang vited speaker at an International Congress of Mathe- Tian has been one of the most influential and versatile maticians (the second time, in 1998, he was actually a figures. From his Ph.D. thesis to his most recent work, plenary speaker). Hofer is one of the founders of mod- his contributions have been distinguished by their di- ern symplectic topology. His work, alone and with col- versity and depth. His most striking work to date con- laborators, on Floer theory, on capacities and applica- cerns the existence of Kähler–Einstein metrics on com- tions to Hamiltonian dynamics, and on cases of the plex manifolds (which was a main theme of the work- Weinstein conjecture in dimension three was trans- shop), but he has made many other significant con- formational. It led to the establishment and the fur- tributions. For instance, he established (with Y. Ruan) ther study by countless researchers of (what is now the associativity of the quantum cohomology ring of called) the Hofer geometry of the Hamiltonian dif- a symplectic manifold, constructed (with Jun Li) mod- feomorphisms groups. More recently, together with uli spaces of curves in algebraic symplectic geometry, Wysocki and Zehnder he is developing polyfold the- elaborated (with J. Morgan) a clear and detailed expo- ory, a wide-reaching extension of usual differential ge- sition of Perelman’s proof of the Poincaré conjecture, ometry particularly adapted to the study of regularity and developed ideas to link Kähler–Ricci flow with the properties of moduli spaces of solutions of PDEs. Mori program in algebraic geometry.

6 Thematic Program

Most relevant to this CRM workshop, however, is one or more distinguished mathematicians are invited Tian’s work on Kähler–Einstein metrics. In his early each year for a period of at least one week, ide- career, he solved the existence question for Kähler– ally one or two months. During their stay the lec- Einstein metrics on compact complex surfaces with turers present a series of lectures on a specialized positive first Chern class, and showed that Fano va- topic. They are also invited to prepare a monograph rieties with a Kähler–Einstein metric must be stable in (see the chapter on publications in the present re- the sense of geometric invariant theory, thus confirm- port for a list of these monographs). At the request ing part of a suggested correspondence by Yau. Pro- of Dr. Aisenstadt, the first lecture given by an Aisen- fessor Tian gave a precise formulation of this corre- stadt chairholder should be accessible to a wide au- spondence, known today as the Yau–Tian–Donaldson dience. Previous holders of the Aisenstadt chair are: conjecture, identifying the obstruction to the existence Marc Kac, Eduardo Zarantonello, Robert Hermann, of Kähler–Einstein metrics with what is now called Marcos Moshinsky, Sybren de Groot, Donald Knuth, the K-stability of the Fano variety. His ideas have in- Jacques-Louis Lions, R. Tyrrell Rockafellar, Yuval spired a tremendous amount of work in recent years, Ne’eman, Gian-Carlo Rota, Laurent Schwartz, Gérard and spectacular progress has been made, culminating Debreu, Philip Holmes, Ronald Graham, Robert Lang- in the complete resolution of the conjecture by Tian lands, Yuri Manin, Jerrold Marsden, Dan Voiculescu, himself, and by Xiuxiong Chen, Simon Donaldson and James Arthur, Eugene B. Dynkin, David P. Ruelle, Song Sun. Robert Bryant, Blaine Lawson, Yves Meyer, Ioan- Professor Tian’s first lecture was expository in nature, nis Karatzas, László Babai, Efim I. Zelmanov, Peter and reviewed the theory and latest progress related to Hall, Sir David Cox, Frans Oort, Joel S. Feldman, Ro- the existence of Kähler–Einstein metrics. The second man Jackiw, Duong H. Phong, Michael S. Waterman, lecture was concerned with a more detailed exposition Arthur T. Winfree, Edward Frenkel, Laurent Lafforgue, of the key ideas of Professor’s Tian most recent work George Lusztig, László Lovász, Endre Szemerédi, Pe- regarding the existence of Kähler–Einstein metrics on ter Sarnak, Shing-Tung Yau, Thomas Yizhao Hou, An- a K-stable Fano variety. The third lecture featured re- drew J. Majda, Manjul Bhargava, K. Soundararajan, cent results on convergence of the Kähler–Ricci flow Terence Tao, Noga Alon, Paul Seymour, Richard Stan- on a Fano variety. ley, John J. Tyson, John Rinzel, Gerhard Huisken, Jean- Christophe Yoccoz, Wendelin Werner, Andrei Ok- Aisenstadt Chair ounkov, Svante Janson, Craig Tracy, Stéphane Mal- lat, Claude Le Bris, Akshay Venkatesh, Yuri Gurevich, The Aisenstadt chair was endowed by Montréal phi- Angus Macintyre, Alexander Razborov, James Robins, lanthropist Dr. André Aisenstadt. Under its auspices, John Preskill, Renato Renner, László Erdős, Elon Lin- denstrauss, Richard M. Schoen.

Activities of the Thematic Year

The reports are presented in the language in which they were submitted. As far as MPE 2013 is concerned,we have given the list of all the activities taking place in Canada but included reports only for the CRM activities.

Workshop Speakers: Spectral Invariants on Non-Compact and Spyros Alexakis (Toronto), Dean Baskin (Northwest- Singular Spaces ern), Jean-Michel Bismut (Paris-Sud), David Borthwick July 23–27, 2012, CRM (Emory), Maxim Braverman (Northeastern), Jochen Sponsored by the CRM, the NSF, and the Australian Brüning (Humboldt), Tanya Christiansen (Missouri), National University Xianzhe Dai (UC Santa Barbara), Kiril Datchev (MIT), Daniel Grieser (Oldenburg), Colin Guillarmou (ÉNS), Organizers: Chris Kottke (Brown), Zhiqin Lu (UC Irvine), Xi- Pierre Albin (UI Urbana-Champaign), Frédéric Rochon aonan Ma (Paris Diderot), Jeremy Marzuola (UNC— (UQAM & ANU) Chapel Hill), Richard Melrose (MIT), Gerardo Mendoza

7 Centre de recherches mathématiqes

(Temple), Jinsung Park (KIAS), Bert-Wolfgang Schulze montrés intéressés à apporter leur contribution, ce qui (Potsdam), Michael Singer (Univ. Coll. London), Gun- devrait mener à un ouvrage intéressant. ther Uhlmann (Washington), Mathai Varghese (Ade- laide), András Vasy (Stanford), Siye Wu (Hong Kong), Mini-course & Workshop Jared Wunsch (Northwestern), Ken-Ichi Yoshikawa The Topology of Algebraic Varieties (Kyoto), Steve Zelditch (Northwestern) September 21–28, 2012, CRM Number of participants: 44 Sponsored by the CRM and the NSF Le premier atelier de l’année thématique a eu lieu au Organizers: CRM du 23 au 27 juillet, 2012. Les organisateurs étaient Rajendra Gurjar (Tata Inst.), Shulim Kaliman (Miami), Pierre Albin (Urbana-Champaign) et Frédéric Rochon Steven Lu (UQAM), Peter Russell (McGill) (UQAM). Il y avait entre 5 et 6 exposés par jour, pour un Lecturers: total de 25 exposés. Les exposés étaient de 50 minutes, Ryoichi Kobayashi (Nagoya), Adrian Langer (War- ce qui a donné suffisamment de temps à chaque con- saw), Terrence Napier (Lehigh), Walter Neumann férencier pour présenter ses résultats, donner une idée (Columbia), Anne Pichon (Aix-Marseille), Mohan Ra- des méthodes utilisées et mentionner des questions ou- machandran (Buffalo) vertes. Même si l’horaire était assez rempli, les partici- Speakers: pants ont aussi eu plusieurs occasions d’échanger, no- Shreeram Abhyankar (Purdue), Donu Arapura (Pur- tamment durant les pauses-café et sur l’heure du lunch. due), Fedor Bogomolov (Courant Inst.), Frédéric Bruno Un mélange intéressant de sujets a été abordé. Cer- Campana (Henri Poincaré), Fabrizio Catanese (Bay- tains exposés portaient sur la théorie de l’indice (ceux reuth), Bruno de Oliveira (Miami), Philippe Eyssi- de Wu, Varghese, Brüning et Kottke) ou sur des in- dieux (Joseph Fourier), Hubert Flenner (Bochum), Lud- variants spectraux apparentés tels l’invariant êta et mil Katzarkov (Miami), JongHae Keum (KIAS), Ry- la torsion analytique (Melrose, Park, Ma, Yoshikawa oichi Kobayashi (Nagoya), Mariusz Koras (Warsaw), et Dai). D’autres portaient plutôt sur la théorie de Frank Kutzschebauch (Bern), Adrian Langer, Michael la diffusion, notamment les exposés de Christiansen, McQuillan (IHÉS), Masayoshi Miyanishi (Kwansei Bortwick, Baskin, Vasy, Datchev, Guillarmou, ou plus Gakuin), Terrence Napier, Madhav Nori (Chicago), généralement sur l’analyse spectrale, comme dans les Bangere Purnaprajna (Kansas), Mohan Ramachandran, exposés de Lu, Marzuola, Wunsch et Grieser. Cer- Sheng-Li Tan (East China NU), Jörg Winkelmann (Bo- tains résultats touchant à la géométrie complexe ont chum) été abordés dans les exposés de Mendoza et Singer. Number of participants: 68 Enfin, certains sujets étaient plus spécialisés, comme Friday September 21 and the following weekend were l’exposé de Jean-Michel Bismut sur le Laplacien hy- occupied by three mini-courses of four lectures each. poelliptique ou l’exposé de Spyros Alexakis utilisant The first mini-course, on topological methods inthe l’analyse non linéaire. Plusieurs conférenciers ont ac- study of singularities (by Anne Pichon and Walter cepté de partager leurs transparents et ces derniers Neumann) was perhaps the most accessible for the sont disponibles sur la page web de l’atelier. audience, which included many postdoctoral fellows Un des beaux moments de l’atelier est sans doute and graduate students. Starting with classical results l’exposé de Jared Wunsch, qui a expliqué avec une on the topology of isolated singularities (Milnor fi- grande clarté son résultat le plus récent obtenu avec bration, iterated torus links, Puiseux expansions), the Dean Baskin. D’ailleurs, en collaboration avec un speakers introduced the concept of metrically con- autre participant de l’atelier, Jeremy Marzuola, ils ont vex singularity, the new Thick–Thin decomposition, l’intention d’écrire un article utilisant leur résultat Carousel structure, and applications to Lipschitz ge- pour obtenir une estimation de Strichartz globale sur ometry of isolated singularities. The lecturers (Ter- des domaines extérieurs à des polygones. rence Napier and Mohan Ramachandran) of the second mini-course discussed the geometry of noncom- En collaboration avec un autre atelier du CRM, celui pact Kähler manifolds and the structure theorem for de juin 2012 portant sur la géométrie des valeurs pro- these objects (in particular they described conditions pres et fonctions propres, nous projetons de publier des under which such a manifold admits a proper holomor- actes de conférence. Plusieurs participants se sont déjà phic map onto a Riemann surface). In the third mini-

8 Thematic Program course, Adrian Langer concentrated on the generaliza- Workshop tion of the Bogomolov–Miyaoka–Yau inequality to sin- Higher Teichmüller–Thurston Theory gular quasiprojective varieties, while R. Kobayashi dis- October 15–19, 2012, CRM cussed the modern approach to Nevanlinna theory that Sponsored by the CRM and the GEAR Network he introduced and that was motivated by the BMY inequality. Organizers: Virginie Charette (Sherbrooke), William M. Gold- The workshop lectures started on Monday, Septem- man (Maryland), François Labourie (Paris-Sud), Anna ber 24. Among these there were several strong reports Wienhard (Princeton) including solutions of old problems. We mention a Speakers: few: M. Koras presented an idea of a solution of the Thierry Barbot (Avignon), Ara Basmajian (Graduate Coolidge–Nagata conjecture stating that any plane ra- Ctr., CUNY & Hunter Coll., CUNY), Martin Bridgeman tional curve with locally irreducible singularities can (Boston Coll.), Suhyoung Choi (KAIST), Jeffrey Dan- be rectified by birational automorphisms of the plane; ciger (UT Austin), Todd A. Drumm (Howard), Viveka F. Kutzschebauch gave a sketch of the solution of the Erlandsson (Graduate Ctr., CUNY), William M. Gold- h Gromov–Vaserstein problem (via Gromov’s -princi- man, François Guéritaud (Lille 1), Tobias Hartnick ple); J. Keum lectured on the algebraic version of the (Technion), Fanny Kassel (CNRS Lille 1), Steven Ker- Montgomery–Yang problem (as suggested by J. Kollar); ckhoff (Stanford), Youngju Kim (KIAS), Evelyn Lamb, in L. Katzarkov’s lecture, phantoms of derived cate- Sean Lawton (Texas-Pan American), Brice Loustau gories were used as a new invariant that allows to show (Paris-Sud), Sara Maloni (Paris-Sud), Karin Melnick nonrationality of a variety even in the case when the (Maryland), Clara Rossi Salvemini (Avignon), Ser Peow intermediate Jacobian does not work; F. Canatese ex- Tan (NU Singapore), Michael Wolf (Rice) plained new results on moduli space of curves whose Number of participants: 34 automorphism groups contain a given finite group; La théorie supérieure de Teichmüller-Thurston traite H. Flenner, reporting on joint work with S. Kaliman notamment d’espaces de déformations de structures and M. Zaidenberg, presented a definitive result on géométriques localement homogènes, de représenta- deformations of affine surfaces with an A1-fibration; tions de groupes fondamentaux de surfaces, et de con- B. Purnaprajna reported on joint work with R. Gurjar nections plates. L’atelier s’est concentré sur les aspects on the fundamental groups of surfaces with finite au- liés aux métriques lorentziennes conformément plates, tomorphism groups, which leads to a solution of the les structures géométriques issues de représentations Shafarevich conjecture for certain interesting classes d’Anosov, ainsi que la géométrie des composantes de of surfaces; F. Campana explained his joint work with Hitchin, laquelle généralise celle de Weil-Petersson sur J. Winkelmann on an attempt to relate special varieties l’espace de Teichmüller. to varieties that satisfy the h-principle, the so-called Oka varieties; M. McQuillan explained his solution of Des présentations ont notamment porté sur la Lang’s conjecture concerning holomorphic curves in métrique de pression sur les représentations de surfaces of general type (which improved upon the Hitchin, les variétés modelées sur l’espace anti-De Sit- Chern inequality bound of Bogomolov). ter, ainsi que les variétés lorentziennes plates. Nous avons aussi pu profiter de présentations portant sur In a lecture liberally annotated with historical reminis- des sujets plus proches de la théorie de Teichmüller cences, S. S. Abhyankar reported on new results on lo- classique, tels que les représentations quasi fuchsi- cal fundamental groups and Galois theory, results that ennes, ainsi que la géométrie lorentzienne. have their origin in his papers on this subject in the American Journal of Mathematics in 1955 and 1956. Il y avait une trentaine de participants, en prove- His talk, in retrospect, had a special poignancy since nance de plusieurs pays: Canada, États-Unis, France, sadly Professor Abhyankar passed away not long after Corée et Singapour. Soulignons que plusieurs jeu- the conference. nes chercheurs, chercheurs postdoctoraux et étudiants gradués, ont eu l’occasion de présenter leurs résultats pendant l’atelier. Nous avons privilégié une formule où il y avait relativement peu de présentations (au plus six

9 Centre de recherches mathématiqes par jour), afin que les gens aient le temps de parlerde Number of participants: 31 leurs travaux et d’échanger informellement. In epidemiology and ecology, models are typically Nous pouvons dire que l’atelier a été un franc succès. developed along one of two directions: directly Nous avons reçu plusieurs courriels de remerciements from available data, incorporating as many empirical et de félicitations pour l’atelier. Les gens ont apprécié records as possible, or conceptually as dynamical sys- la taille de l’atelier: comme nous n’étions que trente tems, incorporating data via estimation of parameters. participants dans des domaines adjacents, nous pou- The means of investigation for these model classes vions échanger aisément entre nous. C’est pour cette are quite distinct, and an important methodologi- raison que l’atelier a sans doute favorisé l’émergence cal problem is the reconciliation of a priori method- de nouvelles collaborations. independent issues when they are described in different terms. Workshop The two main objectives of this workshop wereto Disease Dynamics 2013: Immunization, a • start the interactions for the Thematic Year, by true multi-scale problem breaking community/network barriers between the January 17–19, 2013, PIMS practitioners of different modelling techniques and Sponsored by PIMS, Mitacs, and Mathematics of Planet approaches, and Earth 2013 • follow up on activities held at the CRM on related Organizers: topics in the recent past (on Statistical Methods, in Jessica Conway (Los Alamos Natl. Lab.), Dan Coombs March 2007 and March 2010, respectively). (UBC), Rafael Meza (Michigan) A non-exclusive emphasis has been put on zoonotic Speakers: diseases, given the concentrated expertise at the Uni- Rustom Antia (Emory), Dennis Chao (Fred Hutchi- versité de Montréal, through the Faculté de Médecine son Cancer Res. Ctr.), Miles Davenport (New South Vétérinaire, and the significance and novelty of the Wales), Elamin Elbasha (Merck Res. Labs.), Jane Hef- problems they entail. fernan (York), Katia Koelle (Duke), Jan Medlock (Clem- The sessions of this three-day workshop corresponded son), David Patrick (UBC), Alan Perelson (Los Alamos to the different technical approaches in modelling: dy- Natl. Lab.), Timothy Reluga (Penn State), Jamie K. Scott namical systems with parameter estimation includ- (Simon Fraser), David P. Wilson (New South Wales) ing variability; empirical models (some based on ge- ographical information systems) of zoonotic diseases; Workshop and methodological issues in surveillance and data in- Models and Methods in Ecology and corporation in epidemiological models. Epidemiology February 13–15, 2013, CRM Workshop Sponsored by the CRM and the Society of Mathemati- Establishing the scientific foundation for cal Biology Quantitative Public Health Decision-Making Organizers: April 29–30, 2013, Fields Institute for Research in Jacques Bélair (Montréal), Jianhong Wu (York) Mathematical Sciences Speakers: Sponsored by the Fields Institute for Research in Math- Madhur Anand (Guelph), Tamara Awerbuch (Har- ematical Sciences, Mprime, and Mathematics of Planet vard), Christopher Bauch (Guelph), Lydia Bourouiba Earth 2013 (MIT), David L. Buckeridge (McGill), David A. Camp- bell (Simon Fraser), Frédéric Guichard (McGill), Jo- Organizers: han A. P. Heesterbeek (Utrecht), Patrick Leighton David Buckeridge (McGill), Charmaine Dean (Western (Montréal), Subhash R. Lele (Alberta), Rongsong Liu Ontario) Jianhong Wu (York) (Wyoming), Bernard Moulin (Laval), Calistus Ngong- Speakers: hala (Tennessee), Nicholas Hume Ogden (Montréal), Amy Greer (PHAC), Sarah Henderson (BCCDC), Fran John Takekawa (U.S. Geological Survey), Jianhong Wu Jamieson (PHO), Hedy Jiang (Toronto), Andre Kush- (York), Huaiping Zhu (York) niruk (Victoria), Seyed Moghadas (York), Trisalyn Nel-

10 Thematic Program son (Victoria), Beate Sander (PHO), Cécile Tremblay eties, and Eliashberg who explained recent advances (INSPQ) in symplectic flexibility; Number of participants: 42 • Mirror symmetry, possibly the most “explosive” topic relating symplectic topology to mathematical Workshop physics, was discussed by Ganatra, Sheridan, Perutz, J-Holomorphic Curves in Symplectic Lau and Nadler. In particular, Sheridan explained his Geometry, Topology and Dynamics proof of the HMS conjecture in a number of cases; April 29–May 10, 2013, CRM • Advances in symplectic dynamics appeared in the presentations of Entov, Khanevsky and Buhovsky; Organizers: • Hamiltonian dynamics applications were covered by Denis Auroux (UC Berkeley), Octav Cornea (Mont- talks of Usher, Schlenk, Gürel; réal), Yael Karshon (Toronto), François Lalonde (Mont- • New perspectives on Lagrangian topology were réal), Leonid Polterovich (Tel Aviv) reflected in talks of Biran, Woodward, Borman, Speakers: Solomon, Ekholm; Mohammed Abouzaid (Columbia), Paul Biran (ETH • Legendrian topology topics were discussed in talks Zürich), Strom Borman (Chicago), Lev Buhovsky (Tel of Hutchings and Honda. In particular, Hutchings’ Aviv), Olguta Buse (IUPUI), Tobias Ekholm (Uppsala), talk on applications of his Embedded Contact Ho- Yakov Eliashberg (Stanford), Michael Entov (Tech- mology described some of the most fruitful recent nion), Urs Frauenfelder (Seoul NU), Kenji Fukaya (Ky- developments in the study of Reeb dynamics; oto), Sheel Ganatra (Stanford), Basak Gürel (Van- • Foundational issues that come into focus today ap- derbilt), Richard Hind (Notre Dame), Ko Honda peared in the presentations of McDuff, Fukaya, and (Southern California), Michael Hutchings (UC Berke- Frauenfelder; ley), Michael Khanevsky (Chicago), Siu-Cheong Lau • Finally, the talks of Oancea, Tolman, and Liu touched (Harvard), Robert Lipshitz (Columbia), Chiu-Chu Liu on other topics of high interest today, among them (Columbia), Dusa McDuff (Columbia), David Nadler string topology and enumerative invariants. (UC Berkeley), Alexandru Oancea (UPMC), Tim Pe- 2. Three insightful lecture series: The talks mentioned rutz (UT Austin), Sheila Sandon (Nantes), Felix Schlenk above were complemented by lecture series, partic- (Neuchâtel), Paul Seidel (MIT), Nicholas Sheridan ularly accessible to graduate students and young re- (IAS), Jake Solomon (Hebrew), Susan Tolman (UI searchers. Urbana-Champaign), Michael Usher (Georgia), Katrin • Hofer talked about potential applications of today’s Wehrheim (MIT), Jean-Yves Welschinger (Lyon 1), most refined symplectic techniques to celestial me- Christopher Woodward (Rutgers) chanics. The origins of symplectic topology lie in Number of participants: 98 problems that emerged from celestial mechanics, in This workshop consisted of 38 one-hour lectures, in- particular the n-body problem. Hofer’s perspective cluding three series of three one-hour lectures (one was that time has come for the modern tools of sym- of which was the Aisenstadt Chair series delivered by plectic topology to be applied again effectively to Helmut Hofer). The other two minicourses were given the mechanics of the solar system and, in particular, by Abouzaid and Sandon, respectively. There are three space travel; different aspects of this workshop that made it a very • Abouzaid discussed the delicate details of coher- successful and productive meeting: ent orientations in relation to the interplay between 1. High quality talks on the hottest topics in the sub- string topology and symplectic homology of cotan- ject: gent bundles; • Breakthroughs in classical problems were described • Sandon explained the discrete metrics on contacto- in talks of Buse and Hind (who proved a remark- morphism groups that she recently introduced as able form of packing stability), Seidel who de- well as related techniques and conjectures. scribed a new approach to multiple Lagrangian non- 3. A high number of young brilliant researchers: It intersections, Welshinger who explained his ap- became clear, in part as a result of this conference, proach to estimating Betti numbers of algebraic vari- that symplectic topology is at a very special moment in its development. Suddenly, a new generation is

11 Centre de recherches mathématiqes entering the field with great energy and brilliance. major infectious diseases and some less known ones Sheridan, Borman, Ganatra, Abouzaid, Sandon, Perutz, that are plaguing the continent. Buhovsky, Khanevsky, Usher, Frauenfelder, Solomon, Mathematical models are increasingly accepted in the Oancea are all young and extremely promising republic health domain as tools to fight infectious dis- searchers who spoke at this conference. Some of them eases. Modelling is helpful mostly because it allows for have already made an important mark on the field and simple hypothesis testing where most other tests are most of the others will do so in the not too distant fu- impossible. Modelling is also a valuable tool that al- ture. A great contribution to the success of the meet- lows to pinpoint gaps in data collection. The workshop ing was also made by the other participants so that, as focused on some major killers (HIV/AIDS, malaria, a whole, most of the top world researchers in the sub- and tuberculosis) and also considered some diseases ject participated in this event in one form or another. that are, for one reason or another, less in the spotlight: childhood diseases, other viral/bacterial/vector Workshop diseases, poliomyelitis. The objectives of the workshop Major and Neglected Diseases in Africa were the following: May 6–10, 2013, Ottawa • To combine the expertise of public health officials Sponsored by the CRM and the Society of Mathemati- and researchers in biology and mathematical sci- cal Biology ences in the areas of infectious diseases relevant to Organizers: Africa; Julien Arino (Manitoba), Jane Heffernan (York) • To encourage and seek participation of African col- Speakers: leagues, to foster collaborations between Canadian Cameron Browne (Ottawa), David Buckeridge and African researchers; (McGill), Abba Gumel (Manitoba), Jane Heffernan, • To compare experiences in dealing with public Senelani Dorothy Hove-Musekwa (NUST Zimbabwe), health authorities, helping all participants develop a Michael Li (Alberta), Connell McCluskey (Wilfrid Lau- better understanding of this difficult yet crucial as- rier), Elaine Nsoesie (Harvard), Kathleen O’Reilly (Im- pect; perial Coll.), Nitika Pai (McGill), Gauthier Sallet (IN- • To train junior researchers, postdoctoral fellows and RIA Nancy), Kevin Schwartzman (McGill), Robert graduate students. Smith (Ottawa), Donald Sutherland (CSIH), Kate Zin- Each day of this five- dayworkshop was devoted to a szer (McGill), Pascal Zongo (Antilles et Guyane) particular disease or group of diseases, with a few pre- Number of participants: 30 sentations on the disease(s) of interest followed by a The workshop on Major and Neglected Diseases in group discussion on the subject. There were a total of Africa was sponsored by the CRM as part of the Mathe- 18 presentations. Monday had talks about Poliomyeli- matics of Planet Earth (MPE) thematic year. The work- tis (morning) and Schistosomiasis and other neglected shop organizers, Jane Heffernan and Julien Arino, are tropical diseases (afternoon). Each of the next three also members of the Centre for Disease Modelling, a days was devoted to one of the “Big Three” infectious group based at York University. The rationale for the diseases, i.e., the diseases associated with the highest workshop stemmed from the observation that there are mortality rates in Africa: HIV/AIDS was discussed on serious public health implications of the fact that while Tuesday, Malaria on Wednesday, and Tuberculosis on Africa counts 54 countries and 15 percent of the world Thursday. Finally, on Friday morning, the focus shifted population, the combined GDP of African countries to the problem of surveillance. Each day featured four represented in 2003 just over 3 percent of the world’s plenary talks and two discussion sessions. Each disease GDP. From a demographic perspective, Africa is char- topic included a talk from the public health perspec- acterized by an over representation of youth (40 per- tive and a mathematical modelling talk. Each public cent of its population is under 15), and a life expectancy health talk reviewed past and current issues related that is below 65 years (e.g., 31.6 years in Botswana), to the infectious disease epidemiology, with certain compared to 82.6 years in Japan. Several factors con- African regions being highlighted. The mathematical tribute to this low life expectancy (e.g., poverty, inad- modelling talks provided an overview of the current equate health care systems), but the main reason is the modelling literature centered on the infectious disease compounding of these factors with the effect of several in question, and introduced some new models having

12 Thematic Program the potential to address current issues in epidemiol- livered the first two of his four Aisenstadt Chair lec- ogy. In the discussion sessions, participants identified tures. The second week saw the completion of Gabai’s gaps in our knowledge and discussed the role of math- lectures as well as a workshop focusing on recent ad- ematical modelling in the particular thematic areas. A vances and future research directions in the topology group of researchers from the workshop have contin- of 3-dimensional manifolds. Over eighty participants ued discussions and are currently working on a study from North America, Europe and Asia were attracted of community-based care and self-testing in HIV af- to the events. fected communities. Week 1 began with Juan Souto’s mini-course “Eigen- There were 30 registered participants to the work- values of the Laplacian and the topology of hyper- shop, hailing from several countries: 1) Canada (19); bolic 3-manifolds,” which detailed how soft geomet- 2) France (2); 3) French Guyana (1); 4) Ghana (3); 5) ric methods could be used to estimate such eigenval- United Kindgom (1); 6) USA (2); 7) Zimbabwe (2). The ues. The theory was illustrated with examples from presence of participants from African institutions as 3-dimensional geometry leading to a proof that if M well as members of the African diaspora working in is a closed hyperbolic 3-manifold, then the first non- North America and Europe helped the workshop “stay zero eigenvalue of its Laplacian is bounded from above on focus,” since many of the attendees had first-hand by the ratio of a constant depending on the Heegaard experience of the diseases being discussed. The work- genus of M and its volume. The second mini-course, shop was attended by participants with public health presented by Ian Agol, focused on the fundamental and mathematical backgrounds, and participants at di- groups of 3-manifolds, a field which has seen major ad- verse career stages: from master’s students to senior vances over the last decade. The first two lectures dealt researchers and public health officials. with consequences of Perelman’s geometrization theorem and the tameness theorem of Agol and Calegari- Workshop Gabai. The last two lectures outlined the deep work The Topology of 3-Dimensional Manifolds of Dani Wise on special cube complexes as well as May 6–17, 2013, CRM Agol’s contributions in this area leading to his recent proofs of the virtual Haken conjecture, Thurston’s vir- Organizers: tual fibring conjecture, and the subgroup separability Michel Boileau (Paul Sabatier), Steven Boyer (UQAM), of Kleinian groups. Tao Li’s mini-course dealt with Marc Lackenby (Oxford), Alan Reid (UT Austin) the modern theory of Heegaard splittings. After dis- Lecturers: cussing basic examples and properties, strongly irre- Ian Agol (UC Berkeley). Tao Li (Boston Coll.), Juan ducible Heegaard splittings were introduced, leading Souto (UBC) to a proof of the generalized Waldhausen conjecture Speakers: through the use of essential laminations. Other topics Ian Biringer (Boston Coll.), Jeffrey F. Brock (Brown), discussed were applications of the curve complex to Ken Bromberg (Utah), Nathan M. Dunfield (UI Urbana- Heegaard splittings and an outline of a construction Champaign), Stefan Friedl (Köln), Paolo Ghiggini of a 3-manifold whose fundamental group has rank (CNRS & Nantes), Joshua Evan Greene (Boston Coll.), strictly smaller than its Heegaard genus. Each mini- Jesse Johnson (Oklahoma State), Alexander Kolpakov course ended with a list of open problems and future (Vanderbilt), Christopher J. Leininger (UI Urbana- directions. Champaign), Yi Liu (Caltech), Darren Long (UC David Gabai gave two of his four Aisenstadt Chair lec- Santa Barbara), Jessica Purcell (Brigham Young), Saul tures at the end of week 1, both of an expository na- Schleimer (Warwick), Genevieve Walsh (Tufts), Daniel ture. The subject of the first was Poincaré’s contribu- T. Wise (McGill), Zhongtao Wu (Caltech) tions to topology, remarkable for their foundational Number of participants: 82 and seminal nature as well as their impact on subse- The events surrounding the workshop “The topol- quent research. The second lecture surveyed the beau- ogy of 3-dimensional manifolds” were held over two tiful and mysterious field of the volumes of hyperbolic weeks, from May 6 to May 17, 2013. The first week 3-manifolds and discussed Gabai’s ongoing work with was devoted to students and other young mathemati- Meyerhoff and (Nathaniel) Thurston in the area. His cians. Three mini-courses were given by Ian Agol, Tao last two Aisenstadt Chair lectures were incorporated Li, and Juan Souto, respectively, and David Gabai de-

13 Centre de recherches mathématiqes into the workshop held during week 2. They focused work for producing models for hyperbolic 3-manifolds on the topology of the ending lamination space associ- with bounded combinatorial descriptions. He applied ated with a hyperbolic surface. These spaces, important it to describe, for instance, a specific construction of in both hyperbolic geometry and geometric group the- homology 3-spheres Benjamini–Schramm converging ory, are the focus of much current research with many to hyperbolic 3-space. The latter was a key compo- basic questions remaining open. Gabai outlined his re- nent in the talk of Nathan Dunfield, who discussed his cent progress towards characterizing their topology. work with Brock on relations between growth in ho- L2 Fifteen one-hour-long talks of exceptional quality rep- mology, homology, and injectivity radius in tow- resenting the state of the art in a number of areas ers of hyperbolic 3-manifolds. Jessica Purcell outlined of low-dimensional topology were presented in the her studies on the following question: If a geometri- workshop. Dani Wise opened the proceedings with cally finite hyperbolic compression body has a single a talk that outlined his proof with (Piotr) Przytycki unknotting tunnel, is the tunnel isotopic to a geodesic? that the fundamental groups of mixed 3-manifolds are She conjectures the answer is yes. Genevieve Walsh’s virtually special. Groups were also the focus of talks talk focused on her work with Hoffman on Thurston’s by Stefan Friedl, Chris Leininger, and Ken Bromberg. Dehn-surgery graph of 3-manifolds. Along the way Friedl surveyed his recent work with Silver and she explained their construction of the first examples Williams on HNN splittings of knot groups. Leininger of hyperbolic 3-manifolds with weight 1 fundamental described his results with Dowdall and Kapovich on groups that are not obtained via surgery on a knot in topological, geometric, and dynamical relations be- the 3-sphere. tween monodromies of splittings of certain free-by- In adjacent dimensions, Ian Biringer described the ge- cyclic groups. Bromberg reported on joint work with ometric limits of sequences of hyperbolic metrics on Bestvina and Fujiwara determining necessary and suf- surfaces determined by iterations of certain homeo- ficient conditions for the stable commutator length of morphisms of the surface, giving a compressible ver- an element in the mapping class group to be positive. sion of examples due to Kerckhoff–Thurston, Mc- Zhongtao Wu talked about the rational genus of knot Mullen, and Brock. One highlight of the workshop was in a 3-manifold, a topological quantity related to stable Alexander Kolpakov’s description of his recent study commutator length. In particular he discussed inequal- with Martelli of the cusps of finite-volume hyper- ities he determined with Ni using Heegaard-Floer ho- bolic 4-manifolds. In particular, they resolved a long- mology, which imply, for instance, that simple knots standing open problem by constructing the first exam- in lens spaces are genus-minimizing in their homology ples of one-cusped such manifolds. class. Analytic invariants of 3-manifolds have had a pro- Saul Schleimer gave a new proof (joint with Wick- found impact on 3-manifold topology through Ricci ens), based on the train-track machine, of Klarreich’s flow, Heegaard Floer homology, and contact topology theorem: the Gromov boundary of the curve complex over the last decade. Paolo Ghiggini described his foun- is homeomorphic to the space of ending laminations. dational work with Colin and Honda on the isomor- He explained how their proof generalizes to cover the phism between Heegaard Floer homology and embed- Gromov boundary of the arc complex as well. Curve ded contact homology. Josh Greene gave a talk of great complexes were also central in Jesse Johnson’s talk. clarity on his theorem that two reduced, alternating di- He described how the notion of distance for a Hee- agrams for a pair of links are mutants if and only if gaard splitting, and a slight generalization known as the Heegaard Floer homology of the link’s branched subsurface projection distance, can be used to con- double-covers are isomorphic. struct a manifold with multiple distinct low-distance Heegaard splittings of the same (small) genus, anda Workshop manifold with both a high-distance, low-genus Hee- Impact of Climate Change on Biological gaard splitting and a distinct, irreducible high-genus, Invasions and Population Distributions low-distance Heegaard splitting. May 12–17, 2013, BIRS The topology of geometric manifolds arose in several Sponsored by NSERC, the NSF, CONACYT, and the contexts. Jeff Brock described joint work with Min- Ministry of Enterprise and Advanced Education of Al- sky, Namazi, and Souto concerning a general frame- berta

14 Thematic Program

Organizers: Speakers: Henri Berestycki (ÉHÉSS), Alan Hastings (UC Davis), Olivier Biquard (ÉNS), Xiuxiong Chen, Renjie Feng Mark Lewis (Alberta), Péter Molnár (Princeton) (McGill), Akito Futaki (Tokyo), Weiyong He (Ore- Speakers: gon), Hongnian Huang (École Polytechnique), Chi Li Henri Berestycki, Michael Bonsall (Oxford), Christina (Princeton), Toshiki Mabuchi (Osaka), Sean T. Paul Cobbold (Glasgow), Chris Cosner (Miami), Kim Cud- (Wisconsin–Madison), Yann Rollin (Nantes), Yuji Sano dington (Waterloo), Laurent Desvillettes (ÉNS Ca- (Kumamoto), Cristiano Spotti (IHÉS), Ioana Suvaina chan), Odo Diekmann (Utrecht), Claire Dooley (Ox- (Vanderbilt), Christina W. Tønnesen-Friedman (Union ford), William Fagan (Maryland), Jimmy Garnier Coll.), Hajime Tsuji (Sophia), Craig van Coevering (INRA Avignon), François Hamel (Aix-Marseille; IUF), (USTC), Jeff Viaclovsky (Wisconsin–Madison), Ben Alan Hastings, Amy Hurford (Memorial), Alex Kise- Weinkove (Northwestern) lev (Wisconsin–Madison), Yuan Lou (Ohio State), Mark Number of participants: 43 Lewis, Brett Melbourne (CU-Boulder), Ehud Meron This one-week workshop, held at the Centre de (Ben Gurion), Péter Molnár (Princeton), Paul Moor- recherches mathématiques, was focused on the study croft (Harvard), Lionel Roques (INRA Avignon), Luca of the Calabi problem in Kähler Geometry. The work- Rossi (Padova), Rebecca Tyson (UBC Okanagan), Mary shop was attended by over 40 participants, ranging Lou Zeeman (Bowdoin Coll.), Ying Zhou (Washing- from algebraic geometers to differential geometers to ton), Huaiping Zhu (York) analysts. Most participants were speakers and most at- Number of participants: 39 tended every talk. Many new results were reported for the first time during the workshop and many partici- Summer School pants left Montreal ready to work on new projects. Mathematics of Infectious Disease We highlight the two lectures series, one given by X. May 19–27, 2013, York Chen and S. Sun (a total of three lectures) at the be- Sponsored by the Fields Institute for Research in Math- ginning of the workshop and the three Aisenstadt lec- ematical Sciences and Mitacs tures given by G. Tian at the end of the workshop, Organizers: in which the recent breakthrough in the Yau-Tian- Jane Heffernan (York), Neal Madras (York), Seyed Donaldson conjecture in the Fano case was presented. Moghadas (York), Jianhong Wu (York), Huaiping Zhu Other facets of the theory include the study of mod- (York) uli of extremal Kähler metrics and desingularisations Public Lecture Speakers: (talks by O. Biquard, J. Stoppa, I. Suvaina), Sasakian Carlos Castillo-Chavez (Arizona State), Mirjam Kret- Geometry (talks by W. He, C. Tønnesen-Friedman, zschmar (Utrecht), Eduardo Massad (São Paulo) C. van Coevering), evolution equations in Kähler ge- Course Instructors: ometry (talks by A. Futaki, H. Huang, B. Weinkove), Linda J. S. Allen (Texas Tech), Julien Arino (Manitoba), study of algebro-geometric notions of stability (C. Li, Fred Brauer (UBC), Odo Diekmann (Utrecht), David T. Mabuchi, Y. Rollin, S. Paul, Y. Sano), and probabilis- Fisman (Toronto), Jane Heffernan, Ying-Hen Hsieh tic methods (R. Feng). (China Medical), Neal Madras, Seyed M. Moghadas, Thus, in an intensive week, the program succeeded in Beate Sander (PHO), Pauline van den Driessche (Vic- tying together most of the new results in the subject toria), James Watmough (New Brunswick), Ping Yan and a variety of new projects were born. The partici- (PHAC), Huaiping Zhu pants affirmed frequently and spontaneously that the program was a great success. Workshop Extremal Kähler Metrics May 27–June 1st, 2013, CRM

Organizers: Vestislav Apostolov (UQAM), Claudio Arezzo (ICTP), Xiuxiong Chen (Stony Brook), Claude LeBrun (Stony Brook)

15 Centre de recherches mathématiqes

Summer School Moduli spaces appear in a variety of contexts in both The Mathematics Behind Biological mathematics and physics. In physics, they are often, in Invasions some sense, the natural spaces for functional integra- May 19–27, 2013, York tion, after one has quotiented out infinite dimensional Sponsored by PIMS, the International Graduate Train- spaces of symmetries; in mathematics, they exhibit a ing Centre (IGTC) in Mathematical Biology, the Centre bewildering array of structure, whose discovery is of- for Mathematical Biology, the University of Alberta, ten due to intuition from physics. The two-week-long and Mathematics of Planet Earth 2013 extended workshop, Moduli Spaces and their Invari- ants in Mathematical Physics, held June 2 to 14th, 2013, Organizers: was a true meeting of cultures, with all the fruitful in- Thomas Hillen (Alberta), Mark Lewis (Alberta) teraction (and occasional frustration) that this implies. Speakers: It provided an opportunity to see the wide variety of Alan Hastings (UC Davis), Mark Lewis, Jonathan Sher- themes that interplay in the area. Within the limits of ratt (Heriot-Watt), Sergei Petrovskii (Leicester) the availabilities of the different speakers, the conference organised itself around some of these themes, al- Workshop ternating in a rough fashion between more mathemat- Moduli Spaces and Their Invariants in ical topics and more physical ones. These include: Mathematical Physics • Metrics with special holonomy. On these, we saw June 3–14, 2013, CRM deep and interesting results on hyperkähler mani- Organizers: folds presented by Andrew Dancer, Sergey Cherkis, Jacques Hurtubise (McGill), Lisa Jeffrey (Toronto), Jo- on G2 structures by Spiro Karagiannis, and on hyper- hannes Walcher (McGill) complex structures by Misha Verbitsky. Tamas Speakers: Hausel gave some very interesting computational Murad Alim (Harvard), Paul S. Aspinwall (Duke), Tom evidence on the Betti numbers of hyperkähler man- Baird (Memorial), Philip Boalch (ÉNS; CNRS), Vincent ifolds. Bouchard (Alberta), Andrei Căldăraru (Wisconsin– • Calabi–Yau manifolds, their moduli, and their in- Madison), Benoit Charbonneau (St. Jerome), Sergey variants. The geography of the Calabi–Yau mod- Cherkis (Arizona), Andrew Dancer (Oxford), Keshav uli was explored in various aspects by both Paul Das Gupta (McGill), Tudor Dan Dimofte (IAS), Ron Aspinwall and Charles Doran. Around the gen- Donagi (Pennsylvania), Charles Doran (Alberta), Brent eral theme of toric Calabi–Yau and the Bouchard– Doran (ETH Zürich), Bertrand Eynard (CEA/Saclay), Klemm–Marino–Pasquetti conjecture on their rela- Jonathan Fisher (Toronto), Davide Gaiotto (Perime- tion to the Eynard–Orantin invariants, Bertrand Ey- ter Inst.), Peng Gao (Stony Brook), Marco Gualtieri nard gave his explanation and proof for smooth vari- (Toronto), Babak Haghighat (Harvard), John Har- eties, and both Melissa Liu and Vincent Bouchard ex- nad (Concordia), Tamas Hausel (EPFL), Spiro Ka- plained the extension to orbifolds. John Harnad gave rigiannis (Waterloo), Matt Kerr (WUSTL), Boris a survey of various appearances of the tau function Khesin (Toronto), Can Kozcaz (SISSA), Joshua Lapan in the computation of numerical invariants. In a re- (McGill), Chiu-Chu Liu (Columbia), Alexander Mal- lated theme, Tony Pantev talked about the complex oney (McGill), Eckhard Meinrenken (Toronto), Ruxan- moduli of Landau–Ginsburg models. dra Moraru (Waterloo), Hiraku Nakajima (Kyoto), • Symplectic geometry and integrable systems. In some Tony Pantev (Pennsylvania), Brent Pym (Toronto), sense, this is a more classical part of the story, Steven Rayan (Toronto), Mauricio Romo (Kavli Inst.), but with some beautiful surprises: Jonathan Fisher Jihye Seo (McGill), Vivek Shende (UC Berkeley), Jörg gave a talk on analogues of polygon spaces, and Teschner (Hamburg), Valerio Toledano Laredo (North- Boris Khesin explained his generalizations of penta- eastern), Misha Verbitski (Glasgow), Michael Lennox gram maps. Vivek Schende told us about Legendrian Wong (EPFL), Kota Yoshioka (Kobe), Matthew B. knots, and Eckhard Meinrenken explained how we Young (Stony Brook) should understand the Verlinde formulae for non- Number of participants: 71 simply connected groups. • Non-Kähler geometry. In this emergent area, Ruxan- dra Moraru explained some gauge-theoretical work

16 Thematic Program

on balanced HKT manifolds, and Andrei Căldăraru Ooguri-Vafa rings on moduli of Calabi-Yau three- spoke on moduli of sheaves on non-Kähler manifolds that are analogous to quasi-modular forms. folds. Matt Kerr discussed the invariants of algebraic cy- • Wild character varieties and Stokes phenomena. While cles that play a fundamental role at the semi-classical this is in some ways the most classical area of all the level. conference, a clear understanding of the Stokes phe- • M-theory: Supersymmetric localization and the AGT nomenon is only just emerging. Marco Gualtieri and correspondence are but two topics showcasing the Brent Pym explained their new groupoid approach impressive progress in the physical calculation of in- to wild character varieties, Michael Wong gave a variants of moduli spaces in various corners of M- talk on the arithmetic aspects of these varieties, and theory. Babak Haghighat presented his recent work Philip Boalch’s wide-ranging survey explained some on a variant correspondence, with different amounts rather subtle isomorphisms that take place. of supersymmetry and firmly rooted in M-theory. • Gauge theory. The conference opened with a beau- Can Kozcaz calculated the elliptic genus of M2- tiful talk by Hiraku Nakajima, explaining some of branes suspended between M5-branes. the support for the Alday-Gaiotto-Tachikawa (AGT) • Applications: We invited several talks on applica- conjecture on the cohomology ring of instanton tions of moduli spaces for concrete physical ques- moduli spaces; Kota Yoshioka explained some results tions in string theory. From the side of the heterotic on Bridgeland stability and stable sheaves on abelian string, Peng Gao discussed questions of stability in surfaces; Benoit Charbonneau talked about various various classes of bundle constructions on Calabi- aspects of the Nahm transform for spatially periodic Yau threefolds. Keshav Dasgupta took first steps in instantons, Tom Baird on the real aspects of mod- the exploration of gauge/gravity duality in that het- uli of vector bundles over a curve, and Steven Rayan erotic theory. Alex Maloney exposed the relation be- talked on the moduli of twisted Higgs bundles. tween 3D quantum gravity and a number of chal- • Moduli of curves. This other central topic was well lenging problems in moduli of Riemann surfaces. represented by the talks of Ron Donagi, who ex- The conference opened on a mathematical theme, with plained his rather surprising result with Witten on the talk by Hiraku Nakajima; on the other hand, both the structure of supermoduli space, of Brent Doran, weeks closed on a strongly physical note, with Alex who talked about moduli of stable rational curves, Maloney in the first week, and Keshav DasGupta in the and Jihye Seo explaining some of the physical as- second. The conference moved for one day out to Mont pects of the degeneration of hyper-elliptic curves. Saint Hilaire, with talks in the morning and an explo- • Algebraic aspects of moduli. There are quite rich al- ration of the Nature Reserve in the afternoon, with of gebraic structures underlying all of these moduli course more discussion taking place under the stimu- spaces, and some of these appeared in the talks by lation of exercise; the weather gods smiled on us with Valerio Toledano Laredo (“From Yangians to quan- one of the few sunny days in an otherwise rather rainy tum loop algebras via abelian difference equations”) two weeks. One nice aspect of the conference was a and Matthew B. Young (Hall modules of quivers). strong participation by post-doctoral fellows, whose • Computation of Gromov-Witten Invariants. One ex- presence was greatly helped by funding from the NSF, citing recent development in invariants of moduli to whom we are grateful. spaces is supersymmetric localization, amongst others as a tool for computation of Gromov-Witten in- Workshop variants, without mirror symmetry; Joshua Lapan Low-Dimensional Topology after Floer reviewed the closed string story and Mauricio Romo July 8–12, 2013, CRM explained the generalization to open strings. • Quantization and topological strings. Quantization of Organizers: moduli spaces and the associated integrable systems Hans Boden (McMaster), Olivier Collin (UQAM) is a notoriously difficult topic of recurring interest. Speakers: Jörg Teschner explained the quantization of mod- Kenneth Baker (Miami), John Baldwin (Boston Coll.), uli of curves as suggested by the AGT relation to Vincent Colin (Nantes), Christopher Cornwell (Duke), gauge theory. Moving to higher dimensions, Murad John Etnyre (Georgia Tech), Kim A. Froyshov (Aarhus), Alim revisited the structure of Bershadsky-Cecotti- Paolo Ghiggini (CNRS; Nantes), Elisenda Grigsby

17 Centre de recherches mathématiqes

(Boston Coll.), Matthew Hedden (Michigan State), tact, and symplectic topology and the many types of Ko Honda (Southern California), Michael Hutchings Floer homologies have proved very successful for solv- (UC Berkeley), Paul Kirk (IU Bloomington), Ciprian ing outstanding questions in low-dimensional topol- Manolescu (UC Los Angeles), Lenhard L. Ng (Duke), Ja- ogy, and there are signs that more breakthroughs will cob Rasmussen (Cambridge), Nikolai Saveliev (Miami), occur in the near future. This event brought together Clifford Taubes (Harvard), Stefano Vidussi (UC River- leading experts working in these related areas, but also side) a special emphasis was put on the invitation of up- Number of participants: 76 and-coming researchers and graduate students, some The conference focused on the current impact of Floer of whom also attended the SMS summer school on homology methods in low-dimensional topology. In the mathematics and physics of knot homologies (sum- recent years, the interactions between geometric, con- marized in the CRM annual report for the year 2013– 2014).

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–July 2012 Geometric Analysis and 2003–2004 Geometric and Spectral Analysis Spectral Theory 2002–2003 Mathematics in Computer Science June–December 2011 Quantum Information 2001–2002 Groups and Geometry January–June 2011 Statistics 2000–2001 Mathematical Methods in Biology and July–December 2010 Geometric, Combinatorial Medicine and Computational Group Theory 1999–2000 Mathematical Physics January–April 2010 Number Theory as 1998–1999 Number Theory and Arithmetic Experimental and Applied Science Geometry August–December 2009 Mathematical Problems in 1997–1998 Statistics Imaging Science 1996–1997 Combinatorics and Group Theory 2008–2009 Joint CRM–PIMS Program: Challenges 1995–1996 Applied and Numerical Analysis and Perspectives in Probability 1994–1995 Geometry and Topology 2008–2009 Probabilistic Methods in Mathematical 1993–1994 Dynamical Systems and Applications Physics 1992 Probability and Stochastic Control January–June 2008 Dynamical Systems and (special semester) Evolution Equations 1991–1992 Automorphic Forms in Number Theory June–December 2007 Applied Dynamical Systems 1991 Operator Algebras (special semester) January–June 2007 Recent Advances in 1990 Nonlinear PDEs and Applications Combinatorics (concentration period) June–December 2006 Combinatorial Optimization 1988 Shimura Varieties (special semester) 2005–2006 Analysis in Number Theory 1987 Quantum Field Theory (special semester) 2004–2005 The Mathematics of Stochastic and 1987–1988 Fractals: Theory and Application Multiscale Modelling 1987 Structural Rigidity (special semester)

18 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

The 23rd International Meeting on of the distance to Europe where most of the commu- Probabilistic, Combinatorial and nity lies. Asymptotic Methods for the Analysis of This year’s meeting was especially successful with Algorithms (AofA 2012) talks covering a broad range of topics in algorithms June 18–22, 2012, CRM or data structures, combinatorics, discrete probability, Sponsored by the CRM, INRIA, and NSERC or methodology. All the talks were very lively and provided interesting and new points of view on im- Organizers: portant questions or novel applications. A number of Nicolas Broutin (INRIA Rocquencourt), Luc Devroye open problems were raised, in particular by the invited (McGill) speakers, some of which are traditionally chosen in Plenary Lecturers: neighbouring fields in order to provide the participants Amin Coja-Oghlan (Warwick), Michael Drmota (TU with an alternative point of view on the important cur- Wien), Svante Janson (Uppsala), Claire Mathieu rent directions of research in algorithms and random (Brown, CNRS, and ÉNS), Avi Wigderson (IAS) structures. Number of participants: 72 The conference consisted of 5 invited talks by dis- On the topics of algorithms, two of the invited speak- tinguished researchers in the field of algorithms and ers delivered wonderful lectures on approximation al- combinatorial structures: Amin Coja-Oghlan, Michael gorithms (C. Mathieu) and learning (A. Widgerson) Drmota, Svante Janson, Claire Mathieu, and Avi which raised many questions and open problems. Wigderson; and 32 presentations that had been se- J. Gaither presented new results on the number of pro- lected by the program committee after submission of tected nodes in random tries and suffix trees, which a 12-page abstract. have implications on the performance of algorithms manipulating strings. Probabilistic counting and its ap- The meeting is part of a series of conferences and plications were addressed in the talks by M. Fuchs and workshops that has been going on for more than two C. Martinez. O. Roussel presented extensions to shuf- decades. It aims at providing a venue for the people fle products of the widely used Boltzmann samplers. working in the field of theoretical computer science or D. Shymura discussed geometric algorithms for shape discrete mathematics in order to present the recent ad- matching of surprising simplicity that rely on random vances, exchange ideas, and foster new contacts and sampling. C. Fricker demonstrated that the methods collaborations about the asymptotic behaviour of ran- can be applied to other concrete problems such as bike dom combinatorial structures and their applications to sharing systems (BIXI, Vélib’). The other talks on algo- the analysis of algorithms and data structures. The par- rithms included B. Vallée’s demonstration that Euclid’s ticipants have mixed backgrounds going from combi- algorithm is totally Gaussian, J. Fill’s recent work on natorics and complex and asymptotic analysis to prob- the performance of Quicksort measured in number of ability theory and stochastic processes. symbol comparisons, Z. Golebiewski’s new analysis of It is remarkable that the meeting at the CRM showed leader election based on the trie data structure, E. Gas- increasing signs that the community is blending: in siat’s work on lossless compression via adaptive cod- particular, the different groups on which the meeting for countable alphabets, and I. Eisner’s application ing traditionally relies (analysts, combinatorists, prob- of domination analysis to scheduling problems. abilists) are now certainly more porous than they used Discrete probability was addressed in S. Janson’s in- to be. We were glad to see that the proportion of stu- vited lecture on branching processes. Random trees dents and young researchers had not declined, in spite

20 General Program and their properties were also the main topic of the Markus Nebel (Kaiserslautern), and M. D. Ward (Pur- talks by S. Wagner on additive functionals with small due) will gather the best contributions and confirm the toll functions, and V. Kraus on transversals in random success of the conference held at the CRM. trees, which is very surprisingly inspired from applications to antiterrorism. S. Miracle discussed the mixing Workshop time of Markov chains on planar triangulations. Urn N = 2 Jeometry and ApplicationZ models and their asymptotic behaviour were the topic June 20–22, 2012, McGill of the talks of B. Mocrette (random balanced urns) Sponsored by the Mathematical Physics Laboratory and M. Kuba (diminishing urns via death processes). G. Fayolle presented his results with K. Raschel on the Organizers: number of random walks constrained to live in the Keshav Dasgupta (McGill), Jihye Seo (McGill), Jo- quarter plane, which has generated much interesting hannes Wacher (McGill) research since the proof that the generating function Speakers: for Gessel’s walk is algebraic. Y. Ponty discussed the Philip Argyres (Cincinnati), Chris Beem (Simons Ctr.), word collector, a model inspired by the sampling of Clay Cordova (Harvard), Jacques Distler (UT Austin), protein configurations. L. Lhote discussed hidden pat- Amihay Hanany (Imperial Coll.), Ken Intriligator terns in strings under general models of sources. (UC San Diego), Peter Koroteev (Minnesota), Daniel Krefl (UC Berkeley), David Kutasov (Chicago), Satoshi More combinatorial themes were also addressed in Nawata (Perimeter Inst.), Chan Youn Park (Caltech), M. Drmota’s invited lecture on universal results on Ramadevi Pichai (IIT Bombay), Shlomo Razamat (IAS), subcritical random graphs, and A. Coja-Oghlan’s in- Nathan Seiberg (IAS), Sav Sethi (Chicago) troduction to the currently hot topic of phase tran- Number of participants: 19 sitions in random structures and their connection to Supersymmetric theories with 8 supercharges (this be- hardness of optimization problems. Some interesting N = 2 times the minimal amount required for ing new aspects of essential combinatorial structures 4-dimensional Lorentz invariance) are models of rel- were presented by D. Ralaivaosaona (integer parti- ativistic quantum physics that both have nontrivial tions), V. Feray (random partitions), Z. Gao (random perturbative and nonperturbative dynamics, and are compositions), and P. Jacquet (joint string complex- amenable to exact analysis. Ever since the celebrated ity). The talks on combinatorics also included discus- solution of N = 2 supersymmetric gauge theory by sions of less mainstream problems such as random sub- Seiberg and Witten, the investigation of the rich un- groups of a free group (F. Bassino), random polyomi- derlying geometric structure together with its embed- nos in relation to Stokes phenomenon in complex anal- ding into string theory has proven remarkably fruitful. ysis (L. Hickok), and min-weight digital expansions These developments first of all triggered the discovery (C. Heuberger). of dualities in string theory itself. Secondly, they re- Moreover, new methodological advances were pre- sulted in an impressive amount of results of relevance sented by W. Spzankowski on the asymptotic of solu- to pure mathematics. Thirdly, they have been the start- tions of binomial recurrences, J. Cichon on Bernoulli ing point for many of the more convincing recent at- sums, and J. Kieffer on divide-and-conquer recur- tempts to reconstruct particle physics from a funda- rences. Furthermore, B. Gittenberger discussed his mental theory, by breaking N = 2 to N = 1 su- very recent and far reaching results on Gaussian limit persymmetry with branes and fluxes. The last three distributions for the solutions of infinite systems of years have witnessed an impressive revival of interest equations. These advances will certainly be central toa in N = 2 theories. Among recent results that moti- number of applications in combinatorics in the future. vated this workshop, we mention the presentation of a Finally, the authors of abstracts published in the con- new class of superconformal theories by Gaiotto, their ference have been offered the opportunity to submit correspondence with certain 2-dimensional (bosonic) long versions of their work to a special issue of the conformal theories of Liouville type, as well as the Ω journal “Combinatorics, Probability and Computing,” “Nekrasov–Shatashvili” relation between -deformed N = 2 which will be dedicated to the memory of Philippe Fla- theories and quantum integrable systems, and jolet in connection with AofA 2012. This special issue the embedding of all of the above within string theory. edited by N. Broutin (INRIA), J. Fill (Johns Hopkins),

21 Centre de recherches mathématiqes

The scope of the workshop (as hinted by the title) was Hungary, India, the Netherlands, and Sweden, to some somewhat larger and included also supersymmetric of the most exciting subjects of active research in the field theories in other dimensions, and with different area of probabilistic combinatorics. The subjects ad- amounts of supersymmetry. This framework brought dressed at the summer school can be roughly arranged together a number of established researchers, includ- into two overlapping themes: ing several of the pioneers, and representatives of the (1) properties of discrete Markov chains; and new generation who entered the field in recent years. (2) new techniques for understanding structural prop- The goal was to provide a forum for discussion of re- erties of deterministic and random graphs. cent results in the light of original methods and ideas. The majority of the eleven invited speakers stayed for The workshop was hosted by the McGill physics de- at least one full week of the SMS, and four of the partment, and the format was modelled after several speakers (Hatami, McDiarmid, Scott, Winkler) stayed other successful events organized by McGill’s Centre for both weeks. This gave the students plenty of oppor- for High Energy Physics about three to four times tunity to interact with the speakers outside of the lec- a year: two and a half days with around 15 exter- ture hall, which contributed substantially to the scien- nal speakers in a relaxed atmosphere with ample time tific quality of the meeting. (For example, one speaker, for discussions. Such a format represents a particular Prasad Tetali, ended up giving a supplementary “mini- benefit for graduate students around Montréal, who course” to a subset of the students who were inter- have the opportunity to meet and interact with dis- ested in hearing more detail about some of the research tinguished scholars in their chosen field of study. As Tetali touched on in his lectures.) confirmed by many of the participants, the organizers THEME 1: DISCRETE MARKOV CHAINS succeeded in striking the right balance this time again. The flagship lectures on this theme were by Peter Win- Progress in this branch of mathematical physics is ex- kler, who gave a sequence of five ninety-minute talks pected to continue at the same amazing pace, and ev- on random walks on graphs. This (by now) classi- eryone left Montréal looking forward to a future meet- cal subject has lots of beautiful theorems and scores ing. of applications in mathematics and computer science. Summer School Nonetheless, new and remarkable results keep com- Séminaire de Mathématiques Supérieures ing in. Winkler started by reviewing the classical re- 2012 sults in the area, including the connection between random walks and electrical networks and its exten- Probabilistic Combinatorics sions. He then moved to some exciting new research, June 25–July 6, 2012, CRM including recent results and open problems on cover- Sponsored by the Fields Institute for Research in Math- ing the vertices and edges of a graph, the use of po- ematical Sciences, PIMS, the CMS, the Université de tential functions to prove universal bounds for cover Montréal, the MSRI, and the CRM times, and cat-and-mouse (or cop-and-robber) games Organizers: on graphs. James Lee’s talks dovetailed beautifully Louigi Addario-Berry (McGill), Luc Devroye (McGill), with Winkler’s, while consisting of more classically Bruce A. Reed (McGill) probabilistic content. Lee presented his recent tour de Speakers: force with Ding and Peres, relating the cover time of Nikhil Bansal (TU Eindhoven), Hamed Hatami reversible Markov chains to the extremes of an asso- (McGill), Penny Haxell (Waterloo), James R. Lee ciated Gaussian process. This research has now ap- (Washington), Colin McDiarmid (Oxford), Yuval Peres peared in the Annals of Mathematics. Lee provided a (Microsoft Res.), Alex Scott (Oxford), Perla Sousi (Cam- brief background on Gaussian processes and beauti- bridge), Prasad Tetali (Georgia Tech), Eric Vigoda fully presented Talagrand’s majoring measures theo- (Georgia Tech), Peter Winkler (Dartmouth Coll.) rem. He then explained how he, Ding, and Peres used Number of participants: 81 the majorizing measures theory to exhibit a close con- The 2012 Séminaire de Mathématiques Supérieures in- nection between the cover time of a graph and the ex- troduced nearly eighty young researchers from east- pected square of its Gaussian free field. ern and western Canada, the USA, Australia, Belgium, The main tool allowing results for the Gaussian free Brazil, the Czech Republic, England, France, Germany, field to be transferred to the setting of Markov chainsis

22 General Program

the Dynkin isomorphism theory for Markov processes. If Xt has been visited before, then Xt+1−Xt ∼ µ2 While this connection is extremely useful and has al- , else Xt+1−Xt ∼ µ11. ready resulted in solutions to some open questions on (It turns out that 1, 3, and 4 are transient, and it is an cover times, it is also rather mysterious even in ex- open problem to determine transience or recurrence tremely simple examples. Lee discussed some natural for number 2.) Peres then presented a wide range of starting points for possible research into the deeper questions and results on transience, recurrence, and structure behind the Dynkin theory. Prasad Tetali’s speed of random walks on various models of infi- talks, on geometric and functional analysis on graphs, nite graphs, with a particular focus on highlighting were conceptually linked to those of James Lee via basic gaps in our conceptual understanding and cur- the connection between isoperimetric inequalities and rent techniques. Finally, Eric Vigoda’s talks formed a extremes of Gaussian processes. Tetali began with a bridge between the first and second themes, present- review of some classical isoperimetric and functional ing results related to Markov Chain Monte Carlo algo- inequalities in discrete spaces, with applications to rithms for generating random colourings of graphs of concentration of measure and convergence to equilib- bounded degree. Vigoda explained the basic coupling rium of finite Markov chains. He then presented recent technique, and its refinement – known as path cou- results on generalizations of Cheeger-type inequali- pling – due to Bubley and Dyer. He then explained ties and refinements of Brunn-Minkowski inequalities, the well-known result of Mark Jerrum on rapid mixing which suggest new directions for interesting research of the Glauber dynamics for colouring when the num- in geometric and functional analysis on graphs. Perla ber of colours exceeds twice the maximum degree ∆. Sousi presented her recent result, joint with Yuval Vigoda followed this up with various improvements, Peres (and independently proved by Roberto Oliveira) beginning with his own famous result showing rapid on the equivalence of a broad family of notions of mix- mixing for the Glauber dynamics with 11∆/6 colours, ing time. Most notable among these is the fact that for via the analysis of a more complicated chain that flips reversible Markov chains, the mixing time is equiva- 2-colour components. He also showed how a multi- lent to the hitting time of large sets. This easily-stated step coupling can be used to get improved results (as- fact provides a robust equivalent of the mixing time suming lower bounds on the girth and on the maxi- that can be used both to simplify many existing proofs mum degree, ∆). Finally, he explained a beautiful use and to derive new results. Sousi highlighted one such of spectral graph theory to obtain improved results for result, related to a geometric characterization of the planar graphs or graphs embeddable on a fixed surface. mixing time for random walks on trees. THEME 2: COLOURINGS, CLIQUES, AND CONNEC- Yuval Peres’s lectures were on the subject of random TIVITY walks on infinite graphs, which despite being more Many questions in combinatorics concern the relation- classical is still rife with open problems and areas ship between the local and global structure of a graph where our understanding is incomplete. At the outset, or set system. For instance, what can we say about Peres motivated his lectures with the following ques- the subgraphs of a graph with large chromatic num- tion: which of the following random walks on Z are 2 ber? What about graphs without large cliques or in- transient and which are recurrent? dependent sets? How uniformly is it possible to dis- Z t ∈ [4k, 2 4k) (1) In 2, at times · we go up or down tribute edges in a graph? In 7.5 hours of lectures, Alex t ∈ [2 4k, 4k+1) with equal probability. At times · , Scott presented a wide range of results and conjectures we go left or right with equal probability. of this flavour, touching on the Erdős-Hajnal Conjec- Z (2) In 2 , if the current node has been visited before, ture, the Gyárfás-Sumner Conjecture, discrepancy for then move left or right with equal probability; oth- graphs and hypergraphs, and recently developed VC- erwise go up or down with equal probability. dimension techniques. Nikhil Bansal gave another ex- Z |x| ≥ |y| (3) In 2 , if then we go up or down each with tended mini-course of 7.5 hours, which brought the 0.3 probability , and left or right each with proba- participants to the edge of existing knowledge in dis- 0.2 |y| > |x| bility . This is reversed if . crepancy theory. Discrepancy theory deals with the Z µ µ (4) In 3, fix two mean-zero measures 1, 2 that are following type of question. Given a set-system, find µ µ truly 3D (that is, neither 1 nor 2 assigns proba- a red-blue colouring of the elements such that each bility 1 to any hyperplane) with bounded support. set is coloured as evenly as possible. Perhaps surpris-

23 Centre de recherches mathématiqes ingly, this notion has a wide variety of applications also touched on other graph invariants such as edge- both in computer science and mathematics, and sev- chromatic number (chromatic index), list chromatic eral techniques (many of them non-constructive) have number, total chromatic number, achromatic number, been developed to understand the discrepancy of vari- improper chromatic number, and span. Perhaps most ous set-systems. Recently, there have been several new notably, he presented a recent technique that yields developments in discrepancy based on connections to improved estimates for χ(G(n, p)) in the dense case, semidefinite programming. This connection is useful and a surprising “phase change” that occurs when is various ways. It gives efficient polynomial-time al- colouring random geometric graphs. gorithms for several problems for which only non- The subject of influences is key to the understanding constructive results were previously known. It also of phase transitions and sharp thresholds for various leads to several new structural results, such as the properties of discrete systems, including colouring of tightness of the so-called determinant lower bound, graphs, satisfiability of random formulas, and connec- and bounds on the discrepancy of unions of set- tivity of random networks. Hatami presented the basic systems. Bansal presented these results in detail and notion of the influence of a variable on a Boolean func- touched on several related concepts such as corre- tion, then sketched the proof of the Friedgut’s theorem lated Brownian motions, the non-constructive entropy stating that if f : {0, 1}n → {0, 1} has small total in- method, Gaussian rounding, and SDP duality. fluence then it essentially depends on few coordinates. Penny Haxell’s lectures had the intriguing title “a This theorem does not hold when the uniform distribu- topology-free topological method.” Over the last dozen tion on {0, 1}n is replaced with the p-biased distribu- years or so, certain topological methods have been de- tion for a small value of p. He discussed the relevance veloped and used to prove a family of results related of this case to the study of the threshold phenomenon, to the following general problem. Let G be a graph and then sketched the proof of his own recent result, whose vertex set is partitioned into nonempty sets which characterizes the structure of Boolean functions V1,...,Vr. What conditions will guarantee that G con- with small total influences on general product proba- tains an independent set {v1, . . . , vr} such that vi ∈ Vi bility spaces. The latter result has garnered substantial for each i? This family of results includes theorems attention and has recently appeared in the Annals of on matchings in hypergraphs, list colouring, strong Mathematics. colouring, and Aharoni’s proof of Ryser’s longstanding conjecture on packing and covering in tripartite hy- 2nd Conference GNU Octave [free your pergraphs. The topological arguments used are based numbers] on the notion of topological connectivity of simplicial July 16–20, 2012, CRM complexes. Haxell has recently developed a method for Sponsored by the CRM and the Université de Montréal establishing this entire theory using only elementary combinatorial arguments, and this approach was the Organizer: Jordi Gutiérrez Hermoso subject of her SMS lectures. Number of participants: 20 GNU Octave is a free software that is quite similar to Colin McDiarmid presented some recent break- Matlab and thus includes algorithms for the numer- throughs on a classic question in probabilistic graph ical solution of linear and nonlinear problems. It al- theory: what is the typical behaviour of the chromatic lows one to perform other numerical experiments as number χ(G) of a graph G? If Rn denotes some sort of well and provides extensive graphics capabilities for random graph on n vertices, can we determine a func- data visualization and manipulation. Octave is a high- → tion f(n) such that χ(Rn)/f(n) 1 in probability as level interpreted language but can also be used to write → ∞ n ? If so, what is f(n)? Can we bound the typi- non-interactive programs. OctConf2012, which took cal spread of the values χ(Rn)? Is χ(Rn) usually close place at the CRM in July 2012, is part of a series of to ω(Rn), the maximum size of a complete subgraph? workshops geared towards people with an interest in McDiarmid presented a variety of his recent results; his Octave. The workshop was very successful. Over the lectures focused primarily on the classical Erdős-Rényi course of five days, twenty participants were involved, or Bernoulli random graph G(n, p) (both in the dense and all but two were at the workshop for at least four case where p is a constant and in the sparse case where days. The goal of the first two days was to provide np is constant), and on random geometric graphs. He information and the latest updates on development

24 General Program methodologies. The next three days consisted of open that they learn from one another and discuss together discussion and development. The schedule was fol- new avenues that can be explored. The first week of the lowed with almost no modification. We refer the reader meeting was dedicated to minicourses, while the sec- to http://jordi.inversethought.com/blog/octconf-2012- ond week was organized to encourage collaborations report/ for more details. The following talks took and discussions. place: About 30 researchers coming from Europe (France, (1) What is Octave? (Jordi Gutiérrez Hermoso) Italy), Australia, or North America (Canada and USA) (2) Octave’s architecture (Jordi Gutiérrez Hermoso) attended both the minicourses and the workshop. We (3) Status of Octave (John W. Eaton) were very pleased to see that the objectives we set were (4) Octave Speed and Cell Arrays (Daniel Sebald) reached: many collaborations started during this meet- (5) JIT Compiler (Max Brister) ing, and a second “Coxeter groups Meet Convex Geom- (6) The Octave GUI (Jacob Dawid) etry” meeting will be organized within two years most (7) Agora Octave and Packaging (Carlo de Falco, certainly in Europe. David Pinto, and Juan Pablo Carbajal) (8) Bringing Least-Squares Spectral Analysis to Oc- Infinite-Dimensional Lie Theory: Algebra, tave (Ben Lewis) Geometry and Combinatorics (9) BIM package (Carlo de Falco) A CRM–Fields Institute Workshop August 21–24, 2012, CRM Mini-courses & Workshop Coxeter Groups Meet Convex Geometry Organizers: August 13–17 and 20–22, 2012, UQAM Joel Kamnitzer (Toronto), Michael Lau (Laval) Sponsored by LaCIM Speakers: Ibrahim Assem (Sherbrooke), Bojko Bakalov (North Organizers: Carolina State), Ivan Dimitrov (Queen’s), Christo- Christophe Hohlweg (UQAM), Jean-Philippe Labbé pher Dodd (Toronto), Alex Feingold (Binghamton), (UQAM), Carsten Lange (FU Berlin), Vivien Ripoll Dennis Gaitsgory (Harvard), Nicolas Guay (Alberta), (UQAM) Sam Gunningham (Northwestern), Andrew R. Lin- Lecturers: shaw (Brandeis), Pierre Mathieu (Laval), Ivan Mirkovic Matthew Dyer (Notre Dame), Christophe Hohlweg, (UMass Amherst), Dinakar Muthiah (Brown), Shifra Carsten Lange, Vincent Pilaud (École Polytechnique) Reif (Michigan), Hadi Salmasian (Ottawa), Hugh Number of participants: 30 Thomas (New Brunswick), Peter Tingley (MIT & Loy- There are numerous examples of relations between ola), Jethro van Ekeren (MIT & IMPA) convex geometry and Coxeter groups, the most known Number of participants: 42 probably being the construction of the Tits cone. Dur- Infinite-dimensional representations of Lie algebras ing these last years, many interesting other examples and related structures play a vital role in a broad swath have been thoroughly studied, among them: general- of modern mathematics, including vertex algebra the- ized associahedra and permutahedra of finite reflection ory, quantum groups, quivers and cluster algebras, groups; Cambrian fans; brick polytopes and multiasso- geometric representation theory, conformal field the- ciahedra; imaginary cones and infinite root systems. ory, and the Langlands programme. The jointly spon- These nice encounters between Coxeter groups and sored CRM–Fields workshop brought together an en- convex geometry have two main consequences: we ergetic group of more than 40 researchers approaching manage to understand better the combinatorics and ge- the subject from a variety of algebraic, geometric, and ometry of Coxeter groups by encoding some of their combinatorial points of view. characteristics in polytopal or more general convex The first day of the conference featured combinatorial constructions; we also obtain new families of interest- aspects of infinite-dimensional Lie theory. Ivan Dim- ing polytopes, which is very useful in convex geometry itrov explained how some completely elementary com- since such families are fairly rare. binatorial objects, inversion sets, can be used to un- The aim of this meeting was to bring together experts derstand difficult geometric and combinatorial prob- and interested people from both communities, in order lems like the vanishing of the cup product on coho-

25 Centre de recherches mathématiqes mology of flag varieties in Bott–Borel–Weil, and the resentations, and Shifra Reif presented her results on determination of Littlewood–Richardson coefficients. denominator identities for affine Lie superalgebras at Hugh Thomas presented a natural bijection between critical level and some of their interesting applications. certain subcategories of representations of the path al- One of the goals of this jointly sponsored CRM–Fields gebra of a Dynkin quiver and elements of the corre- conference was to bring together the Lie theory com- sponding Weyl group. Ibrahim Assem introduced the munity of central Canada. It is a tribute to the qual- notion of a cluster automorphism and connected this ity and quantity of Lie theory in the region that such definition with the mapping class group of marked, a high-quality conference could be held at the CRM oriented Riemann surfaces. Peter Tingley and Dinakar with a solid majority of participants arriving from uni- Muthiah gave well-motivated introductions to the sub- versities in Ontario, Québec, and the northeast USA. ject of affine Mirkovic–Vilonen polytopes and how A remarkable feature of the conference was the rela- they give a dictionary between Lusztig data associated tive youth of the participants. Seven of the sixteen in- with crystal bases. vited speakers were graduate students or postdoctoral The second day of the conference focused on vertex fellows. They and a number of enthusiastic audience algebras and their applications. Pierre Mathieu gave members made it a memorable week filled with some a super-extension of Jack polynomials, eigenfunctions fantastic mathematics. of the Sutherland Hamiltonian that parametrize singular vectors in highest weight modules of the Virasoro Colloquium Lie algebra. Andy Linshaw discussed a vertex operator Entretiens Jacques-Cartier analogue of Hilbert’s theorem on finite generation of Mathématiques appliquées à la gestion des invariant rings under a reductive group action. Jethro risques van Ekeren presented his recent results on modular November 19–20, 2012, Lyon 1 invariance of spaces of twisted characters for vertex Sponsored by the CNRS, the CRM, ISFA (Lyon 1), superalgebras of nonintegral conformal weight. Bojko AMIES, and the Mprime network Bakalov used the total descendent potential, a generating function for Gromov–Witten invariants, to give Organizers: a McKay-like relation between Kleinian singularities Christophette Blanchet-Scalliet (École Centrale de and representations of W -algebras. Alex Feingold used Lyon), José Garrido (Concordia), Laurent Habsieger vertex operator techniques to calculate affine branch- (CNRS & CRM), Stéphane Loisel (Lyon 1), Manuel ing rules for inclusions given by Dynkin diagram fold- Morales (Montréal), Pierre Ribereau (Lyon 1) ing. Speakers: Patrice Bertail (Paris Ouest), Juliette Blanchet (EPFL), The final two days of the conference emphasized ge- Nicolas Brisebarre (ÉNS Lyon), Rama Cont (CNRS & ometric representation theory, Lie supergroups, and LMPA), Anne-Béatrice Dufour (Lyon 1), Bruno Dupire Lie superalgebras. Dennis Gaitsgory outlined the proof (Bloomberg), Nicole El Karoui (UPMC), Max Fein- of the geometric Langlands conjecture for GL(2), tak- berg (INRA-Paris), Alexis Hannart (CNRS & IFAECI), ing care to point out the easy and difficult parts of the Monique Jeanblanc (Évry), Jacques Légaré (Montréal), proof along the way. Sam Gunningham explained re- Marc-André Lewis (CDPQ), Étienne Marceau (Laval), sults concerning the cohomology of the character va- Guy Métivier (Bordeaux 1), Pietro Millossovich (City, riety of a reductive group. Chris Dodd gave a quick London), Didier Sornette (ETH Zürich), Leroy Stone review of Nakajima quiver varieties before describ- (Montréal) ing a way to categorify Lie algebra actions on quiver Les vingt-cinquièmes Entretiens Jacques-Cartier se D varieties using -modules. Ivan Mirkovic presented sont tenus à Lyon les 19 et 20 novembre 2012, et plus Lusztig’s conjectures in modular representation theory de 50 participants étaient présents. Les organisateurs and explained how to resolve them using localization, de la France étaient Christophette Blanchet-Scalliet, and Nicolas Guay explained how to construct vertex Stéphane Loisel et Pierre Ribereau, et les organisa- operator representations for Yangians associated with teurs du Québec étaient José Garrido, Laurent Hab- affine Lie algebras. Hadi Salmasian surveyed analytic sieger et Manuel Morales. Plus globalement, les Entre- properties of infinite-dimensional Lie supergroups and tiens Jacques-Cartier sont organisés chaque année à la showed how to construct some of their unitary rep- fois par des Français et des Canadiens. Leur vocation

26 General Program est de rapprocher des intervenants issus de milieux qui Colloquium ne se côtoient pas habituellement. Ils sont articulés au- Entretiens Jacques-Cartier tour de quatre grands axes : économique et politique, Aventures en physique mathématique scientifique, social et culturel. November 19–21, 2012, Lyon 1 Le but de ce colloque était d’être un lieu de rencontre Sponsored by the CNRS, the CRM, the Université Lyon où les groupes de recherche industriels et académiques 1, the Université de Savoie, the Laboratoire d’Annecy- pourraient trouver un environnement propice à la dis- le-Vieux de Physique Théorique, and the Fédération cussion scientifique et aux échanges interdisciplinaires MSIF sur le thème de la gestion quantitative des risques (en Organizers: particulier actuariels, financiers, climatiques, environ- John Harnad (Concordia), Claude Roger (Lyon 1), Paul nementaux, de sûreté des calculs, sanitaires et biotech- Sorba (CNRS & LAPTH), Luc Vinet (Montréal) nologiques). L’objectif principal du colloque était donc Speakers: de rapprocher ces deux types d’acteurs et d’encourager Marco Bertola (Concordia), Robert Brandenberger les interactions entre eux: d’un côté, les interven- (McGill), Simon Caron-Huot (Niels Bohr), Matthias tions faites par des chercheurs industriels ont donné Christandl (ETH Zürich), Sylvie Corteel (CNRS & un aperçu des problèmes d’actualité, des outils et des LIAFA); Luminiţa-Iona Cotîrlă (Babeş-Bolyai), Thierry méthodes utilisés en pratique, et de l’autre, la partici- Dauxois (CNRS & Lab./ phys./ ENS Lyon), James pation des chercheurs universitaires a apporté à la dis- Drummond (CNRS & LAPTH), Bertrand Eynard cussion les nouvelles méthodes et modèles récemment (CEA/Saclay), Patrick Ferrari (Bonn), Vincent Genest développés. (Montréal), Yves Grandati (Lorraine), Mihail Mintchev Les sessions et tables rondes du colloque portaient à la (INFN & SNS Pisa), Alexei V. Penskoi (IU Moscow), fois sur la modélisation de ces risques, sur les mesures Yvan Saint-Aubin (Montréal), Vyacheslav Spiridonov utilisées pour les quantifier, sur le risque de modèle, (JINR), Herbert Spohn (TU München), Thomas Strobl sur les techniques d’estimation et aussi sur les prob- (Lyon 1), Serge Tabachnikov (Penn State), Laurent lèmes d’optimisation liés à l’atténuation ou au trans- Vuillon (Savoie), Oleksiy Zhedanov (Donetsk IPE) fert de ces risques. La capacité de réaction rapide étant Many of the most important and fruitful mathemati- souvent clé en gestion des risques, les problématiques cal theories originated in physical problems. This re- de détection de changement de tendance ont aussi été lationship is well known but new and spectacular de- abordées, notamment pour les risques de longévité velopments have illustrated it during the last twenty et climatiques. Ces questions sont intéressantes non years. On the other hand modern physics has always seulement pour les entreprises, mais aussi pour les needed mathematical tools and models and must fol- chercheurs universitaires qui y trouvent une source de low the progress of the mathematical sciences. The nouveaux défis mathématiques. goals of this conference were to gather mathematicians and physicists around some common themes and es- Les intervenants provenant de ces différents champs sential results, and to tighten the already existing con- disciplinaires ont pu constater les similitudes et com- nections between Québec scientists and the scientists plémentarités de leurs approches respectives. Ainsi in the Rhône-Alpes region. Here is the list of lectures l’un des organisateurs (Manuel Morales) a monté un that took place at the conference. projet intitulé “Nouvelle approche de la théorie de la ruine et application en toxicologie” avec d’autres • Solitons: revisiting old questions and recent experi- chercheurs français et canadiens, qui a été déposé ments (T. Dauxois) auprès du Fonds France-Canada pour la Recherche. • Physical and mathematical aspects of quantum wires (M. Mintchev) • Instances of supergeometry in mathematical physics (T. Strobl) • Proof of the BKMP conjecture: relating topological strings to matrix models (B. Eynard) • Pentagram map, twenty years after (S. Tabachnikov)

27 Centre de recherches mathématiqes

• From geometry to inhibitors: the story of protein- Speakers: protein interfaces viewed under the GEMINI soft- José Garrido (Concordia), Christian Genest (McGill), ware (L. Vuillon) Christophe Reutenauer (UQAM), Robert Seiringer • Floquet theory, inflationary cosmology and Ander- (McGill), Luc Vinet (Montréal) son localization (R. Brandenberger) Student Speakers: • Eigenvalue distribution of reduced density matrices Jean-François Arbour, Léo Belzile, Younes Ben-Ghabrit (M. Christandl) (UQAM), Geoffroy Bergeron, Carolyn Campbell • Free energy fluctuations for directed polymers at (McGill), Simon Chatelain (McGill), Mathilde Gerbelli- positive temperature (P. Ferrari) Gauthier, Jonathan Godin (Laval), Asad Haris (McGill), • The principal indecomposable representations of the Nicole Keating (McGill), Aditya Kumar (McGill), Jean Temperley–Lieb algebra and their physical applica- Lagacé (Montréal), Olivier Martin (McGill), Thomas tions (Y. Saint-Aubin) Ng (McGill), Laurent Pelletier (Laval), Michael Snarski • Combinatorics, orthogonal polynomials and ASEP (McGill), Matthew Stevenson (McGill), Mashbat Suzuki (S. Corteel) (McGill) • Recent progress in scattering amplitudes (J. Drum- Number of participants: 97 mond) Depuis maintenant quatre ans, les Séminaires universi- • Riemann-Hilbert problems: a tool of many uses (M. taires en mathématiques à Montréal se font un devoir Bertola) de rassembler les étudiants québécois passionnés par • Elliptic hypergeometric functions, superconformal les mathématiques et la statistique dans la métropole. indices, and integrable systems (V. Spiridonov) Se faisant, l’organisation les encourage à échanger en- • The Kardar-Parisi-Zhang equation and its universal- tre eux et transmettre leur passion pour une branche ity class (H. Spohn) ou une autre de leur discipline d’étude dans une am- • Classical orthogonal polynomials corresponding to biance décontractée. L’évènement vise donc à pro- the operators of Dunkl type (O. Zhedanov) mouvoir les mathématiques, favoriser les échanges • Yang-Mills models in four dimensions: a new kind of entre étudiants de premier cycle en mathématiques, integrable systems (S. Caron-Huot) créer des liens entre les différentes universités de la • New classes of harmonic univalent functions (L.-I. métropole et initier la communauté académique de de- Cotîrlă) main au partage des connaissances. • The algebra of dual 1-Hahn polynomials and the L’édition 2013 aura été marquée par le retour des Sémi- Clebsch-Gordan problem of the quantum algebra naires à l’UQAM et le retour des activités du vendredi sl(2) at q = −1 (V. Genest) soir, permettant des rencontres entre étudiants dans • New rational extensions of solvable potentials with un contexte plus convivial. Cette année, les organisa- finite bound state spectrum and enlarged shape in- teurs se sont fait un devoir de collecter des statistiques variance (Y. Grandati) sur l’évènement qui serviront d’indicateurs-clés pour • Spectral geometry and mathematical physics joint la prochaine édition. C’est ainsi que 83 participants, un quest for extremal metrics (A. V. Penskoi) nombre premier, incluant un groupe de 7 étudiants de SUMM 2013 Québec, sont venus échanger autour d’exposés étudi- ants et de quatre conférences plénières, avec un con- Seminars in Undergraduate Mathematics in férencier invité de chaque université et, cette année, Montréal une présentation sur les opportunités de financement January 25–27, 2013, UQAM et sur les groupes de recherche, faite par le directeur de Sponsored by Concordia University, McGill Univer- l’ISM, Christian Genest. Chaque année, les conférences sity, Université de Montréal, Université du Québec plénières constituent une attraction majeure des Sémi- à Montréal, STUDC, the CRM, the ISM, Maplesoft, naires. Nous avons eu l’honneur d’accueillir cette an- SUMS, MASSA, and the AESS (UQAM) née José Garrido, Luc Vinet, Christophe Reutenauer Organizers: et Robert Seiringer. L’expertise de ces conférenciers Jean-François Arbour (UQAM), Geoffroy Bergeron permit aux participants de s’initier à des sujets de (Montréal), Mathilde Gerbelli-Gauthier (McGill), Léo pointe en mathématiques; elle favorisa aussi la création Belzile (McGill), Kevin Shao (Concordia)

28 General Program de liens entre la communauté universitaire actuelle et research institutes. A secondary goal is to allow stu- celle de demain. dents to develop skills for making presentations; the L’évènement se déroula sans anicroche, et la sat- background talks at the workshop are given by gradu- isfaction manifeste des participants a fait honneur ate students and postdocs. aux nombreux bénévoles et aux organisateurs. Nous The fifth meeting was devoted to the topicof p- sommes très fiers de la participation étudiante, de divisible groups or Barsotti-Tate groups. These ob- l’enthousiasme des conférenciers et de la diversité des jects have become an indispensable tool in many ar- présentations étudiantes de cette année. Le bilinguisme eas in arithmetic geometry, for example in the study of de l’évènement, reflétant la réalité de la communauté Shimura varieties, automorphic representations, Ga- universitaire montréalaise, a été maintenu, avec no- lois representations, and variations of zeta functions. tamment l’introduction de diapositives dans la langue Their usefulness keeps extending into other domains. complémentaire pour les exposés bilingues. Nous es- The workshop attempted to give an overview of the pérons que ces Séminaires sauront former et intéresser subject, starting from the very first definitions and les jeunes chercheurs de demain. results (going back 50 years or so) and ending with Le comité d’organisation tient à remercier les institu- some of the most current topics of interest, such as tions qui lui ont apporté un soutien financier (et qui Rapoport-Zink spaces and Kisin modules. As with pre- sont mentionnées ci-dessus). L’équipe tient également vious meetings, the level of presentations was excep- à souligner la participation des gens de l’Université tionally high and the participants indeed were able to Laval, qui ont assisté aux Séminaires grâce au soutien get a panoramic view of the subjects, as much as can financier du STUDC, le comité étudiant de la Société be done in 10 hours. mathématique du Canada. As with previous workshops, we have made the content of the talks available to the pub- 2013 Montréal–Toronto Workshop in lic. The notes of the present workshop canbe Number Theory found at http://www.math.mcgill.ca/goren/Montreal- p-Divisible Groups Toronto/Montreal-Toronto.5.html. The detailed pro- April 18–19, 2013, CRM gram was as follows: Dylan Attwell-Duval (Defini- Sponsored by CICMA tions and main examples); Luiz Takei (Witt vectors); Patrick Walls (Dieudonné modules); Andrew Fiori Organizers: (Classification of p-divisible groups up to isogeny); Eyal Z. Goren (McGill), Stephen S. Kudla (Toronto) Ying Zong (Deformations, crystals and Grothendieck- Speakers: Messing theory); Amy Cheung (The Serre-Tate theo- Dylan Attwell-Duval (McGill), Francesca Bergam- rems); Francesca Bergamaschi (Kisin Modules); Steve aschi (Milano & Concordia & McGill), Amy Cheung Kudla (Stratification of unitary Shimura varieties); (McGill), Eyal Z. Goren, Andrew Fiori (McGill), Steven Eyal Goren (Stratifications of moduli spaces and p-adic S. Kudla, Luiz Takei (McGill), Patrick Walls (Toronto), uniformization). Ying Zong (Toronto) Number of participants: 42 Adventures in Superspace The Montreal Toronto workshops in number theory April 19–20, 2013, McGill are a joint enterprise of the Centre de recherches Sponsored by the Mathematical Physics Laboratory mathématiques in Montreal and The Fields Institute in Toronto. The meetings are run twice a year as work- Organizers: shops focused on a particular topic in number theory. Robert Brandenberger (McGill), Jim Gates (Maryland), One of their main goals is to foster scientific relation- Martin Rocek (Stony Brook) ships between the Montreal number theory commu- Speakers: nity (including the Université Laval in Québec City and Tirthabir Biswas (Loyola), Cliff Burgess (McMaster), the University of Vermont) and the Toronto number Bernard de Wit (Utrecht), Michael Duff (Imperial theory community (including McMaster University). Coll.), Dan Freedman (MIT), Jim Gates, Renata Kallosh The workshops have been very successful instructional (Stanford), Ulf Lindstrom (Utrecht), Martin Rocek, events, unique within the scope of the activities of the Warren Siegel (Stony Brook), Kelle Stelle (Imperial

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Coll.), Peter van Nieuwenhuizen (Stony Brook), An- Organizers: toine van Proeyen (KU Leuven) Emmanuel Lorin de la Grandmaison (Carleton), Robert Number of participants: 20 Owens (Montréal) This workshop was organized to celebrate the contri- Invited Speakers: butions of Professor Marcus Grisaru to the field of su- Xavier Antoine (Lorraine), Michael Griebel (Bonn), pergravity. We were happy that all of the senior ex- Doron Levy (Maryland) perts in the field of supergravity who together with Other Speakers: Marcus helped create the field accepted our invita- Gustavo Avila-Blanco (Queen’s), Muhammad Awais tion to come to this workshop. In particular, Professors (Victoria), Tucker Carrington (Queen’s), Alexan- Jim Gates (recently awarded the US National Medal dre Desfossés Foucault (Montréal), François Fillion- of Science), Martin Rocek, and Warren Siegel partic- Gourdeau (Montréal), Denis F. Hinz (McGill), Azadeh ipated. Together with Grisaru, the four are authors Jafari (Montréal), Tae-Yeon Kim (McGill), Lahcen of the ground-breaking textbook “Superspace, or One Laayouni (Al Akhawayn), David Lapierre (Montréal), thousand and one lessons in supersymmetry.” Profs. Felicia Magpantay (York), Mike McLeod (Ottawa), de Wit, Duff, Freedman, Lindstrom, Mezincescu, Stelle, Maryam Namazi (CCCMA), David Shirokoff (McGill), Townsend, van Nieuwenhuizen and Van Proeyen are Ilyssa Summer (Arizona State), Alexandra Tcheng all senior experts in the field of supergravity and have (McGill), Jinming Wen (McGill) all at some point collaborated with Marcus Grisaru. It Number of participants: 67 was a rare treat to have all of these experts in the same The Montréal Scientific Computing Days (MSCD) is place at the same time. Here is a list of some of the a workshop quite unique in its format in Québec. talks. This meeting covers a wide spectrum of mathemati- • M. Grisaru & the Eden of Supergravity (J. Gates) cal themes centred around scientific computing: the • Gauge multiplets and gauging in D=2 sigma-models analysis of partial differential equations, numerical (M. Rocek) analysis, computational sciences, high performance • Anomaly multiplets, regrisaruzation & solitons (P. computing, as well as numerous application areas in van Nieuwenhuizen) physics, biology, medicine, finance, etc. As far as is rea- • 3D strings: an open-and-shut case (P. Townsend) sonably possible, the MSCD tries to maintain a good • Generalized Kähler geometry and sigma models (U. balance between theory and applications. The work- Lindstrom) shop that took place in May of this year was the sev- • Superconformal symmetry and higher-dimensional enth in a series that has enjoyed great success in the Lagrangians (A. van Proeyen) past, thanks in particular to the high quality of the in- • A Superspace Odyssey (B. de Wit) vited speakers (whose course notes have been made • UV properties of N=8 and N=4 supergravities (R. available online to participants) and to the active par- Kallosh) ticipation of the graduate students and postdocs. This • UV divergences in maximal and half-maximal super- year 67 people registered for the workshop, and al- gravity (K. Stelle) though the great majority of participants came from • The holographic dual of F-maximization (D. Freed- universities in Québec and Ontario, others came from man) as far afield as Morocco, Texas, and British Columbia. • Vanish without a trace (M. Duff) The MSCD is an ideal opportunity for students and • Towards consistent nonlocal theories of gravity (T. other researchers from various scientific communi- Biswas) ties (physicists, mathematicians, computer scientists, • Supersymmetric cancellations without superpart- etc.) to interact in a welcoming and informal setting. ners: having your cake and eating it too (C. Burgess) The workshop also gives graduate students and postdocs the opportunity of taking short courses, each of Spring School three hours’ duration and pitched at an accessible level, 7th Montréal Scientific Computing Days and given by researchers of international stature. This May 13–15, 2013, CRM year’s invited speakers were Xavier Antoine, Michael Sponsored by the Applied Mathematics Laboratory Griebel, and Doron Levy. Prof. Antoine delivered a series of talks entitled How to truncate a PDE problem set

30 General Program in an unbounded domain: the example of the Schrödinger In recent years, mathematical models have been play- equation. ing an increasing role in cancer studies. The under- The goal of this introductory course was to give an lying complexity of the biological processes requires overview of some of the techniques that can be used researchers to use mathematical models of different to truncate the spatial domain on which is defined a types, including discrete and continuous models, de- partial differential equation in an attempt to minimize terministic and stochastic models, and models with the effect of the truncation operation. At the heart of time delays. The lectures by Prof. Doron Levy were on the presentations was a detailed treatment of absorb- numerical methods for mathematical models of cancer ing boundary condition methods and others for tack- dynamics and on agent-based models (ABM) in can- ling general problems with particular application to cer. In the former topic, we learned about numerical the Schrödinger equation. This equation, which has methods for delayed differential equations and numer- many applications in physics and engineering, leads to ical methods for nonlinear time-dependent PDEs. In difficult questions concerning the mathematical con- the latter topic, Prof. Levy discussed ABMs for solid struction of absorbing boundary conditions as well as tumor growth and the Roeder model of stem cells. He their numerical approximation. In particular, even in went on to explain how to pass from ABMs to PDEs the simplest case, it is necessary to develop nontrivial and concluded his series of talks with a presentation solutions to get numerical schemes with suitable prop- of related techniques, including crime models and a erties (like stability). technique for deriving various Fokker-Planck equations from stochastically interacting particles. The de- In this course, Prof. Antoine discussed the following tailed slides of the mini-courses given by the three in- questions, of increasing difficulty: vited speakers may be downloaded from http://www. • the free space one-dimensional Schrödinger equa- crm.umontreal.ca/Comp13/diapo_e.shtml. tion; As well as being an opportunity for graduate stu- • how to take into account potentials in 1d; dents and post-docs to keep abreast (through the mini- • how to extend the methods to 1d nonlinear prob- courses) of some of the latest research directions in lems; computational applied mathematics, the MSCD also af- • two-dimensional problems; and fords a unique opportunity for these students to make • inclusion of potentials and nonlinearities. an oral presentation on the results of their research, Prof. Griebel’s mini-course of three lectures was on both to their own peer group and to the wider ap- the theme of generalized sparse grids. Efficient applied mathematics community in Québec. In all 16 such proximations for multivariate functions can be de- presentations were given during the workshop, and in rived from a one-dimensional multilevel representa- keeping with tradition, it was expected that a prize (in tion of a function (hierarchical basis, generating sys- the form of a SIAM book token) would be awarded tem, (pre)wavelet system, Fourier series, eigenfunction for the best presentation. The overall standard of stu- series, or similar methods) by a product construction to dent and postdoc talks, however, was very high and obtain a multilevel system for the many-dimensional the choice of the most deserving candidate was ex- case and a subsequent proper truncation of the re- ceptionally difficult. The scientific committee (com- sulting series expansion. This leads to so-called sparse posed of Yves Bourgault, from the University of Ot- grids, which promise to cope with the curse of di- tawa, Emmanuel Lorin de la Grandmaison, and Robert mensionality in conventional product discretizations, G. Owens) decided that the prize should be awarded at least to some extent. First, Prof. Griebel discussed ex aequo to Alexandre Desfossés Foucault, Felicia Mag- regular sparse grids and their approximation and cost pantay, and Alexandra Tcheng. These three are warmly complexities. Besides regular sparse grids, one can also congratulated on the excellence of their research and construct (by means of an optimization process) spe- the clarity and impact of their presentations. cific problem-dependent sparse grids that exhibit optimal asymptotic complexity estimates for various situ- Workshop ations, error norms, and regularity assumptions. Prof. N = 2 Jeometry and ApplicationZ Part II Griebel presented such methods in detail and, in con- May 22–24, 2013, McGill clusion, discussed various applications.

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Organizers: physics communities. There were two math review Keshav Dasgupta (McGill), Jihye Seo (McGill), Jo- talks by local researchers and eight physics talks from hannes Walcher (McGill) external speakers. Speakers: According to Chan Youn Park, M2 branes between two Richard Eager (Kavli Inst.), John Harnad (Concor- M5 branes wrapping a Seiberg-Witten curve are de- dia), Simeon Hellerman (Kavli Inst.), Jacques Hurtubise scribed by a 2d N = (2, 2) Landau Ginzburg model (McGill), Kazunobu Maruyoshi (Caltech), Domenico with chiral fields and superpotential. He discussed how Orlando (CERN), Chan Youn Park (Caltech), Jaewon to construct spectral networks to analyze the BPS spec- Song (UC San Diego), Masahito Yamazaki (Princeton) tra and their wall-crossing in his talk “Spectral net- Number of participants: 33 work and BPS spectrum of SCFT.” He studied exam- N This workshop was a second installment of = ples of spectral networks to illustrate how to utilize 2 Jeometry and ApplicationZ. Last year’s partic- the results in identifying SCFTs that have different de- ipants, Kenneth Intriligator (UC San Diego) and scriptions. He performed a similar analysis and com- Nathan Seiberg (IAS), acknowledged the first install- puted central charges and gauge/flavour charges for ment in their preprint “Aspects of 3d N = 2 Chern- the Argyres-Douglas theory, an interacting SCFT the- Simons-Matter Theories,” which appeared this May ory with 4d and N=2 with mutually nonlocal massless on arxiv, as arXiv:1305.1633. It was also mentioned states. in the New York Times. This year’s focus was more N mathematical, featuring superconformal index count- The TN theory is a = 2 SCFT theory obtained by compactifying a 6d (2,0) theory of M5 branes on a ing, Vasiliev’s theories, superconnection constraint 3 equations, Chern-Simons theory, Sasaki-Einstein, lens sphere with three full punctures with SU(N) flavour space, and topological string. symmetry, with no Lagrangian description. Kazunobu Maruyoshi gave a talk entitled “N = 1 Dynamics The theme of the workshop was 4-dimensional super- with TN superconformal field theories,” in which he symmetric field theories. There have been lots of inter- explained the coupling of TN ’s to N = 1 vector multi- est and progress recently in this area. Most pioneer- plets. By reducing Csaki–Schmaltz–Skiba–Terning du- ing works are a new set of theories called “class S,” ality, he and his collaborators obtain a duality be- which is obtained by wrapping M5 branes on a Rie- tween conventional theory (such as supersymmetric mann surface, by Gaiotto-Moore-Neitzke and Alday- QCD) and non-conventional theory. He showed that Gaiotto-Tachikawa correspondence relating a certain the theory exhibits confinement, superconformal, and N class of 4-dimensional = 2 superconformal theo- Abelian Coulomb phases, depending on the manner ries to 2-dimensional (bosonic) conformal theories, and of coupling TN theories to N = 1 vector multiplets. “Nekrasov-Shatashvili” relation between Ω-deformed In particular, a N = 1 SU(N) gauge theory coupled N = 2 theories and quantum integrable systems. to two TN theories, which flows to a superconformal Equipped with cluster coordinates and bipartite net- fixed point, has dual descriptions with gauge singlet works, studies of N = 2 theories are gaining even fields, and this leads to, by Higgsing, a new duality of larger momentum these days, signaling potential rel- N = 1 SQCD with Nf = 2N. N evance to brane tilings in = 1 quiver and scattering Masahito Yamazaki and Richard Eager discussed in- N amplitudes of = 4 super Yang-Mills theory. These dex computation, to test S-duality and AdS/CFT cor- are pioneered by Xie, Franco, Yamazaki, Cachazo, respondence. Although the Lagrangian description is Arkani-Hamed et al. A close relationship between su- often used in Feynman diagrams in QFT, it is not fun- persymmetric field theories and totally non-negative damental (as seen from recent works by Freddy Cac- Grassmannians is studied with varying amount of su- hazo and Nima Arkani-Hamed). Gauge symmetry is ≤ N ≤ persymmetry 1 8. also not fundamental: it is considered to be a redun- The workshop also included supersymmetric field the- dancy and it can even change under Seiberg duality. ories in other dimensions, and with different amounts In Yamazaki’s talk “4d N = 2 Lens indices from of supersymmetry. There were many discussions of S-duality,” he asks whether (Gaiotto-like) S-duality is string compactification, Vasiliev theory, AdS/CFT, S- fundamental to QFT. “Is S-duality powerful enough to dualities, Wilson loops, etc. The organizers provided characterize a theory completely?” might be too ambi- an interface for interactions between the math and tious a question and ambiguous. So he tries to answer

32 General Program the following question: “Is S-duality powerful enough BCFG group (in 2d and 4d theories) from ADE (in 6d to characterize the lens space index completely?” He theory). In simple language, folded Lie algebras can be finds that the lens index, which is a partition function obtained by various foldings as a 6d theory is compact- 1 3 computed on S × S /Zr, is almost completely deter- ified onto 2d and 4d theories. This work was inspired mined by S-duality and that S-duality is indeed pow- by Rastelli et al’s work on the correspondence between erful. 4d index and 2d TQFT. There were many discussions The superconformal index is the partition function of about the scheme-dependence of the Nekrasov parti- the (1+d)-dimensional superconformal field theory on tion function. S1 × Sd with supersymmetric boundary conditions. It There were two talks related to the Chern-Simons is also the generating function of the number of op- theory. Masahito Yamazaki talked about “3d Chern- erators weighted by their fermion number. The index Simons from M5-branes.” He discussed 3d theories is independent of the exact marginal deformations of coming from the 6d theory of M5 branes. He discussed the theory, and is calculable if the UV Lagrangian is the partition function of 5d N = 2 SYM, which is the known. In a talk titled “Superconformal indices in di- dimensional reduction of the 6d theory. By supersym- mensions 2, 3, and 4,” Eager considered the gauge the- metric localization the 5d partition function reduces to ory index, the gravity index, and the elliptic genus in that of the 3d pure Chern-Simons theory. This work order to check the AdS/CFT correspondence. He com- had two goals: one is to improve the conceptual under- puted the superconformal index of M2 branes prob- standing of AGT (Alday-Gaiotto-Tachikawa), which is ing the cone over an arbitrary Sasaki–Einstein seven- a 4d-2d correspondence, and the other is to formulate manifold and that of a D3 brane probing the Calabi– a 3d-3d equivalence of AGT. There were many discus- Yau cone. The index should be invariant under Seiberg sions about the role of the U(1) orbit inside the 6d in- duality and AdS/CFT. His talk also led to a discus- ternal geometry as we compactify the 6d theory into a sion about the spectrum of Sasaki–Einstein manifolds 5d SYM theory. and solving Heun’s equation. The second-order equa- The talk “Chern-Simons-Matter Theory and its Holo- tion reduces to a linear equation for the BPS spectrum. graphic Dual” (by Simeon Hellerman) was about de- There were questions about the choice of contour. bunking many myths around Vasiliev theory. In his We had two talks related to the Nekrasov’s partition invigorating talk, he emphasized the beauty of N = function and the Ω deformation. The Ω background 4 SYM and left a famous quote: that physics text- was introduced by Nekrasov to regularize the 4d in- books must discuss N = 4 SYM before they discuss stanton partition function and reproduce the results Maxwell’s theory of electromagnetism. The biggest of Seiberg-Witten. The Ω deformation is controlled by problem with Vasiliev theory and the proposal for its two parameters ε1,2 and various interesting limits ex- AdS/CFT dual comes from the counting of degrees of ist, such as topological string on Calabi–Yau, Samson’s freedom. Hellerman emphasized that Vasiliev theory limit (quantum integrable model), refined topological does not have a consistent ultraviolet completion, and string, and AGT. de Sitter / CFT is not viable in its current form. Itwas Domenico Orlando talked about how the Ω defor- very alarming and insightful in many ways. He men- mation can be understood from the viewpoint of tioned his work in progress on branes in topological old-fashioned string theory, based on Neveu-Schwarz string theory, and there were many questions about fields. His talk was entitled “the Ω deformation from gravitons built out of open strings, and the possibil- S3 string and M-theory.” It allowed one to understand ity of addressing the higher-genus case (beyond ). localization in geometric terms. The Ω deformation Hellerman led an afternoon discussion session and the is an effective 4d action for the fluctuations ofthe upshot was that the Chern-Simons theory has no local degrees of freedom and the correction to the spectrum, M5-branes. The parameter ε1,2 appears as a non- commutativity parameter in the quantum spectral if not zero, is very small (exponentially suppressed). curve, and there appears a Riemann surface embedded In order to foster more interaction between math- in a non-commutative complex plane. ematicians and physicists, the workshop included 2 In a talk entitled “The ABCDEFG of 4d/2d Corre- other mathematical talks. The results have significance spondence,” Jaewon Song explained how to obtain the for many recent works in the physics literature on superspace null polygonal Wilson loops in supersym-

33 Centre de recherches mathématiqes metric Yang-Mills theories. In recent computations of Speakers: super null polygonal Wilson loop amplitudes in super- Philip Boalch (CNRS; ÉNS), Sergey Cherkis (Arizona), space by Beisert, He, Vergu, et al, an essential ingredi- Tamàs Hausel (EPFL), Andrew Neitzke (UT Austin), ent is the super null line constraint equations, which Lauren Williams (UC Berkeley) provide the necessary conditions for the “thickened Number of participants: 62 null line” integrations to be well defined. GAP 2013 consisted of five minicourses, each three Jacques Hurtubise gave a talk entitled “The geome- hours long, given by Philip Boalch, Sergey Cherkis, try of supersymmetric Yang-Mills in four dimensions,” Tamás Hausel, Andy Neitzke, and Lauren Williams, about his work with John Harnad and Steve Shnider on to a mixed audience consisting of graduate students, superconnection constraint equations. Hurtubise pre- postdoctoral researchers, and senior researchers. The sented the d = 4 results connecting the constraint longer format meant that speakers could go into equations and the field equations for N = 0, 1, 2, 3. greater depth and cover more of the field than would Another talk was given by John Harnad, under the title have otherwise been possible. The common focus of “Constraints and field equations for d = 10, N = 1 topic, that of wall crossing phenomena in moduli SYM,” presenting the analogous results for d = 10, spaces, also meant that the audience could focus for N = 1, which (by dimensional reduction) also give an extended period of time on a smaller number of a simpler derivation of the d = 6, N = 2 and d = 4, concepts and their interrelations. The most remarkable N = 4 cases, with a summary of how the twistor cor- outcomes of the workshop format were emergent re- respondences extend to arbitrary dimensions. Harnad lationships between the talks that even the speakers reviewed the equivalence between the constraint equa- had not intended. On many occasions, heated discus- tions and the field equations in the d = 10, N = 1 SYM sions erupted during the talks between various experts theory, underlying Witten’s “super-twistor-like trans- among the speakers and the audience about possible form” and the dimensional reduction procedure that extensions and applications of the presented results. implies the corresponding results for d = 6, N = 2 Indeed, what began as a pedagogical exercise rapidly and d = 4, N = 4. became a real-time research workshop. The workshop was hosted by the McGill physics de- Philip Boalch used his lectures as an opportunity to department and had the same format as other successful scribe an important family of moduli spaces that has events organized by McGill’s Center for High-Energy occupied his research for many years: the wild char- Physics about three to four times a year: Two and a half acter varieties. These are moduli spaces of meromor- days with several external speakers in a relaxed atmo- phic connections on Riemann surfaces, but with irreg- sphere with ample time for discussions. Such a format ular singularities. The study of irregular singularities is of particular benefit for graduate students around and their associated Stokes phenomena have tradition- Montréal, who have the opportunity to meet and inter- ally been viewed as highly technical and abstruse, but act with distinguished scholars in their chosen field of through his recent work Boalch has clarified, general- study. Everyone left Montréal looking forward to a fu- ized, and significantly extended the theory, exposing ture meeting. This year’s participants were of the opin- its beauty as well as its many applications in mathe- ion that our workshop was really lovely, *extremely* matical physics. In addition to surveying the structure stimulating, and informative. theory of these spaces, Boalch explained the appear- ance of these moduli spaces in several important areas GAP 2013: Geometry And Physics including quantum groups. May 30–June 1st, 2013, CRM Tamás Hausel’s minicourse focused on his recent re- Sponsored by the Perimeter Institute for Theoretical markable computations and conjectures concerning Physics, the University of Waterloo Faculty of Mathe- the Betti numbers of the character varieties that are matics, the CRM, and the McMaster University Faculty diffeomorphic to the moduli space of Higgs bundles. of Science These computations were made by expressing the Organizers: character varieties as algebraic varieties over finite Marco Gualtieri (Toronto), Spiro Karigiannis (Water- fields and then counting rational points using char- loo), Ruxandra Moraru (Waterloo), Johannes Walcher acter formulas for representations of finite groups of (McGill), McKenzie Wang (McMaster) Lie type. His results are the culmination of many years

34 General Program of research into the topology of Higgs moduli spaces, proach to his recent papers, and was particularly in- and he was able to describe very clearly the train of spiring to the many people in the audience who study thought leading from Hitchin’s original work directly Stokes phenomena and irregular singularities. His lec- to his recent papers, as well as the work of Ngo on the tures were also remarkable in the number of open fundamental lemma. mathematical questions that were posed: the exciting Sergey Cherkis, in only three lectures, was able to de- prospect of developing these offshoots, especially the scribe the vast subject of gravitational instantons, cov- connection to Lauren Williams’ talks on cluster alge- ering ALE, ALF, ALG, and ALH spaces, and their beau- bras, motivated many questions from the audience. tiful explicit constructions as moduli spaces. He de- Lauren Williams presented what is perhaps the clear- scribed in a unified manner the various tools which est and most straightforward description of cluster al- are used in this story, starting with the ADHM con- gebras yet. Starting with startlingly simple combinato- struction, Nahm’s equations, and the Nahm trans- rial setups, she quickly layered these together to obtain form, among others. There was also an introduction to a description of the cluster structure on Grassmanni- twistor theory, toric geometry, and even tropical ge- ans, describing all the major features of the theory of ometry. Cherkis’ lecture series was particularly inspir- cluster algebras along the way, including the relation ing to the graduate students in attendance, who may to bordered surfaces, triangulations, ADE quivers, and have learned many of the techniques mentioned in his mutations, among many others. The connections be- course, but not seen how they are applied to solve deep tween the various topics touched upon by Williams problems in mathematical physics. and the other talks were surprising to many, includ- Andy Neitzke used the opportunity given him by the ing to the other speakers. triple of lectures to describe his body of work with In conclusion, the new format of the GAP 2013 con- Gaiotto and Moore on Spectral Networks in a com- ference at the CRM was a surprisingly effective one, pletely novel way: rather than focusing on the use of not only for student researchers attempting to enter spectral networks for possibly determining the Hyper- the field, but also for the senior researchers present, Kähler metric on the moduli space of Higgs bundles, who may not always glean, from the published papers, Neitzke focused instead on the potential for finding ex- as many insights as one does when the experts them- plicit solutions to Hitchin’s equations. This approach selves are teaching their subject. provided a much more direct and less front-loaded ap-

Colloquium and Seminar 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 2012–2013 the colloquium coordinators were Iosif Polterovich (Montréal) and Mikaël Pichot (McGill).

September 14, 2012 October 12, 2012 Robert McCann (Toronto) Rupert Frank (Princeton & Caltech) A glimpse at the differential topology and geometry of Symmetry and reflection positivity optimal transportation November 2, 2012 September 21, 2012 Jürg Fröhlich (ETH Zürich) Walter Neumann (Columbia) Dissipative motion from a Hamiltonian point of view Geometry of complex surface singularities

35 Centre de recherches mathématiqes

November 16, 2012 February 8, 2013 Konstantina Trivisa (Maryland) Sergei Tabachnikov (Penn State) On the Doi model for the suspension of rod-like molecules Pentagram map, twenty years after & related equations February 15, 2013 November 23, 2012 Nilima Nigam (Simon Fraser) Alexander Gamburd (Graduate Ctr., CUNY) Eigenproblems, numerical approximation and proof Expander graphs, thin groups, and superstrong approxi- March 1, 2013 mation Frithjof Lutscher (Ottawa) December 7, 2012 Mathematical models for river ecosystems Yuri Tschinkel (NYU & Simons Found.) March 28, 2013 Igusa integrals Victor Guillemin (MIT) January 25, 2013 Moser averaging Sheila Sandon (CNRS; Nantes) April 5, 2013 Global rigidity in contact topology Ehud DeShalit (Hebrew) February 1, 2013 Integral structures in p-adic representations Elliott Lieb (Princeton) April 12, 2013 Proof of a 35-year-old conjecture for the entropy of SU(2) Narutaka Ozawa (Kyoto) coherent states, and its generalization Quantum correlations and Tsirelson’s problem

CRM–ISM–GERAD Statistics Colloquium

In 2012–2013 the organizing team of the Statistics Colloquium included Mylène Bédard (Montréal), Simon Guil- lotte (UQAM), Abbas Khalili (McGill), Lea Popovic (Concordia), and David A. Stephens (Concordia).

September 21, 2012 January 18, 2013 Fang Yao (Toronto) Victor Chernozhukov (MIT) Regularized semiparametric functional linear regression Inference on treatment effects after selection amongst October 19, 2012 high-dimensional controls David Madigan (Columbia) March 22, 2013 Observational studies in healthcare: are they any good? Hélène Massam (York) November 23, 2012 The hyper Dirichlet revisited: a characterization Peter Müller (UT Austin) April 12, 2013 A nonparametric Bayesian model for local clustering Arup Bose (ISI Kolkota) December 14, 2012 Consistency of large dimensional sample covariance ma- Raymond J. Carroll (Texas A&M) trix under weak dependence What Percentage of children in the U.S. are eating a healthy diet ? A statistical approach

36 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. The reports are presented in the language in which they were submitted.

Activities of the Multidisciplinary and Industrial Program

6th International Conference on this ICITS, the organizers therefore decided to make a Information Theoretic Security (ICITS) special “workshop track,” in addition to the more stan- August 15–17, 2012, Montréal dard “conference track,” where the speakers needed to Sponsored by the CRM, the Institute for Quantum submit only a one-page abstract that will appear in the Computing (University of Waterloo), and INTRIQ (a proceedings. This new format (with both a conference strategic cluster funded by the FRQNT) track and a workshop track) was a big success, both in quality and quantity, and having an additional track Organizers: also increased the number of participants. Jürg Wullschleger (Montréal), Alain Tapp (Montréal), Claude Crépeau (McGill), Adam D. Smith (Penn State), Montréal Spring School of Olivier Coutu (Montréal) Population Genomics and Genetic Number of participants: 58 Edidemiology The International Conference on Information Theo- May 27–31, 2013, Collège Jean-de-Brébeuf retic Security (ICITS) is a conference about all aspects Sponsored by Génome Québec, the CHU Sainte- of information-theoretic security. Its aim is to bring to- Justine Research Centre, the CRM, the Université de gether researchers from all over the world from the ar- Montréal, and McGill University eas of cryptography, information theory and quantum information. The conference was created as a succes- Organizers: sor of the “IEEE Information Theory Workshop on The- Luis Barreiro (Montréal), Gillian Greig, Aurélie Labbe ory and Practice in Information-Theoretic Security” on (McGill), Damian Labuda (Montréal), Jean-François Awaji Island, Japan, and takes place every 18 months, Lefebvre alternating between Asia, Europe and North Amer- Scientific Committee: ica. Previous ICITS conferences were held in Madrid Jamie Engert (McGill), France Gagnon (Toronto), Maja (Spain), Calgary (Canada), Shizuoka (Japan), and Am- Krajinovic (Montréal), Marie-Hélène Roy-Gagnon sterdam (The Netherlands). ICITS 2012 was held from (Montréal), Julian Little (Ottawa), Erwin Schurr August 15 to 17, 2012 in Montréal. (McGill), Terry Lynn Young (Memorial) Speakers: As in previous ICITS conferences, the plenary talks Anna Di Rienzo (Chicago), Youssef Idaghdour (Mont- were given by the leading researchers in the field. One réal), Joseph Pickrell (Harvard), Hélène Vézina of the highlights of this conference was the talk by Salil (UQAC), Ma’n H. Zawati (McGill) Vadhan from Harvard University, who gave a presen- Instructors: tation about “The Many Entropies of One-Way Func- Alexandre Alcaïs (Paris Descartes), Will Astle (McGill), tions.” The other plenary talks were given by Serge Luis Barreiro, Guillaume Bourque (McGill), Laurent Fehr (CWI Amsterdam), Patrick Hayden (McGill Uni- Excoffier (Bern), Celia Greenwood (McGill), Nicolas versity), Negar Kiyavash (University of Illinois at Ur- Lartillot (Montréal), Guillaume Lettre (Montréal), Lluís bana-Champaign), Xin Li (University of Washington) Quintana-Murci (Inst. Pasteur), Joseph Pickrell and Krzysztof Pietrzak (IST Austria). Number of participants: 63 The usual process for conferences in Computer Science The objective of the School was to provide training in is that all submitted papers first undergo a careful re- rapidly developing disciplines that are becoming in- viewing process, and all papers that are accepted are creasingly important in health sciences, such as sta- not only presented at the conference, but also appear tistical genetics, human evolutionary genetics, popu- in the conference’s proceedings. Previous ICITS con- lation genomics and bioinformatics. The training was ferences also used this format, but it turned out not to based on real-data examples from the research of the be optimal for information theorists and physicists. For

38 Multidisciplinary and Industrial Program instructors’ laboratories. In one module we also pre- troductory courses from previous years that are posted sented genealogical resources specific to Québec. on our web site. The school consisted of five days of lectures andcom- For the 6th edition of the Montréal spring school, puter labs. Days 1 and 2 covered introductory con- there were 47 participants (28 from Québec, 8 from cepts in human population, medical genomics, and ge- Ontario, 5 from the USA, 3 from Europe, and 3 from netic epidemiology. Days 3 to 5 consisted of concur- South America) and 15 faculty members from Québec, rent sessions in advanced concepts in population ge- France, Switzerland, and the USA. The school was a nomics/statistical genetics and in genetic epidemiol- great success this year. Participants really enjoyed the ogy. Before attending the school, participants were in- broad scope of the workshop and found that it pro- vited to review basic concepts in genetics, epidemiol- vided great networking opportunities. The practical ogy, biostatistics and R-programming, by studying in- computer component was also greatly appreciated.

39 CRM Prizes CRM Prizes

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 collaboration 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 in its own resources, to propel leading Canadian scientists into the spotlight, giving them international recognition when they most need it.

CRM–Fields–PIMS Prize 2013 Awarded to Bruce Reed

important contributions being in random structures, graph minors, and graph colouring. The 2013 CRM– Fields–PIMS Prize recognizes his profound contributions to difficult and important problems in the areas of graph minors, graph colouring, algorithmic graph theory, random graphs, and the probabilistic analysis of algorithms. The reader will find a detailed description of Professor Reed’s contributions in the Spring 2013 edition of the 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- Bruce Reed ematical sciences. In 2005 PIMS became an equal Bruce Reed received his degrees in Mathematics and partner in the awarding of the prize and its name in Computer Science at McGill University. Follow- was changed to the CRM–Fields–PIMS Prize. A coming postdoctoral fellowships and faculty positions in mittee appointed by the three institutes chooses the Europe, Canada, and the USA, he joined the faculty recipient. The previous recipients of the prize are of McGill University in 2001: he currently holds the H.S.M. (Donald) Coxeter (1995), George A. Elliott Canada Research Chair in Graph Theory and was (1996), James Arthur (1997), Robert V. Moody (1998), elected as a Fellow of the Royal Society of Canada in Stephen A. Cook (1999), Israel Michael Sigal (2000), 2009. William T. Tutte (2001), John B. Friedlander (2002), Bruce Reed has played a leading role in a broad range John McKay (2003), Edwin Perkins (2003), Donald A. of research areas in discrete mathematics and theoret- Dawson (2004), David Boyd (2005), Nicole Tomczak- ical computer science. He is best known for his work Jaegermann (2006), Joel S. Feldman (2007), Allan on areas within graph theory, with many of his most Borodin (2008), Martin Barlow (2009), Gordon Slade (2010), Marc Lewis (2011), and Stevo Todorcevic (2012).

André-Aisenstadt Prize 2013 Awarded to Spyros Alexakis

Dr. Alexakis obtained a B.A. degree from the Univer- different directions. His main contribution, published sity of Athens in 1999 and a Ph.D. from Princeton Uni- as a research monograph in the prestigious Annals of versity, under the supervision of Charles Fefferman, in Mathematics Studies of Princeton University, is a solu- 2005. He held a Clay Research Fellowship as well as tion to a conjecture of Deser and Schwimmer regard- a Sloan Fellowship, and has been at the University of ing the structure of global conformal invariants. Sec- Toronto since 2008. Working in the areas of analysis ondly, together with Klainerman and Ionescu, he made and mathematical physics, alone and with collabora- important progress in the understanding of the Kerr tors, he has obtained striking results in at least three solutions to Einstein’s equations. Finally, jointly with

41 Centre de recherches mathématiqes

achievements in pure and applied mathematics by talented young Canadian mathematicians. This prize consists of a $3,000 award and a medal. The recipient is chosen by the International Scientific Advisory Com- mittee of the CRM. At the time of consideration, can- didates must be Canadian citizens or permanent resi- dents of Canada, and no more than seven years from their Ph.D. The previous recipients of the André-Aisenstadt Prize are Niky Kamran (1992), Ian Putnam (1993), Michael Ward (1995), Nigel Higson (1995), Adrian S. Lewis (1996), Lisa Jeffrey (1997), Henri Darmon (1997), Spyros Alexakis Boris Khesin (1998), John Toth (1999), Changfeng Gui Mazzeo, he obtained deep results concerning minimal (2000), Eckhard Meinrenken (2001), Jinyi Chen (2002), surfaces with bounded Wilmore energy. This impres- Alexander Brudnyi (2003), Vinayak Vatsal (2004), Ravi sive research is described by Dr. Alexakis himself in Vakil (2005), Iosif Polterovich (2006), Tai-Peng Tsai the Fall 2013 edition of the Bulletin du CRM. (2006), Alexander E. Holroyd (2007), Gregory G. Smith (2007), József Solymosi (2008), Jonathan Taylor (2008), The André-Aisenstadt Prize Valentin Blomer (2009), Omer Angel (2010), Joel Kam- nitzer (2011), Marco Gualtieri (2012), and Young-Heon Created in 1991, the André-Aisenstadt Mathematics Kim (2012). Prize is intended to recognize and reward research

The CRM–SSC Prize 2013 Awarded to Derek Bingham

Derek Bingham obtained Statistics in the Department of Statistics and Actuarial a B.Sc. in Applied Mathe- Science. matics at Concordia Uni- D. Bingham’s research interests lie in the design and versity in 1991. After sev- analysis of experiments in the physical and engineer- eral co-op jobs that were ing sciences. He has made contributions in the devel- entirely statistical in na- opment of statistical methodology for the design and ture, he decided to pur- analysis of experiments on complex computer simu- sue an M.Sc. in Statis- lators, fractional factorial designs for multi-stage ex- tics at Carleton Univer- periments, and optimal robust parameter designs for sity where he received product variation reduction. Much of his research has the Senate Medal in 1994 been motivated through scientific collaborations. For for his thesis work. Derek example, his work on fractional factorial split-plot de- also worked full-time Derek Bingham signs arose from interactions with scientists in the for- at Andersen Consulting est industry. Recent work on computer experiments from 1993 to 1995. He moved out west in 1995 to pur- and uncertainty quantification is the direct result of sue his Ph.D. studies at Simon Fraser University (SFU) collaboration with scientists at the Los Alamos Na- under the supervision of Randy Sitter. He received his tional Laboratory, the US National Center for Atmo- Ph.D. from the Department of Mathematics and Statis- spheric Research, and the Center for Radiative Shock tics at SFU in 1999, winning the Governor General’s Hydrodynamics at the University of Michigan. A com- Gold Medal. After graduation he joined the Depart- mon theme in this work is the development of a frame- ment of Statistics at the University of Michigan as an work for assessing the uncertainty in predictions made Assistant Professor. In 2003 he moved back to SFU from mathematical or computer models of physical as the Canada Research Chair (Tier II) in Industrial processes.

42 CRM Prizes

During his career, D. Bingham has published over The CRM–SSC Prize forty papers in peer-reviewed journals and other ref- ereed contributions. His work has appeared regularly The SSC, founded in 1977, is dedicated to the promo- in top-tier journals on statistics and experimental de- tion of excellence in statistical research and practice. sign, including the Annals of Statistics, the Journal of The prestigious CRM–SSC Prize, jointly sponsored by the American Statistical Association, Biometrika, and the SSC and the CRM, is given each year to a Canadian Technometrics. He co-authored a paper on variable se- statistician in recognition of outstanding contributions lection in computer experiments that won the 2006 to the discipline during the recipient’s first 15 years af- Jack Youden Prize for best expository paper published ter earning a doctorate. in Technometrics. He has also published many papers Derek Bingham is the fifteenth recipient of the CRM– in high-impact scientific and engineering journals fo- SSC Prize. The previous winners of the award are cusing on the application of statistical design methods. Christian Genest (1999), Robert J. Tibshirani (2000), His role in the statistics community (at the Canadian Colleen D. Cutler (2001), Larry A. Wasserman (2002), and international level) is important: he is Associate Charmaine B. Dean (2003), Randy Sitter (2004), Jiahua Editor for several journals and he is involved in re- Chen (2005), Jeffrey Rosenthal (2006), Richard Cook search councils and SSC activities, in particular by be- (2007), Paul Gustafson (2008), Hugh Chipman (2009), ing a member of the Development Committee for the Grace Y. Yi (2010), Edward Susko (2011), and Chang- Canadian Statistical Institute. bao Wu (2012).

43 The CRM Outreach Program The CRM Outreach Program

n 2012–2013 several public lectures geared towards a broad audience took place at the CRM. Their format was I the same as the format of the Grandes Conférences du CRM, which feature outstanding lecturers able to convey the beauty and power of mathematical research to a wide audience. The first two lectures below were part ofa CRM program of lectures on the theme “Mathematics of Planet Earth 2013”; the third and fourth lectures were part of the Cross-Canada Series of Lectures on the same theme. The fifth lecture was part ofthe Grandes Conférences series. In 2012–2013, 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.

Mathematics of Planet Earth 2013 — CRM Public Lectures

Mathematicians Listen as the Earth Rumbles Ingrid Daubechies (Duke University) by Christiane Rousseau (Université de Montréal)

On April 10, 2013, In- physicists to conjecture that these islands arose from grid Daubechies deliv- a volcanic plume, that is, a sort of volcanic chimney ered the fourth MPE through the mantle. (Mathematics of Planet Recall that the mantle depth is approximately equal to Earth) lecture in the Si- half the radius of the Earth. The shifting of the sur- mons Lecture Series. face tectonic plate might explain the successive for- At least 400 persons mation of islands that are aligned, and the age differ- attended her lecture at ences between the islands could be computed by us- the Coeur des sciences ing the distances between them and the speed of the (Université du Québec tectonic plate. Further proof is needed, however, in or- à Montréal). Ingrid der for the scientific community to acknowledge that Daubechies gave her this conjecture is true. One way of proving the conjec- splendid lecture in ture would be to “see” the plume. Remote sensing is a Ingrid Daubechies French and dubbed it tool for exploring the interior of the Earth: one sends herself in English (in front of an empty classroom!). signals towards the interior and analyzes the reflected French and English videos are available at the site or refracted signals on the various layers of the Earth. http://www.videocrm.ca/. This technique is used when looking for oil deposits. Many people associate Mathematics of Planet The plumes are so far below the Earth’s crust, how- Earth 2013 with issues related to climate change ever, that man-made signals are not powerful enough and sustainable development. The lecture by Ingrid for conducting a remote sensing analysis. The only sig- Daubechies, however, fell under the first MPE theme, nals that allow a detailed analysis at such depths are “A planet to discover.” In it Daubechies described her the seismic waves generated by large earthquakes. In- collaboration with geophysicists and their very re- grid Daubechies and her team had access to large data cent results concerning the formation of isolated vol- banks that contain the recordings of seismic waves (as canic islands. On the floor of the oceans, the most captured by various stations across the globe). recent rocks are found along the ridges where tec- Since the data are available, all that is required is a tonic plates diverge. The volcanic activity along those good tool for analyzing them. The problem is not triv- ridges pushes magma from the mantle upwards, and ial. The plumes are very thin and the perturbation of this magma is transformed into new rocks. There ex- a seismic wave speed going through a plume is of the ist, however, isolated volcanic islands such as Hawaii, order of 1%. Two seismologists, Tony Dahlen and Gu- Tahiti, the Azores, Cape Verde, etc. In the Hawaii ust Noleta, contacted Ingrid Daubechies in 2005 to de- archipelago, the islands are aligned in order of determine whether wavelets could help them solve this creasing age, with the largest (and most recent) island problem. Indeed, Raffaella Montelli’s promising results being the easternmost island. This observation led geo- had shown that the analysis of seismic waves allowed

45 Centre de recherches mathématiqes one to detect perturbation zones for pressure waves (P- izontal means and vertical differences of pixel pairs; waves) associated with earthquakes. Such zones had the third matrix contains the vertical means and hori- been identified and there was an exact correspon- zontal differences of pixel pairs; and the fourth matrix dence between them and some isolated volcanic is- contains the horizontal and vertical differences of the lands; the temperature of the ocean floor was higher pixel pairs. This process (i.e., the replacement of ama- in these zones. Because plumes are very thin and the trix by four smaller matrices) is repeated on the first perturbation of the P-waves speed is small, there is matrix. So far no information has been lost. a high risk of making an error when reconstructing Ingrid Daubechies explained how wavelets allow one the Earth’s internal structure, unless one makes use of to compress information and how details in a small re- high-performance tools. In this regard wavelets are the gion can be extracted (in spite of the fact that much in- perfect tool for analyzing local details in small regions. formation has been compressed). The use of wavelets Moreover wavelet analysis allows one to concentrate in image reconstruction prevents errors in numeri- on those small regions and disregard the other regions. cal reconstruction and ensures that the singular re- During her lecture, Ingrid Daubechies gave a mini- gions identified within the image are indeed special. course on wavelet analysis as it is applied to digital im- Ingrid Daubechies displayed “clean” images produced ages. By grayscale digital image we mean a matrix of by wavelet analysis (i.e., images from which artificial numbers including, for each pixel, the “gray intensity” regions have been removed). She was able to announce of that pixel. This matrix is used to build four smaller (“hot off the press”) that her collaborators and herself matrices. The first of these contains the horizontal and had obtained the first results for the whole Earth with vertical means of pixel pairs (where the pixels in a pair real data! The public was delighted by her lecture and are neighbours); the second matrix contains the hor- asked many questions.

Königsberg’s Bridges, Holland’s Dikes, and the Fall of Wall Street Paul Embrechts (École Polytechnique Fédérale de Lausanne) by Christian Genest and Johanna G. Nešlehová (McGill University)

more than 150 articles on these research topics. Finan- cial institutions and international regulatory bodies frequently ask him for advice. In his lecture he wished to illustrate (in simple and concrete terms) the contribution of mathematics to the design of protective measures against epidemics, floods, financial crises, and other catastrophes of this nature. The contribution of mathematics lies in the thorough examination of risk factors, the estimation of the probability of exceed- ing critical levels, and the study of contagion and risk propagation in banking and social networks. The lecture began with the famous problem ofthe Paul Embrechts seven bridges in the town of Königsberg: is it possi- The Grandes Conférences du CRM always attract many ble to go around the city while crossing each bridge people, even when they take place on a Friday night. one time and one time only? Euler proved that it is not Furthermore, on May 10, 2013, the lecture was tak- possible and gave a simple and general technique to ing place within the 8th edition of the “24 heures de solve the problem, for any number of bridges and any science”, which attracted a large audience. This audi- bridge configuration. Euler’s solution marked the be- ence was wondering what relations existed between ginning of graph theory. In his lecture Paul Embrechts “Königsberg’s bridges, Holland’s dikes, and the fall of demonstrated the use of graph theory for modelling Wall Street” (the topics mentioned in the title of Paul the complex interdependence network between finan- Embrechts’ lecture). Paul Embrechts specializes in the cial institutions and evaluating the risk of a bankruptcy theory of extreme values and quantitative risk man- bringing about the collapse of the world’s financial sys- agement. He has written several influential books and tem (because of cross-undertakings). Basing himself on

46 The CRM Outreach Program results published in Nature in August 2012, he also ex- dict and evaluate black swan events and try to avoid plained how statistical and graphical tools have been them. used to evaluate the increase in the systemic risk dur- As they say, it never rains but it pours! Large floods oc- ing the mortgage loans crisis, when the risk of a single cur in several regions simultaneously; the movements default triggering a domino effect was very high. of the stock market often trigger the simultaneous fall On a conceptual level, the protection of banks against of many assets; and several debtors may all of a sudden default risks is similar to the defense of the North Sea become unable to fulfill their engagements. When they flat country against floods and storm tides. Nowadays, forget this, financial institutions underestimate their in many places, regulatory bodies demand that finan- risk. In 2009 the media blamed the downfall of Wall cial institutions set aside capital reserves large enough Street on the “Gaussian copula”, which financial ana- to offset the risk of large monetary losses. These cap- lysts were using to compute the probability of multi- ital reserves play a role analogous to that of dikes ple payment defaults (see for instance “The Formula along the seashore. After the devastating tidal wave that Killed Wall Street” in the Financial Times of April that occurred in 1953, the government of the Nether- 24, 2009). Paul Embrechts told his audience that this lands started building large engineering structures to comment by the media made as little sense as blam- protect the shore. By taking costs and various technical ing the formula E = mc2 (due to Einstein) for the constraints into account, the Delta Works Commission destruction caused by atomic bombs! He also stated determined an acceptable level of flood risk for each of that it was ironical to accuse university researchers of the relevant regions. For instance, it was agreed that having caused the crisis (at least indirectly), because in the south of Holland, dikes should be able to with- they have never stopped pointing out the deficiencies stand a flood occurring at most once every 10000 years. of the methods used in the financial industry. As early How can one estimate such a risk when there are no as 1998, Paul Embrechts and his team had warned that data on the magnitude of a flood occurring once every the “Formula that Killed Wall Street” underestimated, 10000 years? Paul Embrechts explained that the theory to a considerable extent, the risk of simultaneous ex- of extreme values enables one to extrapolate beyond treme events. the observed values. It is noteworthy that the research At the end of this fascinating lecture, many people in carried out in this field is due, to a large extent, to prob- the audience must have pondered the concluding re- abilists and statisticians who grew up in the vicinity of mark by Professor Embrechts, which concerned the the North Sea. Paul Embrechts himself was born a few importance of communication. Scientific excellence days after the 1953 tidal wave, very close to the affected and best practices go hand in hand thanks to a con- region. stant dialogue. The powerful stochastic models and in- In finance, the bestsellers by Nassim Nicholas Taleb ference techniques that are available to us will yield have popularized the phrase “black swan,” which de- their full potential only if their users listen to the re- notes a rare and unpredictable event having major con- searchers instead of considering them as scientists en- sequences. Thus it should not surprise us that infi- sconced in their ivory towers. nance, the theory of extreme values can be used to pre-

47 Centre de recherches mathématiqes

Mathematics of Planet Earth 2013 — Cross-Canada Series of Lectures

The Mathematics of Light and Sound Nilima Nigam (Simon Fraser University) by Jacques Hurtubise (McGill University)

the school of Vaisheshika), to the 17th century (with Newton’s experiments pointing to the corpuscular nature of light and Huygens’ arguments in favour of the wave nature of light) and the 19th and 20th centuries (with experiments on diffraction and the photoelectric effect that led to the wave-particle duality). As for sound, Nilima Nigam started from the har- mony of spheres and spoke about the experiments for analyzing the harmonics of sound, while displaying sonograms of a few simple sounds but also of James Brown’s voice. She analyzed for her audience the sym- Nilima Nigam metries underlying Bach’s music and explained the successive refinements in our understanding of the so- Within the framework of the MPE series organized by lutions to wave equations. She concluded her lecture the Canadian Mathematical Society and the Canadian with a very modern theme: the possibility of making Mathematical Institutes, Professor Nilima Nigam gave some regions of the space impervious to sound or light a superb public lecture on February 15, 2013. In front waves by a fine-tuning of refraction indices. Although of a large audience, she presented and developed vari- this has not been achieved in the case of visible light ations on the themes of sound and light, especially fo- waves, it has been demonstrated recently that some cusing on the description, the understanding, and the regions can be made impervious to micro-waves or exploration of these phenomena. Nilima Nigam gave a sound waves. In summary, Nilima Nigam gave us ac- sweeping historical account of the study of light, from cess to a broad spectrum of science and mathematics, the Greeks (i.e., Empedocles) and the Romans (i.e., Lu- which bodes well for the other lectures in the series cretius), through the Indians of the same period (i.e., (http://cms.math.ca/Events/MPE2013/).

The mathematics of ‘fracking’ Anthony Peirce (University of British Columbia)

“Fracking” is used by of a pressurized viscous fluid. In his lecture Anthony the oil and gas indus- Peirce provided examples of natural HF and situations try to enhance the pro- in which HF techniques are used in industrial prob- duction of hydrocarbons. lems. Natural examples of HF include the formation Recently there has been of dykes by the intrusion of pressurized magma from considerable controversy deep chambers. They are also used in a multiplicity of surrounding the frack- engineering applications, including: the deliberate for- ing process due to en- mation of fracture surfaces in granite quarries; waste vironmental concerns. disposal; remediation of contaminated soils; cave in- Fracking makes use of a ducement in mining; and, as mentioned above, the process called hydraulic fracturing of hydrocarbon bearing rocks in order to fracturing (HF) by which enhance productivity of oil and gas wells. Novel and tensile fractures are in- Anthony Peirce emerging applications of this technology include CO2 duced to propagate in brittle materials by the injection

48 The CRM Outreach Program sequestration and the enhancement of fracture net- tance in the location of the fracture-free boundary. He works to capture geothermal energy. also discussed the challenges for efficient and robust Anthony Peirce showed how dimensional reasoning numerical modelling of the 2-3D HF problem and some can be used to identify the fundamental power-law techniques recently developed to resolve these prob- relationships between the variables depending on the lems, including: a novel Implicit Level Set Algorithm balance between the dominant physical processes that for solving the free boundary problem; an Extended are active. He described the governing equations in 1- Finite Element (XFEM) methodology for HF; and a 2D as well as 2-3D models of HF, which involve a cou- Kalman Filter methodology to identify the location of pled system of degenerate nonlinear integro-partial propagating fractures from remote measurements. The differential equations as well as a free boundary. He efficacy of these techniques was demonstrated with demonstrated that a re-scaling of these models and numerical results. The interested reader may consult dominant balance arguments can be used to identify the site http://www.math.ubc.ca/~peirce. special asymptotic solutions that are of crucial impor-

Grandes Conférences du CRM

From Einstein to Wheeler: Throwing Some Light on the Wave-Particle Duality Alain Aspect (Institut d’Optique, Palaiseau) by Gilles Brassard (Université de Montréal)

On October 25, mystery of quantum mechanics, changed his mind 2012, the lecture later on and acknowledged that intrication is as mys- hall of the Good- terious as duality. It is remarkable that Aspect’s work man Agora was full shed light on two mysteries! of people enjoying The conference began with a history of a fascinating a splendid “Grande question: what is the nature of light? More precisely, is Conférence” de- it composed of waves or particles? From ancient Egypt livered with hu- and Greece, Alain Aspect led his audience to the debate mour and rigour between Huygens and Newton more than three cen- by Alain Aspect, turies ago. Huygens could explain in a simple fashion a French physi- the well-known phenomena of reflection and refrac- cist who is also tion while Newton argued that the chromatic decom- a professor at the Alain Aspect position of light through a prism indicated that light Institut d’Optique was composed of particles of various colours. New- (Palaiseau, France). Alain Aspect is an expert popu- ton’s fame ensured the adoption of his views by sci- ralizer of science: he apologized to his audience after entists, at least until the work of Young and Fresnel his very first equation, saying that even people who in 1822: it is then that the “wave” won out, because of cannot read music can appreciate a good concert. He interference, diffraction, and polarization phenomena, is considered as a potential Nobel Prize winner, on particularly the “Young’s slits” experiment. This exper- account of work carried out at the beginning of the iment consists of letting a beam of light go through 1980s and demonstrating (on a distance of several me- two slits and observing so-called interference bands, ters) the reality of quantum intrication, a phenomenon i.e., bands that are alternatively bright and dark, on viewed by Einstein as troublesome. Alain Aspect did a screen behind the slits. Around thirty years later, not address this topic, however, but the wave-particle Maxwell determined that light waves were actually duality, a phenomenon whose complete reality was electromagnetic waves. Everything seemed so clear at demonstrated for the first time by himself a few years that point that one could be forgiven for thinking, at later. Note that Richard Feynman, renowned for hav- the end of the XIXth century, that the study of the- ing said that the wave-particle duality is the first great oretical physics was complete. Lord Kelvin, however,

49 Centre de recherches mathématiqes pointed out that two unexplained “clouds” remained, lated photons (also called “unique photons”). This ex- and these clouds gave rise to the two great revolutions periment was finally carried out in 1985 by Alain As- in XXth century physics: relativity and quantum me- pect and his first doctoral student, Philippe Grangier. chanics. Alain Aspect stated boldly that the latter was How does one produce unique photons? With a dead- the most extraordinary theory ever devised by the hu- pan sense of humour, Alain Aspect began his expla- man species. nation by giving us a so-called “kitchen recipe”. While In 1905 Einstein had the audacity of proposing a “par- going from an excited state to its ground state, an atom ticle” theory of light in order to explain the photo- produces one and only one photon. Thus to produce a electric effect. This heretical theory was not immedi- unique photon, it suffices to take a single atom, to “ex- ately accepted and Millikan tried to show that is was cite” it, and to wait! Unfortunately no one knew how false through experiments, but these experiments ac- to isolate an atom in 1985. In looking for a method tually corroborated Einstein’s theory in 1915 and Ein- of producing unique photons, Alain Aspect took his stein won the Nobel Prize for Physics in 1922. How can inspiration from the montage that had allowed him one reconcile this “particle definition” of light with the to prove the existence of intrication a few years be- diffraction, interference, and polarization experiments fore. One designs an assembly of atoms emitting mil- by Young and Fresnel? Is light a wave or does it consist lions of photons every second, but these photons are of particles? Einstein answered this question in 1909 by emitted in pairs of different colours. Each emission of putting forward the wave-particle duality, which was a green photon (551 nm) is followed, a few nanosec- at the heart of Alain Aspect’s lecture. This theory pos- onds later, by the emission of a violet photon (423 nm). tulates that light is composed of indivisible particles Hence one only has to detect green photons to know (which have been called “photons” since 1926), but that whether they are the “harbingers”, with a high proba- each photon can behave like a wave and in particular bility, of the emission of a unique violet photon. At the interfere with itself when going through two slits. How time this montage required a cumbersome equipment can we know whether this is a good model of light? whose manipulation was akin to an art. Alain Aspect could not refrain from mentioning that this experiment In the 1950s Feynman imagined a thought experiment can be carried out nowadays in a “disgustingly simple” with a purely pedagogical goal. If one could redo the fashion! Young slits’ experiment by sending one photon at a time towards the slits, then one could exclude the Alain Aspect and Philippe Grangier were at last able classical theory, according to which a photon going to realize the thought experiment proposed by Richard through one of the slits interferes with another photon Feynman and to observe (naturally) the results pre- going through the other slit. Feynman was not suggest- dicted by quantum mechanics. Thus it took more than ing to carry out this experiment since nobody was able 75 years to verify the theory of wave-particle duality to manipulate individual photons at the time! It is easy, first stated by Einstein in 1909! But neither the story however, to emit a light beam containing a number of nor the lecture ended with this achievement: on the photons following a Poisson law whose intensity can contrary, things became even more fascinating. be chosen a priori. This seems to entail the feasibility When our photon comes across a beam splitter, will it of an experiment with a beam so thin that the pho- behave like a wave and follow the two paths simulta- tons would go through the slits one by one, like the neously (like the photon of Young’s experiment, which drops of a faucet that leaks very slowly. Unfortunately goes through the two slits at the same time) or like a this would not correspond to Feynman’s experiment, particle and follow one of the two paths? It seems that since the Poisson law still allows for the possibility of this “decision” depends upon what will be “required” of several photons within a very short interval. Indeed, the photon later on! If the two potential paths are re- a mathematical computation shows that a purely cla- combined, then an interference phenomenon will oc- sical theory, in which no photon goes through more cur, which suggests a “wave-like” behaviour. On the than one slit, accounts in an exact fashion for the in- other hand, if one attemps to detect the two paths inde- terference phenomena that would be observed in such pendently, only one of the “detections” will be success- an experiment! ful, which suggests a “particle-like” behaviour. Does Therefore, if one wishes to realize Feynman’s experi- the photon that comes across a beam splitter have to ment in practice, one must get hold of a source of iso- “open out its antennas” (this is my phrase) in order to

50 The CRM Outreach Program choose a behaviour depending upon the continuation How is all of this possible? Alain Aspect suggested that of its path? In 1978 John Archibald Wheeler proposed “when one does not understand anything any more, a thought experiment called “delayed choice”, in which one goes back to Niels Bohr” and added (with a smile) the continuation of the photon path is chosen ran- that Bohr’s writings are “like those of Nostradamus.” domly just after the photon has gone through the beam Indeed they are often very obscure. Aspect provoked splitter. By now you must have guessed that Alain As- the laughter of the audience by stating that in Bohr’s pect did also carry out this experiment (in 2007) and explanations, one finds not only the wave-particle du- that quantum mechanics triumphed one more time! ality but the complementarity between accuracy and Note that other researchers had carried out this exper- clarity. He also said that “with geniuses, one is allowed iment before him, but not with a source of unique pho- to make jokes!” tons; hence their experiments did not prove anything. Aspect concluded his lecture by outlining the concept Alain Aspect concluded this section of his lecture by underlying quantum cryptography, which he calls a stating that “the delayed choice experiment is hard on “true revolution” (thank you!) and proves that ask- the photon!” Being modest (as always), he added that ing fundamental questions may lead to practical ap- his experiment had succeeded because “we had very plications. Allow me to add: “Long live fundamental good students.” Let us mention particularly Vincent research!” Our unforgettable lecturer gave us a last Jacques, the first doctoral student of Jean-François Roy, present, a family snapshot depicting four generations himself the first doctoral student of Philippe Rangier of researchers: Vincent Jacques, Jean-François Roch, (Alain Aspect’s first doctoral student, as you may re- Philippe Grangier, and of course Alain Aspect himself. call). It is a great family history! This magical night ended with thunderous applause. Thank you Alain for your generosity!

51 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 associations. 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 ports visits of French mathematicians to members of Mathematical Sciences and the Pacific the CRM and vice versa. In 2012-2013 the following Institute for the Mathematical Sciences French mathematicians visited the CRM: Marie Al- benque (CNRS, Palaiseau), Mattia Cafasso (Angers), Since the early 1990s two other research institutes Pierre Conte (CEA/Saclay), Virgile Ducet (Ph.D. stu- have joined the CRM on the Canadian scene: Toronto’s dent in Marseille), Gérard Freixas i Montplet (CNRS, Fields Institute for Research in Mathematical Sciences Paris), Emmanuel Fricain (Lille), Carlo Gasbarri (Stras- and the Pacific Institute for the Mathematical Sciences bourg), Paolo Ghiggini (CNRS, Nantes), Pierre Ille (PIMS). As well as coordinating their scientific activi- (CNRS, Marseille), Muath Karaki (Ph.D. student in ties, the three institutes have worked closely on a va- Lille and Lyon), Annalisa Panati (Toulon), Vincent Pi- riety of initiatives, the most important of which is the laud (CNRS, Palaiseau), Claude-Alain Pillet (Toulon), Mprime network. The three institutes are also involved Jean-Philippe Préaux (Marseille), Erwan Rousseau in other initiatives, such as the CRM–Fields–PIMS (Marseille), and Sheila Sandon (CNRS, Strasbourg). Prize awarded in recognition of outstanding accom- Three Montréal researchers (Louigi Addario-Berry, plishments in the mathematical sciences in Canada. It from McGill, Laurent Habsieger, the UMI director, was created in 1994 as the CRM–Fields Prize and be- and Geña Hahn, from the Université de Montréal) came the CRM–Fields–PIMS Prize in 2006. The admin- visited colleagues in France thanks to the UMI. For istrative responsibility for this prize rotates between more information we refer the reader to the site the three institutes. www.crm.umontreal.ca/UMI/. In 2012-2013 the relationship between the CRM and French researchers also National and International Collaborations resulted in the organization of two colloquia within the Entretiens Jacques-Cartier: a colloquium on risk man- The CRM collaborates with research centres inthe agement and a colloquium on mathematical physics. Montréal area, especially the Groupe d’études et de re- We refer the reader to the section on the CRM general cherche en analyse des décisions (GERAD). The CRM, program for reports on these colloquia. the ISM, and GERAD jointly organize a weekly statistics colloquium (see the section General Program). The The CRM has signed agreements with the European CRM is a partner of the Banff International Research Union. For instance, in 2006 the CRM and the ISM Station (BIRS). signed an agreement with the ALGANT consortium (where ALGANT stands for Algebra, Geometry, Num- The researchers belonging to the CRM or a CRM lab- ber Theory) to further the exchange of graduate stu- oratory enjoy close collaborations with French col- dents. In 2010 the CRM was one of the 12 partners leagues, in particular CNRS and INRIA researchers. to sign an agreement with SISSA (an Italian centre) to In 2011 an Unité Mixte Internationale (UMI) of the promote exchanges of visiting researchers specializing CNRS was established at the CRM. This UMI sup-

53 Centre de recherches mathématiqes in mathematical physics. SISSA (International School ical sciences, bringing together academia, industry, for Advanced Studies, in English) is based in Trieste and the public sector to develop cutting edge mathe- and is a university dedicated to the training of grad- matical tools vital to our knowledge-based economy. uate students. In December 2012 the CRM signed an Known as Mitacs (Mathematics of Information Tech- agreement with the Institute of Mathematics and Com- nology and Complex Systems) from 1999 to 2011, it puter Science of the Academy of Sciences of Moldova. is a pan-Canadian network whose creation was pro- The purpose of this agreement is to exchange profes- posed by the three Canadian mathematical sciences in- sors for lectures and research projects, to conduct joint stitutes (the CRM, the Fields Institute for Research in research projects, and to support joint supervision and Mathematical Sciences, and PIMS). The organization tutoring of Ph.D. students. now called Mathematics of Information Technology The CRM has signed two agreements with the TataIn- and Complex Systems is not focused solely on math- stitute of Fundamental Research (TIFR), a prestigious ematics but on the development of the next generation research centre in India. The scope of the first agree- of innovators with vital scientific and business skills ment was applied mathematics and it was signed in (see www.mitacs.ca). 2006 between the CRM and the TIFR Centre for Appli- The purpose of the Mprime network (formerly known cable Mathematics in Bangalore. The scope of the sec- as Mathematics of Information Technology and Com- ond agreement was pure mathematics and was signed plex Systems) was to lead Canada’s effort in the gen- in 2011 between the CRM and the Mumbai TIFR. eration, application, and commercialization of new In its publishing activities, the CRM is continuing its mathematical tools and methodologies within a world- partnership with the American Mathematical Society class research program. In order to do so, Mprime initi- (AMS), in particular through its two series of joint pub- ated and fostered linkages with industrial, governmen- lications, the CRM Monograph Series and the CRM tal, and not-for-profit organizations. Mprime research Proceedings & Lecture Notes. A CRM Series in Mathe- focuses on five key sectors of the economy: biomedical matical Physics is published by Springer. The CRM has and health sector; environment and natural resources; exchange agreements with the Fields Institute for Re- information processing; risk and finance; and commu- search in Mathematical Sciences, PIMS, the MSRI, the nication, networks, and security. Institute for Mathematics and its Applications (Uni- Atlantic Association for Research in the versity of Minnesota), the École normale supérieure Mathematical Sciences (AARMS) (France), the Isaac Newton Institute, the Institut des Hautes Études Scientifiques (France), and BIRS. AARMS was founded in March 1996 at a time when the National Network for Research in the Mathemati- Associations and Professional Societies cal Sciences was being discussed and planned. AARMS The CRM maintains close ties with the different pro- exists to encourage and advance research in all mathe- fessional societies in the mathematical sciences: CMS, matical sciences (including statistics and computer sci- CAIMS, SSC, and CAP. The president of the CMS is an ence) in the Atlantic region. In addition AARMS acts as ex-officio member of the International Scientific Advi- a regional voice in discussions of the mathematical sci- sory Committee of the CRM. The CRM has also sup- ences on a national level. Since its inception, AARMS ported financially certain initiatives of the CMS, such has played an important role in the research activities as the mathematical camps. Together with the other in the Atlantic region, sponsoring or co-sponsoring institutes, the CRM organizes or sponsors special ses- numerous meetings and workshops. In the summer sions at the CMS, CAIMS, and SSC meetings. The CRM of 2002, AARMS initiated an annual Summer School awards a prize each year jointly with the SSC; simi- for graduate students and promising undergraduates. larly, it awards a prize each year with the CAP in math- AARMS is grateful to Canada’s three mathematical in- ematical and theoretical physics. stitutes (the CRM, the Fields Institute for Research in Mathematical Sciences, and PIMS), as well as to the The Mprime Network member universities, for providing funding for its activities. Its member universities are Acadia University, The Mprime network (www.mprime.ca) is the only Cape Breton University, Dalhousie University, Memo- Network of Centres of Excellence for the mathemat- rial University of Newfoundland, Mount Allison Uni-

54 CRM Partnerships versity, St. Francis Xavier University, Saint Mary’s and teaching releases so that University of Ottawa fac- University, the Université de Moncton, the University ulty members can undertake research with colleagues of New Brunswick, and the University of Prince Ed- in the laboratories of the CRM or participate in the sci- ward Island. Finally AARMS receives some financial entific activities of the CRM. support from the provinces of New Brunswick and Nova Scotia. One can find information on the activi- CRM–University of Ottawa Distinguished ties of AARMS at the following web site: http://www. Lecture Series aarms.math.ca. The series features talks by prominent mathematicians Academic Partners from Canada and abroad on topics at the forefront of today’s mathematical research. In 2012–2013 there The activities of the CRM rest on a solid basis ofco- were two such talks at the University of Ottawa. operation with regional universities, in particular the Free probability and random matrices, by Alice Guion- Montréal universities, and most particularly the Uni- net (MIT), on March 1st, 2013 versité de Montréal, whose support for the CRM has been unfailing. The Université de Montréal releases Familles d’algèbres de quaternions et d’octonions, by five of its faculty members to work at the CRMeach Philippe Gille (École Normale Supérieure, Paris), on year, and the support of these faculty members is an April 5, 2013 essential asset for the scientific activities of the CRM. There is in addition a regular program of teaching re- Network for Computing and Mathematical leases for the other Montréal universities, bringing the Modeling (ncm₂) equivalent of another two positions to the CRM each The CRM is one of the founding members ofthe year. On an ad-hoc basis linked to the thematic pro- Network for Computing and Mathematical Modeling gram, the CRM has also been arranging the release of (ncm₂), a network created by several research cen- research personnel from nearby universities such as tres in order to respond to the needs of industry in Laval, Sherbrooke, Queen’s, and Ottawa. The partner- fields related to computing and mathematical mod- ships of the CRM with the other research institutes in elling. The research of the network focuses onfive the Montréal area have been very profitable. major themes: risk management, information process- With the financial support of the Université de Mont- ing, imaging and parallel computing, transport and réal, McGill University, the Université du Québec à telecommunications, and health and electronic com- Montréal, Concordia University, and Université Laval, merce. The ncm₂ was founded by the CRM, the Centre as well as grants from NSERC and the Fonds de re- de recherche en calcul appliqué (CERCA), the Cen- cherche du Québec – Nature et technologies (FRQNT), ter for Interuniversity Research and Analysis on Or- the CRM finances the activities of its nine laboratories, ganizations (CIRANO), the Centre for Research on which collectively represent the most active branches Transportation (CRT), the Computer Research Insti- of the mathematical sciences. These laboratories are tute of Montréal (CRIM), and the Institut national de la the perfect illustration of scientific vitality and serve to recherche scientifique – Télécommunications (INRS- feed the national and international scientific programs Télécom). At the present time the following centres are of the CRM. The reader may refer to the section Re- members of the ncm₂: CIRANO, CRM, CIRRELT, INRS- search Laboratories for a description of the activities ÉMT, and GERAD. of each of these laboratories. Regroupement Neuroimagerie/Québec Association with the University of Ottawa (RNQ)

In 2003, the Department of Mathematics and Statistics In recent years, the PhysNum laboratory of the CRM of the University of Ottawa became a member of the has developed a strong collaborative network with var- CRM. In partnership with the University of Ottawa, ious partners in neuroimaging in the Montréal area. the CRM cofinances the CRM–University of Ottawa This network became an officially recognized network Distinguished Lecture Series, postdoctoral fellowships, with the founding of the Regroupement Neuroima- gerie/Québec (RNQ), under the umbrella of the Insti-

55 Centre de recherches mathématiqes tut universitaire de gériatrie de Montréal. One of the imaging at FMPMC Pitié-La Salpêtrière (Paris), whose strongest alliances of the CRM within that network director is Dr. Habib Benali. is its association with the Inserm laboratory for brain

Joint Initiatives

The annual meetings of the CMS, SSC, and CAIMS, as 2012 CMS Summer Meeting well as some of their training and promotion activi- June 2–4, 2012, Regina ties, are jointly sponsored by the CRM, the Fields In- http://cms.math.ca/Events/summer12/ stitute for Research in Mathematical Sciences, PIMS, 40th Annual Meeting of the Statistical Society of and Mprime. The annual meetings of the societies Canada allow Canadian mathematicians and statisticians to June 3–6, 2012, Guelph keep abreast of their colleagues’ work, to organize ses- http://www.ssc.ca/en/meetings/2012/ sions on emerging topics, and attend lectures given Canadian Applied and Industrial Mathematics Annual by world-renowned mathematicians or prize winners. Meeting, CAIMS 2012 One can find more information on the societies bycon- June 24–28, 2012, the Fields Institute for Research in sulting their respective web sites (http://www.cms. Mathematical Sciences math.ca/, http://www.ssc.ca/, and http://www. http://www.fields.utoronto.ca/programs/ caims.ca/). Note that the CRM was the host of the scientific/11-12/CAIMS_SCMAI/ 2012 CMS Winter Meeting, which took place at the Fairmont Queen Elizabeth Hotel in Montréal. 2012 CMS Winter Meeting December 7–10, 2012, Fairmont Queen Elizabeth, Montréal http://cms.math.ca/Events/winter12/

56 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 journal 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 colloquia, 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 fellows to supervise undergraduate students doing re- of its member departments, in order to turn them into search. a great school of mathematics. Thus the ISM coordinates the graduate studies of the mathematics depart- CRM–ISM Postdoctoral Fellowships ments, supports the sharing of expertise among its re- The CRM–ISM postdoctoral fellowships enable searchers, and facilitates student mobility between the promising young researchers to devote themselves to Montréal 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. Also they are a vital quium, the CRM–ISM–GERAD Statistics Colloquium, link between the professors and the students, espe-

58 Mathematical Education cially when they organize on their own study groups Olivier Gingras (Montréal) on emerging topics. Scholarship co-financed by Pavel Winternitz Supervisor : Danilo Riglioni CRM–ISM 2012–2013 Postdoctoral Fellows Topic : Superintegrable systems Jessica Banks (Ph.D., Oxford) works with Steven Duration : May 1 – August 31 (3.5 months) Boyer in the field of low-dimensional topology, espe- Samuel Laferrière (McGill) cially knot theory. Scholarship co-financed by Frédéric Rochon Vorrapan Chandee (Ph.D., Stanford) works with Supervisor : Carl Tipler Chantal David and Andrew Granville on analytic and Topic : Riemann-Roch theorem on singular surfaces probabilistic number theory, L-functions, the theory Duration : May 1 – July 31 (3 months) of random matrices, and quadratic forms. Thomas Ng (McGill) Adam Harper (Ph.D., Cambridge) works with An- Scholarship co-financed by Dmitry Jakobson drew Granville in analytic number theory. Supervisor : Suresh Eswarathasan Dmitry Kolomenskiy (Ph.D., Université de Pro- Topic : Spectrum and eigenfunctions of Laplacian on vence) works in applied mathematics with Robert compact, finite area and infinite area hyperbolic sur- Owens and Jean-Christophe Nave. faces Duration : May 1 – July 31 (3 months) Antonio Lei (Ph.D., Cambridge) works with Henri Darmon in algebraic number theory. Manuela Pineros-Rodriguez (Montréal) Alejandro Morales (Ph.D., MIT) works with Fran- Scholarship co-financed by Dimitris Koukoulopoulos çois Bergeron in algebraic and enumerative combina- Supervisor : Mariah Hamel torics. Topic : Encryption, factorization, and primality testing algorithms Yakov Savelyev (Ph.D., Stony Brook) works with Oc- Duration : May 1 – August 31 (4 months) tav Cornea and François Lalonde in symplectic and differential geometry. His main interests are Floer theory William Wright (McGill) and Gromov-Witten theory in dynamical systems and Scholarship co-financed by Henri Darmon mathematical physics. Supervisor : Miljan Brakocevic Topic : Rational points on modular elliptic curves Undergraduate Summer Scholarships Duration : May 1 – August 31 (4 months) Dongliang Zhang (McGill) In collaboration with the CRM and the ISM professors, Scholarship co-financed by David Stephens the ISM awards summer scholarships to promising un- Supervisor : Will Astle dergraduates who want to do research during the sum- Topic : Model selection in complex settings mer and plan to study mathematics at the graduate Duration : May 1–August 31 (4 months) level. These undergraduates are supervised by postdoctoral fellows, who in general are supervising students ISM Graduate Student Conference for the first time. The reader will find below the listof the undergraduate scholars for the summer of 2013. Each year the ISM sponsors and supports the organi- Alex De Serre Rothney (Bishop’s) zation of the ISM Graduate Student Conference (“Col- Scholarship co-financed by Trevor Jones and Brad loque pan-québécois des étudiants de l’ISM”). Orga- Willms nized by and for the students of the partner univer- Supervisors : Trevor Jones and Brad Willms sities, the 14th Conference was held on May 17–19, Topic : Symmetric Toeplitz Matrix 2013, at McGill University. It was organized by Hadi Duration : May 1 – August 31 (4 months) Bigdely, Kael Dixon, Olivier Mercier, and Juan Igna- cio Restrepo and attended by around 80 participants. Nicholas Galbraith (McGill) The program featured five plenary lectures and presen- Scholarship co-financed by Steven Boyer tations by students. The plenary lectures were given Supervisor : Jessica Banks by Marc Lackenby from the University of Oxford (Rei- Topic : Physical Knot Theory dmeister moves for the unknot), Robert Pollack from Duration : May 1 – July 15 (2,5 months)

59 Centre de recherches mathématiqes

Boston University (Congruences and families of modu- cromαth magazine aims to draw more young people to lar forms), David Wolfson from McGill University (The the mathematical sciences. Accromαth, whose editor- Statistical analysis of survival data : A personal journey), in-chief is André Ross, has two issues per year and Yves Bourgault from the University of Ottawa (Modèles is available free of charge in all the high schools and et calculs en électrophysiologie cardiaque), and Moham- cégeps of Québec. Accromαth is designed by an ex- mad Najafi Ivaki from Concordia University (Centro- ceptional team of researchers and instructors with a affine normal flows). Note that Mr. Ivaki was awarded broad experience in the promotion of mathematics; it the Carl-Herz Prize for 2013. provides high school and cégep teachers with stimulat- The following students gave talks during the Confer- ing and topical articles on the most recent discoveries ence: Adam Alcolado (McGill), Jean Auger (Laval), Mo- and applications, as well as articles on the history of hammad Bardestani (Montréal), Léo Belzile (McGill), mathematics and its links with the arts. Yara Elias (McGill), Marc Éthier (Sherbrooke), An- The last year was particularly fruitful for Accromαth. drew Fiori (McGill), Alexandre Foucault (Mont- The Spring 2013 issue was devoted to the Mathemat- réal), Patrick Letendre (Laval), Maryam Lotfipour ics of Planet Earth, so as to be included in the world- (Montréal), Thierry Moisan (Laval), Leta Montopoli wide year on the same theme. More than 8000 copies (McGill), Sébastien Picard (McGill), Emilie Picard- of that issue were printed, thanks to the extraordi- Cantin (Laval), Benoît Pouliot (Laval), Ben Smith nary support of the Canadian Mathematical Society (McGill), Mashbat Suzuki (McGill) et Jean-Sébastien ($1200) and the FRQNT ($2000). Copies of the special Turcotte (Montréal). issue were also printed and distributed in 14 French- speaking African countries, thanks to the support of Promotion of the Mathematical Sciences the Canadian Commission for Unesco ($3000), the In- ternational Commission on Mathematical Instruction Produced by the ISM and financed by the ISM, the ($1000 US), UNESCO ($2000), and the International CRM, the CMS, and the Mprime network, the Ac- Mathematical Union (€2000).

Other Joint Initiatives

56e Congrès de l’Association Mathématique “Sciences et mathématiques en action” and du Québec “Association québécoise des jeux October 12–13, 2012, Cégep de Sainte-Foy mathématiques”

As usual the CRM was a sponsor of the “Association The CRM contributes to the “Sciences et mathéma- Mathématique du Québec” conference, which took tiques en action” program, created by Professor Jean- place at the Cégep de Sainte-Foy and whose theme Marie De Koninck from Université Laval in order to was Les mathématiques ludiques (Recreational mathe- popularize mathematics and science for high school matics). students and the general public. We refer the reader to the site www.smac.ulaval.ca for more information. The CRM also supports the Association québécoise des jeux mathématiques (aqjm.fsg.ulaval.ca).

60 Research Laboratories Centre de recherches mathématiqes

n 2012–2013 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 the Laboratory: Adrian Vetta (algorithmic game theory) and Bruce Shepherd (combinatorial optimization The Applied Mathematics Laboratory is a research net- and graph theory). In the 2012–2013 academic year 17 work of 23 applied mathematicians, engineers, com- M.Sc. students, 27 Ph.D. students, and 15 postdoctoral puter scientists, and chemists, based in Montréal. The fellows were supervised or cosupervised by members Laboratory exists primarily to stimulate research and of the Applied Mathematics Laboratory. About 10 of collaboration in the applied mathematical research ar- these students and PDFs graduated in 2012–2013 and eas of its members by fostering discussion and the cre- they have moved on to positions in industry (Ora- ation of ideas through conferences, workshops, and cle, Nuance) and academia (Texas at Austin, Grenoble, seminars, and the furtherance of research through Montréal, INRS). its visitors’ program and the appointment of talented postdoctoral fellows. The Laboratory is also very con- Members of the Laboratory cerned with the training of young researchers and supports travel and conference attendance of its postdoc- Regular members toral fellows. Robert G. Owens (Montréal), Director (until January The research interests of the Laboratory members are 8th, 2013) quite diverse although there are a number of com- Mechanics, numerical simulation of complex fluids mon threads that make interchange and collaboration Adam M. Oberman (McGill), Director (from January both possible and fruitful. Active areas of research 8th, 2013) represented within the Laboratory include, for exam- Numerical solution and analysis of nonlinear elliptic ple, the application of dynamical systems theory to partial differential equations complex phenomena, high-dimensional chaos, and bi- André D. Bandrauk (Sherbrooke) ology. There is an interest in numerical linear alge- Quantum chemistry bra and its applications, including the design, analysis, Peter Bartello (McGill) and implementation of effective computer algorithms. Turbulence, CFD Amongst the membership one will also find expertise in numerical simulation, applied dynamical systems, Jacques Bélair (Montréal) quantum chemistry, turbulence, combustion, biome- Dynamical systems in physiology chanics, numerical methods in fluid mechanics and Anne Bourlioux (Montréal) electromagnetism, hp-finite element methods, molec- Modelling, numerical simulation in turbulent combus- ular dynamics, control, optimization, preconditioners, tion and large-scale eigenvalue problems. Xiao-Wen Chang (McGill) Numerical linear algebra and applications News and highlights Rustum Choksi (McGill) Calculus of variations, nonlinear partial differential The Applied Mathematics Laboratory has strengths in equations, problems arising in materials science, self- traditional areas of continuous applied mathematics assembly of diblock copolymers and magnetic domain (notably partial differential equations, applied analy- formation in type-1 superconductors and ferromag- sis, and numerical methods), but discrete mathemat- nets ics and optimization are increasingly important in ap- Eusebius J. Doedel (Concordia) plications. From now on these topics will be well rep- Numerical analysis, dynamical systems, differential resented in the Laboratory, because two McGill pro- equations, bifurcation theory, scientific software fessors working in discrete mathematics have joined

62 Research Laboratories

Eliot Fried (McGill) Associate members Mechanics and thermodynamics of continuous media Tucker Carrington (Queen’s) George Haller (McGill) Chemical dynamics Theory of nonlinear dynamical systems, fluid mechan- Martin J. Gander (Genève) ics, Hamiltonian systems, singular perturbation theory Domain decomposition, preconditioning Antony R. Humphries (McGill) Jean-Philippe Lessard (Laval) Numerical analysis, differential equations Dynamical systems, rigourous computational meth- Emmanuel Lorin de la Grandmaison (Carleton) ods, PDEs, delay differential equations, topological Numerical analysis for hyperbolic systems, quantum methods chemistry, complex applications of finite volumes, Nilima Nigam (Simon Fraser) computer science Applied analysis, numerical methods in electromag- Sherwin A. Maslowe (McGill) netism Asymptotic methods, fluid mechanics Paul F. Tupper (Simon Fraser) Jean-Christophe Nave (McGill) Numerical analysis, stochastic processes, statistical Numerical analysis, PDE, interface problems, level set mechanics methods, fluid mechanics, computer graphics Thomas P. Wihler (Bern) Gantumur Tsogtgerel (McGill) Numerical analysis, computational methods for PDEs Applied mathematics, partial differential equations, Jean-Paul Zolésio (INRIA Sophia Antipolis) general relativity Control, optimization Jian-Jun Xu (McGill) Asymptotics and numerical analysis, nonlinear PDEs, materials science

CICMA — Centre Interuniversitaire en Calcul Mathématique Algébrique

Description the work of Gauss and Dirichlet and leading to the modern conjectures of Deligne, Beilinson, and Bloch– CICMA brings together researchers working in num- Kato. On the other hand, the Langlands program pos- ber theory, geometric group theory, and algebraic tulates a close link between arithmetic L-functions and geometry. Algebraic geometry is a broad discipline automorphic representations. Analytic number theory with strong connections to a variety of areas ranging studies profound and subtle questions about the distri- from arithmetic to theoretical physics. Eyal Goren and bution of prime numbers, using powerful techniques Adrian Iovita are leading experts in applying algebro- from analysis, notably the theory of functions of a geometric techniques to problems motivated by num- complex variable and spectral theory. Number theory ber theory, notably the study of Shimura varieties and in all its different flavours is particularly well repre- p-adic cohomology theories. John McKay is one of the sented in the laboratory, with Darmon, Goren, Iovita, instigators of the moonshine program, which ties to- and Kassaei on the arithmetic and automorphic side, gether in a surprising way certain notions in the theory and David, Granville, Kisilevsky, Koukoulopoulos, and of modular forms, arithmetic geometry, and theoreti- Lalín on the more analytic side of the subject. cal physics. Geometric group theory is a vibrant subject that has melded geometric and algebraic methods News and highlights in deep and powerful ways, leading to novel insights in both subjects. Dani Wise and Mikaël Pichot are world- CICMA is well known internationally for attracting renowned specialists in this central area. top quality students and PDFs from around the world. Each year the Laboratory organizes a dazzling array Contemporary algebraic number theory has developed of activities that foster the exchange of ideas between over the last decades following two major trends. On students and researchers, from Montréal and the rest one hand, there is the theory of special values of L- of the world: (a) the Québec-Vermont Number The- functions attached to arithmetic objects, originating in ory Seminar (which has become the most important

63 Centre de recherches mathématiqes forum in Canada for the presentation of the latest de- uli spaces of abelian varieties, Hilbert modular forms, velopments in number theory); (b) the Québec- Maine p-adic modular forms Conference; (c) the Montreal-Toronto Workshops in Andrew Granville (Montréal) Number Theory; (d) the Bellairs Workshop in Num- Analytic number theory, arithmetic geometry, combi- ber Theory (the topic of the May 2013 workshop was natorics “Arithmetic intersection theory on Shimura varieties Heekyoung Hahn (McGill) and derivatives of L- functions”); (e) the SHAPE (Sémi- Eisenstein series, L-functions, trace formula, q-series, naire Henri-Adrian-Payman-Eyal); and (f) The Ana- theta functions and partitions lytic Number Theory Seminar. In the 2012–2013 aca- Adrian Iovita (Concordia) demic year 5 undergraduate students, 28 M.Sc. stu- Number theory, p-adic cohomology dents, 42 Ph.D. students, and 16 postdoctoral fellows Olga Kharlampovich (McGill) were supervised or cosupervised by CICMA members. Combinatorial group theory and Lie algebras Regular members of the Laboratory Hershy Kisilevsky (Concordia) L-functions, Iwasawa theory, elliptic curves, class field Henri Darmon (McGill), Director theory Algebraic number theory, arithmetic geometry, John Labute (McGill) L-functions, Diophantine equations, elliptic curves Pro-p-groups, Lie algebras, Galois theory Hugo Chapdelaine (Laval) Matilde Lalín (Montréal) Algebraic number theory, algebraic geometry Mahler measures, L-functions, zeta functions Chris J. Cummins (Concordia) Claude Levesque (Laval) Group theory, modular functions, moonshine Algebraic number theory, units, class number, cyclo- Chantal David (Concordia) tomic fields Analytic number theory, L-functions Michael Makkai (McGill) Jean-Marie De Koninck (Laval) Mathematical logic Analytic number theory: distribution of prime num- John McKay (Concordia) bers, factorization of numbers, asymptotic behaviour Computational group theory, sporadic groups, compu- of arithmetic functions, Riemann zeta function tation of Galois groups David S. Dummit (Vermont) M. Ram Murty (Queen’s) Algebraic number theory, arithmetic algebraic geome- Number theory: Artin’s conjecture, elliptic curves, try, computational mathematics modular forms, automorphic forms, Langlands pro- David Ford (Concordia) gram, Selberg’s conjectures, sieve methods, cryptogra- Computational number theory, algorithmic number phy theory Damien Roy (Ottawa) Jayce R. Getz (McGill) Transcendental number theory Number theory Peter Russell (McGill) Eyal Z. Goren (McGill) Algebraic geometry Arithmetic geometry, algebraic number theory, mod- Francisco Thaine (Concordia) Cyclotomic fields, cyclotomy, rational points on curves

CIRGET — Centre Interuniversitaire de Recherches en Géométrie et Topolo- gie

Description experience of the universe. They are a focal point of modern mathematics and indeed several domains of Geometry and topology are fundamental disciplines mathematics have recently shown a strong trend to- of mathematics whose richness and vitality, evident wards a geometrization of ideas and methods: two throughout human history, reflect a deep link to our cases in point are mathematical physics and number

64 Research Laboratories theory. CIRGET, based at UQAM, is composed of sev- Octav Cornea (Montréal) enteen full members, four associate members, and a Algebraic topology, dynamical systems large number of postdoctoral fellows and graduate stu- Pengfei Guan (McGill) dents working in this broad field. The main themes to Partial differential equations, geometric analysis, sev- be pursued in the coming years include the topological eral complex variables classification of 3-dimensional manifolds; the quanti- Jacques Hurtubise (McGill) zation of Hitchin systems and the geometric Langlands Algebraic geometry, integrable systems, gauge theory, program; the classification of special Kähler metrics; moduli spaces the study of symplectic invariants, especially in dimen- André Joyal (UQAM) sion 4; non-linear partial differential equations in Rie- Algebraic topology, category theory mannian geometry, convex geometry, and general rel- Niky Kamran (McGill) ativity; and Hamiltonian dynamical systems. Geometric approach to partial differential equations News and highlights François Lalonde (Montréal) Symplectic topology and geometry, global analysis on In 2012–2013 CIRGET and its members prepared and manifolds, infinite dimensional transformation groups organized three major events: the 2012–2013 Thematic Steven Lu (UQAM) Year; the short program on Rational Points, Rational Chern number inequalities, semistability of tensorial Curves and Entire Holomorphic Curves on Projective sheaves, log jets, log and hyperbolic geometry, alge- Varieties; and the SMS 2013 Summer School. With the braic degeneracy CRM, CIRGET was able to leverage additional fund- Iosif Polterovich (Montréal) ing from a number of international sources, including Geometric analysis, spectral theory, functional analy- over $200,000 from the NSF to support young Ameri- sis, differential geometry, partial differential equations can mathematicians who participated in the activities. Frédéric Rochon (UQAM) Nine of CIRGET’s doctoral students and PDFs finish- Geometric analysis, global analysis on singular spaces, ing in 2012–2013 have obtained positions (tenure-track index theory on manifolds with boundary or permanent): two in Canada, one in Scotland, one in Peter Russell (McGill) Australia, and 5 in France. In the 2012–2013 academic Algebraic geometry year one undergraduate student, 25 M.Sc. students, 30 Ph.D. students, and 24 postdoctoral fellows were su- Johannes Walcher (McGill) pervised or cosupervised by CIRGET members. Mirror symmetry for open strings, nongeometric string compactifications Members of the Laboratory Daniel T. Wise (McGill) Geometric group theory, low-dimensional topology Regular members Associate members Vestislav Apostolov (UQAM), Director Complex geometry, Kähler geometry S. Twareque Ali (Concordia) Steven Boyer (UQAM) Coherent states, wavelets, quantization techniques, Topology of manifolds, low-dimensional geometry and harmonic analysis, Wigner functions topology John Harnad (Concordia) Abraham Broer (Montréal) Mathematical physics, classical and quantum physics, Algebraic transformation groups, invariant theory geometrical methods, integrable systems, group theo- Virginie Charette (Sherbrooke) retical methods, random matrices, isomonodromic de- Discrete group actions on affine varieties, Lorentz formations, isospectral flows manifolds, Riemann surfaces discretization, discrete Dmitry Jakobson (McGill) differential geometry Pure mathematics, global analysis, spectral geometry, Olivier Collin (UQAM) quantum chaos, harmonic analysis, eigenvalues and Invariants of knots and 3-manifolds arising from global eigenfunctions analysis John A. Toth (McGill) Microlocal analysis, partial differential equations

65 Centre de recherches mathématiqes

GIREF — Groupe Interdisciplinaire de Recherche en Éléments Finis

Description Regular members

The recent advances in computer hardware and soft- André Fortin (Laval), Director ware allow researchers to model and simulate physi- Finite elements method, instationary viscous flows, cal phenomena whose complexity is unheard of. These mixing problems problems are characterized by nonlinear laws, non- André Garon (Polytechnique Montréal), Deputy Di- differentiable friction laws, large-deformation geome- rector tries, complex solid-solid or fluid-solid interactions, Thermohydraulics, fluid mechanics, finite elements problems in multiphysics, etc. Such problems can be method, hydraulic turbines, mechanics of biofluids: found everywhere in industrial environments, espe- stents and pumps cially in the design and fabrication of high-technology Youssef Belhamadia (Alberta) products. Thus the members of GIREF (“Groupe In- Mathematical modelling and numerical simulation of terdisciplinaire de Recherche en Éléments Finis,” or phase change problems, adaptive meshing for insta- in English “Interdisciplinary Research Group in Finite tionary problems in 2 and 3 dimensions, numerical Element Methods”) aim to develop original numeri- modelling of cryosurgery, numerical modelling of the cal methods for solving cutting-edge industrial prob- electromechanical wave in the heart lems in nonlinear mechanics. Their work concern pure Yves Bourgault (Ottawa) mathematics, computer science, software engineering, Computational fluid dynamics, numerical methods, fi- and engineering. The GIREF members propose gen- nite elements method, mathematical modelling, me- eral methods that can be used for diverse industrial chanics of continuous media applications. The some 27 member researchers reflect Michel C. Delfour (Montréal) the interdisciplinary nature of the Laboratory and are Control, optimization, design, shells, calculus, biome- based at the Université Laval, the École Polytechnique chanics de Montréal, as well as the Universities of Moncton, Michel Fortin (Laval) Ottawa, and Alberta. Numerical analysis of partial differential equations, numerical methods in fluid mechanics, optimization News and highlights and optimal control for partial differential equations GIREF is active in fluid and solid mechanics. Its in- Robert Guénette (Laval) dustrial partnerships, notably in the fields of pneumat- Numerical methods in non-Newtonian fluid mechanics and manufacturing of wood-based products, give a ics, rheological models, Hamiltonian formulation very applied flavour to the research carried out byits Hassan Manouzi (Laval) members (especially within the NSERC Research Chair Numerical analysis, applications of mathematics to en- in High Performance Scientific Computing held by A. gineering Fortin). GIREF also applies mathematical techniques to Dominique Pelletier (Polytechnique Montréal) problems from biology. GIREF was the official host of Fluid mechanics and heat transfer, finite elements the Annual Meeting of the Canadian Applied and In- method, adaptive finite elements methods for com- dustrial Mathematics Society (CAIMS), which gathered pressible and incompressible flows, modelling and sim- over 200 participants in Québec City in June 2013. In ulation of laminar and turbulent viscous flows, mod- 2013 GIREF recruited N. Doyon, an expert on digital elling and simulation of fluid-structure interactions modelling in the neurosciences, who is now a member Roger Pierre (Laval) of the biomedical modelling group along with Garon Numerical analysis of partial differential equations (École Polytechnique), Delfour (Université de Mont- José Urquiza (Laval) réal), and Bourgault (University of Ottawa). In the Numerical analysis, control of partial differential equa- 2012–2013 academic year one undergraduate student, tions 12 M.Sc. students, 11 Ph.D. students, and 4 postdoctoral fellows were carrying out research at GIREF.

66 Research Laboratories

Associate members Vincent François (UQTR) Integration of the finite elements method into Pierre Blanchet (FPInnovations) computer-aided design Nanotechnology for wood products Yves Fortin (Laval) Alain Charbonneau (UQO) Forestry, forest engineering Numerical simulation of optical wave guides, finite elements method, numerical methods, statistical machine Augustin Gakwaya (Laval) translation, automated text categorization Aerospatial and aeronautical engineering, numerical modelling, computer-assisted design Alain Cloutier (Laval) Forestry, forest engineering Guy Gendron (Laval) Composite materials, optimization and modelling of Marie-Laure Dano (Laval) structures Mechanics and production of composite materials, in- telligent mechanical systems Jean-François Hétu (NRC-IMI) Numerical modelling of processes Claire Deschênes (Laval) Axial hydraulic turbines Jean-Loup Robert (Laval) Numerical models of free surface flows, transport and Guy Dumas (Laval) diffusion models with stochastic components, unified Mechanical engineering, physics of fluids modelling in a saturated and aerated environment Mohamed Farhloul (Moncton) Yves Secretan (INRS-ETE) Finite elements and finite volumes method, partial dif- Numerical methods for finite elements, mesh genera- ferential equations, applications of the mixed finite el- tion and adaptation, error estimation, hydrodynamics ements method to fluid mechanics, numerical analysis in 2 dimensions, advection-diffusion phenomena Marie-Isabelle Farinas (UQAC) René Therrien (Laval) Modelling, numerical simulation, computational fluid Underground water flows, hydrology, geothermics mechanics, design of turbo engines (cardiac pump), optimization

LaCIM — Laboratoire de Combinatoire et d’Informatique Mathématique

Description News and highlights

LaCIM (French acronym meaning “Combinatorics and The main research areas of LaCIM are algebraic com- Mathematical Computer Science Laboratory”) is home binatorics, bioinformatics, and mathematical computer to mathematics and theoretical computer science re- science. The support of the CRM has made it possible searchers whose interests comprise discrete mathe- for 8 full-time postdocs to be involved in the LaCIM matics and the mathematical aspects of computer sci- research activities, on top of all the graduate students ence. Founded in 1989, LaCIM includes 15 regular and undergraduate trainees. It is noteworthy that 25% members, 5 associate members, and 16 collaborating of the talks at this year’s edition of FPSAC (the main in- members. It welcomes postdoctoral fellows and its reg- ternational conference in algebraic combinatorics and ular members supervise or cosupervise many M.Sc. a very selective one) have coauthors who are (current and Ph.D. students, as well as undergraduate and cegep or past) PDFs or students of LaCIM. The expertise of summer research students. Many renowned mathe- the CRM in organizing meetings helped LaCIM hold maticians visit LaCIM and collaborate with its mem- an international conference in Cetraro, Italy, in July bers in the following areas: enumerative and bijec- 2013 (“Words, Codes, and Algebraic Combinatorics – A tive combinatorics, theory of species, algebraic com- conference in honor of Christophe Reutenauer’s 60th binatorics, combinatorics of finite and infinite words, birthday”). In the 2012–2013 academic year 18 M.Sc. discrete geometry, theory of languages and automata, students, 28 Ph.D. students, and 10 postdoctoral fel- Gray codes, bioinformatics, and combinatorial opti- lows were supervised or cosupervised by LaCIM mem- mization. bers.

67 Centre de recherches mathématiqes

Members of the Laboratory to various parameters, use of Pfaffians and determi- nants in enumeration Regular members Cédric Lamathe (UQAM) Srečko Brlek (UQAM), Director Combinatorics of tree-like structures, theory of Combinatorics of words, algorithmics species, indicator series of partially labeled structures Ibrahim Assem (Sherbrooke) and asymmetric structures Representation theory Luc Lapointe (Talca) Anne Bergeron (UQAM) Algebraic combinatorics, symmetric functions, inte- Bioinformatics grable systems, supersymmetries François Bergeron (UQAM) Odile Marcotte (UQAM & CRM) Combinatorics, algebra, representations of finite Combinatorial optimization, integer programming, groups graph theory Thomas Brüstle (Sherbrooke & Bishop’s) Dominic Rochon (UQTR) Algebraic combinatorics, cluster algebras, triangula- Complex analysis, hypercomplex numbers tions of surfaces, stochastic differential equations, Collaborating members mathematical models in finance Cedric Chauve (Simon Fraser & UQAM) Marcello Aguiar (Texas A&M) Enumerative combinatorics, trees, bioinformatics Algebraic combinatorics, non-commutative algebra, Hopf algebras and quantum groups, category theory Sylvie Hamel (Montréal) Bioinformatics and algorithms, theory of languages Robert Bédard (UQAM) and automata, algebraic combinatorics Representations of finite groups, Lie theory Christophe Hohlweg (UQAM) Luc Bélair (UQAM) Algebra, algebraic combinatorics, convex geometry Mathematical logic, model theory Gilbert Labelle (UQAM) Nantel Bergeron (York) Enumerative combinatorics, analysis Applied algebra Shiping Liu (Sherbrooke) Pierre Bouchard (UQAM) Representation theory Commutative algebra, algebraic geometry and combinatorics Vladimir Makarenkov (UQAM) Computational biology, mathematical classification Michel Bousquet (Vieux-Montréal) 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 Franco Saliola (UQAM) Sylvie Corteel (LIAFA & CNRS) Algebraic combinatorics, group representations Enumerative and bijective combinatorics, partitions of Timothy R. S. Walsh (UQAM) integers, q-series Algorithmics, enumerative combinatorics, graph the- Adriano Garsia (UC San Diego) ory Algebraic combinatorics, symmetric functions, har- Associate members monic and coinvariant spaces, quasiharmonic and quasi-invariant functions Pierre Lalonde (Maisonneuve) Alain Goupil (UQTR) Enumerative and bijective combinatorics, alternating Combinatorics, algebra, linear representations of sign matrices, enumeration of involutions with respect groups, symmetric group

68 Research Laboratories

André Joyal (UQAM) databases (OLAP), data mining, time series, collabora- Algebraic topology, category theory tive filtering, information retrieval Jacques Labelle (UQAM) Simon Plouffe Combinatorics, topology Integer sequences, generalized expansions of real num- Louise Laforest (UQAM) bers Data structures, combinatorics, asymptotic analysis, Xavier G. Viennot (Bordeaux 1) quaternary trees Enumerative, algebraic, and bijective combinatorics, Daniel Lemire (TÉLUQ) interactions between combinatorics, theoretical infor- Database theory, data warehousing, multidimensional matics, and theoretical physics

Mathematical Analysis

Description M. Najafi Ivaki, who obtained his Ph.D. at Concordia under the supervision of A. Stancu. In the 2012–2013 At the same time classical and central to modern math- academic year 3 undergraduate students, 36 M.Sc. stu- ematics, analysis involves the study of continuous sys- dents, 39 Ph.D. students, and 19 postdoctoral fellows tems, from dynamical systems to solutions of par- were supervised or cosupervised by members of the tial differential equations and spectra of operators. In Mathematical Analysis Laboratory. 2012–2013 the Laboratory included 28 regular and 10 associate members working at ten different universi- Members of the Laboratory ties in Canada, the United Kingdom, and France. The members of the Laboratory work in the following ar- Regular members eas: harmonic analysis, complex analysis and several Dmitry Jakobson (McGill), Director complex variables, potential theory, functional analy- Pure mathematics, global analysis, spectral geometry, sis, Banach algebras, microlocal analysis, analysis on quantum chaos, harmonic analysis, eigenvalues and manifolds, nonsmooth analysis, spectral theory, partial eigenfunctions differential equations, geometric analysis, ergodic theory and dynamical systems, control theory, mathemat- Line Baribeau (Laval) ical physics, applied mathematics, probability, nonlin- Complex and functional analysis, Banach algebras, ear analysis, nonlinear differential equations, topolog- holomorphic iterations, discrete groups ical methods in differential equations, fluid dynamics, Abraham Boyarsky (Concordia) and turbulence. Dynamical systems Francis H. Clarke (Lyon 1) News and highlights Nonlinear and dynamic analysis, control theory, calculus of variations As is typical for the Mathematical Analysis Labora- Galia Dafni (Concordia) tory, the year 2012–2013 featured many collaborative Harmonic analysis, partial differential equations, com- and training activities. Another activity was the highly plex variables successful “Workshop on Invariant Subspaces of the Shift Operator” (in August 2013). In Montréal the long- Donald A. Dawson (Carleton) running Analysis Seminar is now taking place at dif- Probability, stochastic processes ferent Montréal universities and has been renamed S. W. Drury (McGill) the “Montréal Analysis Seminar”. French researchers Harmonic analysis, matrix theory Fricain, Pillet, and Panati visited the Laboratory and a Richard Fournier (Dawson) group of five McGill students spent 6 weeks at the IHP Complex analysis, function theory in Paris and two weeks at a summer school in Autran. Marlène Frigon (Montréal) Y. Canzani, a 2013 Ph.D. from McGill supervised by D. Nonlinear analysis, differential equations, fixed point Jakobson and J. Toth, is now a Benjamin Pierce Fellow theory, critical point theory, multivalent analysis at Harvard. The 2013 Carl Herz Prize was awarded to

69 Centre de recherches mathématiqes

Paul M. Gauthier (Montréal) Alexander Shnirelman (Concordia) Complex analysis, holomorphy, harmonicity, analytic Applications of geometric analysis to fluids and “weak” approximation solutions of the Euler and Navier-Stokes equations Pawel Gora (Concordia) Alina Stancu (Concordia) Ergodic theory, dynamical systems, fractal geometry Geometric analysis Frédéric Gourdeau (Laval) Ron J. Stern (Concordia) Banach algebras, cohomology, amenability, functional Functional analysis and theory of operators, linear and analysis nonlinear systems, non-smooth analysis, stability, op- Vojkan Jakšić (McGill) timal order Mathematical physics, quantum statistical mechanics, John A. Toth (McGill) random Schrödinger operators Spectral theory, semi-classical analysis, microlocal Tomasz Kaczynski (Sherbrooke) analysis, Hamiltonian mechanics Topological methods, Conley index, applications to dynamical systems Associate members Ivo Klemes (McGill) Octavian Cornea (Montréal) Harmonic analysis, trigonometric series Algebraic topology, dynamical systems Alexey Kokotov (Concordia) Richard Duncan (Montréal) Spectral geometry of Riemann surfaces, hyperbolic Ergodic theory, martingale theory, probability theory partial differential equations in Banach spaces Paul Koosis (McGill) Kohur Gowrisankaran (McGill) Harmonic analysis Potential theory Javad Mashreghi (Laval) Pengfei Guan (McGill) Complex analysis, harmonic analysis, Hardy spaces Partial differential equations, geometric analysis, sev- Iosif Polterovich (Montréal) eral complex variables Geometric analysis, spectral theory, functional analy- John Harnad (Concordia) sis, differential geometry, partial differential equations Mathematical physics, classical and quantum physics, Thomas J. Ransford (Laval) geometrical methods, integrable systems, group theo- Complex and harmonic analysis, functional analysis retical methods, random matrices, isomonodromic de- and theory of operators, spectral analysis, potential formations, isospectral flows theory Niky Kamran (McGill) Dominic Rochon (UQTR) Geometric approach to partial differential equations Complex analysis, hypercomplex numbers Dmitry Korotkin (Concordia) Jérémie Rostand (Laval) Integrable systems, isomonodromic deformations, Complex analysis, experimental mathematics classical and quantum gravity, Frobenius varieties Christiane Rousseau (Montréal) Nilima Nigam (Simon Fraser) Dynamical systems, bifurcations, qualitative theory, Applied analysis, numerical methods in electromag- polynomial systems, analytic invariants, integrable netism systems Yiannis N. Petridis (University College London) Dana Schlomiuk (Montréal) Automorphic forms and their spectral theory, analytic Global analysis, dynamical systems, singularities, bi- number theory, spectral and scattering theory of man- furcations, algebraic curves, primary integral ifolds Robert Seiringer (McGill) Samuel Zaidman (Montréal) Many-body quantum systems, Bose-Einstein conden- Functional analysis and differential equations in ab- sates stract spaces, pseudo-differential operators

70 Research Laboratories

Mathematical Physics

Description Members of the Laboratory

The mathematical physics group is one of the oldest Regular members and most active at the CRM. It consists of 18 regu- John Harnad (Concordia), Director lar members, 10 local associate members, all full-time Mathematical physics, classical and quantum physics, faculty members at one of the participating universi- geometrical methods, integrable systems, group theo- ties, and 7 external associate members working per- retical methods, random matrices, isomonodromic de- manently at universities and research laboratories in formations, isospectral flows Europe, the U.S., or Mexico. The group carries out research in many of the most active areas of mathe- S. Twareque Ali (Concordia) matical physics: coherent nonlinear systems in fluids, Coherent states, wavelets, quantization techniques, optics, and plasmas; classical and quantum integrable harmonic analysis, Wigner functions systems; the spectral theory of random matrices; per- Marco Bertola (Concordia) colation phenomena; conformal field theory; quantum Axiomatic quantum field theory, invariant theory of statistical mechanics; spectral and scattering theory discrete groups, random matrices, isomonodromic de- of random Schrödinger operators; quasi-crystals; rela- formations tivity; spectral transform methods; foundational ques- Robert Brandenberger (McGill) tions in quantization; asymptotics of eigenstates; co- Theoretical Cosmology herent states; wavelets; supersymmetry; the symmetry Keshav Dasgupta (McGill) analysis of PDEs and difference equations; representa- Heavy ion collision theory in the energy range tion theory of Lie groups and quantum groups; and the 30MeV/nucleon to many GeV/nucleon mathematical structure of classical and quantum field theories. Alfred Michel Grundland (UQTR) Symmetry of differential equations in physics News and highlights Richard L. Hall (Concordia) Spectra of Schrödinger, Klein-Gordon, Dirac, and Two of the Laboratory members, J. Hurtubise and Salpeter operators, many-body problems, relativis- J. Walcher, were on the scientific committee of the tic scattering theory, iterative solution to ODEs and 2012–2013 Thematic Year and organized the workshop boundary-value problems “Moduli spaces and their invariants in mathematical Jacques Hurtubise (McGill) physics.” R. Brandenberger organized the workshop Algebraic geometry, integrable systems, gauge theory, “Adventures in Superspace” in April 2013: its partici- moduli spaces pants included nearly all the pioneers in supersymmet- Véronique Hussin (Montréal) ric field theory. Several prizes and distinctions were Group theory, Lie algebras and applications in physics, awarded to Laboratory members recently: L. Vinet was supersymmetries in classical and quantum mechanics awarded the CAP–CRM Prize in 2012; R. Seiringer was awarded an NSERC E. W. R. Steacie Memorial Fellow- Dmitry Korotkin (Concordia) ship in 2012; J. Walcher was appointed to a Canada Integrable systems, isomonodromic deformations, Research Chair (Tier II); and M. Grundland obtained classical and quantum gravity, Frobenius varieties a “Research fellowship” from the Digiteo Foundation. Pierre Mathieu (Laval) In the 2012–2013 academic year 10 undergraduate stu- Conformal field theory, classical and quantum inte- dents, 29 M.Sc. students, 47 Ph.D. students, and 30 post- grable systems, affine Lie algebras doctoral fellows were supervised or cosupervised by Manu Paranjape (Montréal) members of the Mathematical Physics Laboratory. Theoretical particle physics: field theory, solitons, noncommutative geometry, alternative gravity

71 Centre de recherches mathématiqes

Jiří Patera (Montréal) Alexander Its (IUPUI) Applications of group theory, quasi-crystals, Lie alge- Soliton theory, integrable systems, special functions, bras mathematical physics Yvan Saint-Aubin (Montréal) Dmitry Jakobson (McGill) Conformal field theory, statistical mechanics, 2- Pure mathematics, global analysis, spectral geometry, dimensional phase transition model quantum chaos, harmonic analysis, eigenvalues and Robert Seiringer (McGill) eigenfunctions Quantum many-body systems, Bose-Einstein conden- Vojkan Jakšić (McGill) sates, Ginzburg-Landau theory, Gross-Pitaevskii the- Mathematical physics, quantum statistical mechanics, ory, bosons random Schrödinger operators Vasilisa Shramchenko (Sherbrooke) Niky Kamran (McGill) Frobenius manifolds, integrable systems, Riemann- Geometric approach to partial differential equations Hilbert problems, isomonodromic deformations of sys- François Lalonde (Montréal) tems of linear differential equations, function theory Symplectic topology and geometry, global analysis on on Riemann surfaces manifolds, Hamiltonian systems Luc Vinet (Montréal) Decio Levi (Roma Tre) Symmetry properties of systems, special functions Symmetries of differential and difference equations, Johannes Walcher (McGill) integrable nonlinear equations on the lattice and re- Mirror symmetry for open strings, non-geometric ductive perturbation theory on the lattice string compactifications Alexander Maloney (McGill) Pavel Winternitz (Montréal) String theory, particle physics, cosmology, quantum Methods of group theory in physics, nonlinear phe- gravity nomena, symmetries of difference equations, superin- Alexander Shnirelman (Concordia) tegrability Applications of geometrical analysis to fluids and “weak” solutions of the Euler and Navier-Stokes equa- Associate members tions Robert Conte (CEA/Saclay) John A. Toth (McGill) Integrable and partially integrable systems, Painlevé Spectral theory, semi-classical analysis, microlocal analysis, exact solutions, finite difference equations analysis, Hamiltonian mechanics Chris Cummins (Concordia) Alexander Turbiner (UNAM, Mexico) Group theory, modular functions, moonshine Quantum mechanics, atomic and molecular physics, Stéphane Durand (Édouard-Montpetit) variational methods Classical and quantum physics, mathematical physics, Carolyne M. Van Vliet (Montréal & Miami) symmetries, parasupersymmetries, fractional super- Non-equilibrium statistical mechanics, fluctuations symmetries, KdV equations, quantum mechanics, rel- and stochastic processes, quantum transport in con- ativity densed matter, electronic behaviour in submicron Bertrand Eynard (CEA/Saclay) quantum devices Matrix models, integrable systems, string theory, rela- Peter Zograf (Steklov Mathematical Institute, St. Pe- tionship between matrix models, integrability, and al- tersburg) gebraic geometry Geometry of moduli spaces, automorphic forms, spec- Jean-Pierre Gazeau (Paris Diderot) tral geometry Coherent states, wavelets, relativistic quantum frames, symmetry groups for beta-lattices

72 Research Laboratories

PhysNum

Description to improve concurrent therapy consisting of oncologi- cal drugs and their adjuvants. Applied mathematics now plays an important role in the biomedical field and especially the neuro- News and highlights sciences. The research activity at PhysNum has two main themes: pharmacometrics and brain imaging. In In October 2013 Ciuciu and Lina prepared a work- particular shop held in October 2013, the Workshop on Scale- free Dynamics and Networks in Neurosciences. Phys- • Jean-Marc Lina (École de technologie supérieure) Num partners with the Athena team within INRIA and Habib Benali (Université Pierre et Marie Curie) (Sophia-Antipolis, France) and an international labo- work on the multimodal imaging of the spinal cord; ratory, LINeM, within INSERM (the French Health Re- search Institute). In the 2012–2013 academic year 18 • Lina and Christophe Grova (McGill University) M.Sc. students, 25 Ph.D. students, and 8 postdoctoral work on multiresolution and multimodal imaging in fellows were supervised or cosupervised by PhysNum magneto-electrophysiology; members.

• Benali and Maxime Descoteaux (Université de Sher- Members of the Laboratory brooke) study models of the anatomical and functional connectivity of the brain; Regular members • Grova studies neurovascular models in epilepsy; Jean-Marc Lina (ÉTS), Director Wavelets, statistical modelling and brain imaging, ma- • Lina studies sparse representations, inverse prob- chine learning lems, and brain wave synchronization; and Alain Arnéodo (ÉNS Lyon & CNRS) • Lina analyzes scale-invariant processes in electro- Fractals and wavelets physiology. Habib Benali (UPMC) Quantitative analysis in brain imaging, medical imag- Fahima Nekka and her team conduct research in phar- ing and multimodal systems macometrics, a discipline whose goal is to interpret Maxime Descoteaux (Sherbrooke) and describe pharmacological phenomena in a quanti- Medical imaging, image analysis and processing, com- tative manner, so as to support rational therapeutic de- puter vision, applied mathematics cisions and improvement of patient health. They have developed a whole framework of probabilistic pharma- Christophe Grova (McGill) cometrics in which different sources of variability and Statistical signal processing, localization of epileptic the nonlinearity of the system are accounted for. The spikes using distributed sources modelling, and mul- team is working on compliance metrics and ranking timodal analysis of EEG source localization and simul- and on direct and inverse problems related to patient taneous EEG-fMRI data analysis drug behaviour and the therapeutic effect of drugs. It Frédéric Lesage (Polytechnique Montréal) is conceiving tools that shed new light on drug devel- Conformal theory, integrable systems, inverse prob- opment and evaluation in terms of efficacy and bioe- lems, optical imaging quivalence; revisiting classical concepts in pharmacol- Fahima Nekka (Montréal) ogy and updating their formulation; developing mod- Pharmacokinetics, development of mathematical tools els for drug interactions; integrating physiology with from fractal geometry and harmonic analysis for ex- behaviour to create a real fingerprint of drugs; inte- tracting information, applications to pharmacology grating advanced hematopoietic models with PK/PD and medicine

73 Centre de recherches mathématiqes

Statistics

Description 2013), the “3rd Graduate Student Workshop on Actuar- ial and Financial Mathematics” (December 2013), and Statistics is central to many endeavours in society. the “Concordia Workshop on Nonparametric Curve Be it through surveys from sampling, clinical trials to Smoothing” (December 2013). study various biomedical treatments, or experimental designs in agriculture or industry, statistical method- Members of the Laboratory ology can be found everywhere in science. Recently, statistics has undergone a revolution in its techniques Regular members and approaches. This revolution has been driven by Louis-Paul Rivest (Laval), Director the need to analyze very large data sets and data with Linear models, robustness, directional data, sampling, more complex structure, and by the advent of power- applications in finance ful computers. For example, statistical methodology is now addressing problems whose structure is very com- Belkacem Abdous (Laval) plex, such as the analysis of brain images or genome Biostatistics, health research methodology, construc- data, and new methodology is being developed, such tion and validation of measuring tools in the health as data mining, for large data sets. Note that the name sector of the Laboratory must be interpreted broadly, as some Jean-François Angers (Montréal) of its members are actuaries, probabilists, or biostatis- Decision theory, Bayesian statistics, robustness with ticians. respect to prior information, function estimation One of the aims of the Laboratory is to structure the Masoud Asgharian (McGill) Québec statistical community so that it can participate Survival analysis, change-point problems, simulated in this revolution at a time when an important renewal annealing and its variants, optimization of academic personnel is taking place. This structure al- Yoshua Bengio (Montréal) lows the Québec community to participate in Canada- Statistical learning algorithms, neural networks, nu- wide programs organized by the three Canadian math- cleus models, probabilistic models, data mining, appli- ematics institutes. The Laboratory is formed of the cations in finance and statistical language modelling leaders of the Québec school of statistics, who work Martin Bilodeau (Montréal) on topics such as statistical learning and neural net- Multivariate analysis, decision theory, asymptotic works, survey sampling, analysis of functional data, methods statistical analysis of images, dependence structures, Yogendra P. Chaubey (Concordia) Bayesian analysis, analysis of time series and financial Sampling, linear models, resampling, survival analysis data, and resampling methods. Pierre Duchesne (Montréal) News and highlights Time series, sampling, multivariate analysis Thierry Duchesne (Laval) Nowadays the analysis of unimaginably vast amounts Survival analysis, longitudinal data analysis, missing of data poses significant challenges, both methodolog- data, modelling of losses, insurance of catastrophic ically and in terms of HQP training. The Laboratory incidents, nonparametric inference, model selection, contributes to this effort through an average of 150 warranty scientific publications per year and extensive graduate Debbie J. Dupuis (HEC Montréal) supervision. This year 130 M.Sc. and 86 Ph.D. students Extreme values, robustness were supervised or co-supervised by Laboratory mem- Sorana Froda (UQAM) bers; those who completed their studies found imme- Nonparametric methods in function estimation, ap- diate employment after their studies. Of the 10 PDFs, plications of stochastic modelling in biology and four found tenure-track positions in Canada while the medicine six others are still in training. The CRM provided financial support for the Montreal Spring School of “Pop- Christian Genest (McGill) ulation Genomics and Genetic Epidemiology” (May Multidimensional data analysis, dependence measures,

74 Research Laboratories nonparametric statistics, decision theory, applications Wei Sun (Concordia) in actuarial science, finance, and psychology Nonlinear filtering and its applications, stochastic Nadia Ghazzali (Laval) analysis, statistical inference, stochastic modelling Multidimensional data analysis, neural networks and David B. Wolfson (McGill) genetic algorithms, applications in astrophysics and Change-point problems, survival analysis, Bayesian biostatistics statistics, optimal design, applications in medicine Aurélie Labbe (McGill) Biostatistics and statistical genetics Associate members Fabrice Larribe (UQAM) Juli Atherton (McGill) Statistical genetics and biostatistics Biostatistics, optimal Bayesian design, change-point Christian Léger (Montréal) problems, survival analysis, applications to genetics Resampling methods, adaptive estimation, model se- Mylène Bédard (Montréal) lection, robustness, applications in data mining Optimal scaling, Metropolis-Hastings algorithms Brenda MacGibbon (UQAM) Anne-Catherine Favre (Laval) Mathematical statistics, decision theory, biostatistics Statistical hydrology, analysis and modelling of time Éric Marchand (Sherbrooke) series Statistical inference, Bayesian statistics, multivariate José Garrido (Concordia) analysis and probability Risk theory, insurance statistics Alejandro Murua (Montréal) David Haziza (Montréal) Data mining, machine learning, object recognition, Sampling theory, inference with missing data, robust signal processing, and various applications of statistics inference and probability to bioinformatics and the social and Lajmi Lakhal Chaïeb (Laval) health sciences Multidimensional analysis of survival data, analysis of François Perron (Montréal) recurrent events, semi-parametric models and incom- Decision theory, multidimensional data analysis, plete data Bayesian statistics Geneviève Lefebvre (UQAM) James Ramsay (McGill) Bayesian and computational statistics, biostatistics Functional data analysis, smoothing and nonparamet- Erica E. M. Moodie (McGill) ric regression, curve registration Causal inference, optimal dynamic treatment regimes, Bruno Rémillard (HEC Montréal) longitudinal data, dose-response relationships Probability theory, empirical processes, time series, Manuel Morales (Montréal) nonlinear filtering, applications in finance Mathematical finance, applied stochastic processes, Roch Roy (Montréal) ruin theory, actuarial science, Lévy processes, math- Time series analysis, predictive methods, applications ematics of insurance in econometrics and epidemiology Johanna Nešlehová (McGill) Arusharka Sen (Concordia) Multivariate analysis, dependence modelling, non- Statistical inference of truncated data, nonparametric parametric and asymptotic statistics, multivariate ex- function estimation treme value theory, empirical processes, applications Russell Steele (McGill) to biostatistics, neuroscience and risk management Bayesian approaches to mixing modelling, multiple Robert W. Platt (McGill) imputation Biostatistics and statistical methods for pediatric and David Stephens (McGill) perinatal epidemiology. Bayesian statistics, Markov Chain Monte Carlo and Lea Popovic (Concordia) applications to bioinformatics, statistical genetics, and Probability theory and its applications to evolutionary time series analysis biology, population genetics, and cell biology

75 Publications Publications

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 Lecture Notes of the 50th Séminaire de Mathématiques appeared in 2012–2013 or that will be published soon. Supérieures (SMS), Montréal, 2011, vol. 56, 2013. André Boivin & Javad Mashreghi (eds.), Complex Anal- American Mathematical Society ysis and Potential Theory, vol. 55, 2012. CRM Monograph Series Libor Šnobl & Pavel Winternitz, Classification and American Mathematical Society Identification of Lie Algebras, to appear Contemporary Mathematics (Centre de Recherches Mathématiques Proceedings) Pavel Bleher & Karl Liechty, Random Matrices and the Six-Vertex Model, to appear. Chantal David, Matilde Lalín & Michelle Manes (eds.), Jean-Pierre Labesse & Jean-Loup Waldspurger, La For- Women in Numbers 2: Research Directions in Number mule des Traces Tordue d’après le Friday Morning Sem- Theory, to appear. inar, vol. 31, 2013. Omid Amini, Matthew Baker & Xander Faber (eds.), Tropical and Non-Archimedean Geometry, to appear. American Mathematical Society CRM Proceedings & Lecture Notes Galia Dafni, Robert John McCann & Alina Stancu (eds.), Analysis and Geometry of Metric Measure Spaces:

Previous Titles

American Mathematical Society Dana Schlomiuk, Andrei A. Bolibrukh, Sergei Yako- CRM Monograph Series venko, Vadim Kaloshin & Alexandru Buium, On Finite- ness in Differential Equations and Diophantine Geome- Joseph H. Silverman, Moduli Spaces and Arithmetic Dy- try, vol. 24, 2005. namics, vol 30, 2012. Prakash Panangaden & Franck van Breugel (eds.), Marcelo Aguiar & Swapneel Mahajan, Monoidal Cate- Mathematical Techniques for Analyzing Concurrent and gories, Species and Hopf Algebras, vol 29, 2010. Probabilistic Systems, vol. 23, 2004. Saugata Ghosh, Skew-Orthogonal Polynomials and Ran- Montserrat Alsina & Pilar Bayer, Quaternion Orders, dom Matrix Theory, vol. 28, 2009. Quadratic Forms, and Shimura Curves, vol. 22, 2004. Jean Berstel, Aaron Lauve, Christophe Reutenauer & Andrei Tyurin, Quantization, Classical and Quantum Franco V. Saliola, Combinatorics on Words: Christoffel Field Theory and Theta Functions, vol. 21, 2003. Words and Repetitions in Words, vol. 27, 2008. Joel Feldman, Horst Knörrer & Eugene Trubowitz, Rie- Victor Guillemin & Reyer Sjamaar, Convexity Proper- mann Surfaces of Infinite Genus, vol. 20, 2003. ties of Hamiltonian Group Actions, vol. 26, 2005. *Laurent Lafforgue, Chirurgie des grassmanniennes, *Andrew J. Majda, Rafail V. Abramov & Marcus J. vol. 19, 2003. Grote, Information Theory and Stochastics for Multiscale Nonlinear Systems, vol. 25, 2005. *George Lusztig, Hecke Algebras with Unequal Param- eters, vol. 18, 2003.

77 Centre de recherches mathématiqes

Michael Barr, Acyclic Models, vol. 17, 2002. Dmitry Jakobson, Stéphane Nonnenmacher & Iosif *Joel Feldman, Horst Knörrer & Eugene Trubowitz, Polterovich (eds.), Spectrum and Dynamics, vol. 52, Fermionic Functional Integrals and the Renormalization 2010. Group, vol. 16, 2002. Javad Mashreghi, Thomas Ransford & Kristian Jose I. Burgos, The Regulators of Beilinson and Borel, Siep (eds.), Hilbert Spaces of Analytic Functions, vol. 51, vol. 15, 2002. 2010. Eyal Z. Goren, Lectures on Hilbert Modular Varieties and P. Robert Kotiuga (ed.), A Celebration of the Mathemat- Modular Forms, vol. 14, 2002. ical Legacy of Raoul Bott, vol. 50, 2009. Michael Baake & Robert V. Moody (eds.), Directions in Miguel Abreu, François Lalonde & Leonid Poltero- Mathematical Quasicrystals, vol. 13, 2000. vich (eds.), New Perspectives and Challenges in Symplec- tic Field Theory, vol. 49, 2009. Masayoshi Miyanishi, Open Algebraic Surfaces, vol. 12, 2001. David Avis, David Bremner & Antoine Deza (eds.), Polyhedral Computation, vol. 48, 2009. Spencer J. Bloch, Higher Regulators, Algebraic K- Theory, and Zeta Functions of Elliptic Curves, vol. 11, John Harnad & Pavel Winternitz (eds.), Groups and 2000. Symmetries: From Neolithic Scots to John McKay, vol. 47, 2009. James D. Lewis, A Survey of the Hodge Conjecture, 2nd edition, vol. 10, 1999 (with an appendix from B. Brent Jean-Marie De Koninck, Andrew Granville & Florian Gordon). Luca (eds.), Anatomy of Integers, vol. 46, 2008. *Yves Meyer, Wavelets, Vibrations and Scaling, vol. 9, Panos M. Pardalos & Pierre Hansen (eds.), Data Mining 1997. and Mathematical Programming, vol. 45, 2008. *Ioannis Karatzas, Lectures on Mathematics of Finance, Stanley Alama, Lia Bronsard & Peter Sternberg (eds.), vol. 8, 1996. Singularities in PDE and the Calculus of Variations, vol. 44, 2007. John Milton, Dynamics of Small Neural Populations, vol. 7, 1996. Andrew Granville, Melvyn B. Nathanson & Jozsef Solymosi (eds.), Additive Combinatorics, vol. 43, 2007. *Eugene B. Dynkin, An Introduction to Branching Measure-Valued Processes, vol. 6, 1994. Donald A. Dawson, Vojkan Jakšić & Boris Vain- berg (eds.), Probability and Mathematical Physics: A Andrew M. Bruckner, Differentiation of Real Functions, Volume in Honor of Stanislav Molchanov, vol. 42, 2007. vol. 5, 1994. André Bandrauk, Michel C. Delfour & Claude *David Ruelle, Dynamical Zeta Functions for Piecewise Le Bris (eds.), High-Dimensional Partial Differential Monotone Maps of the Interval, vol. 4, 1994. Equations in Science and Engineering, vol. 41, 2007. V. Kumar Murty, Introduction to Abelian Varieties, Vestislav Apostolov, Andrew Dancer, Nigel Hitchin vol. 3, 1993. & McKenzie Wang (eds.), Perspectives in Comparison, Maximilian Ya. Antimirov, Andrei A. Kolyshkin & Generalized and Special Geometry, vol. 40, 2006. Rémi Vaillancourt, Applied Integral Transforms, vol. 2, Pavel Winternitz, David Gomez-Ullate, Arieh Iserles, 1993. Decio Levi, Peter J. Olver, Reinout Quispel & Piergiulio *Dan V. Voiculescu, Kenneth J. Dykema & Alexandru Tempesta (eds.), Group Theory and Numerical Analysis, Nica, Free Random Variables, vol. 1, 1992. vol. 39, 2005. American Mathematical Society Jacques Hurtubise & Eyal Markman (eds.), Algebraic CRM Proceedings & Lecture Notes Structures and Moduli Spaces, vol. 38, 2004. Piergiulio Tempesta, Pavel Winternitz, John Harnad, Daniel Daigle, Richard Ganong & Mariusz Koras (eds.), Willard Miller Jr., George Pogosyan & Miguel A. Ro- Affine Algebraic Geometry: The Russell Festschrift, driguez (eds.), Superintegrability in Classical and Quan- vol. 54, 2011. tum Systems, vol. 37, 2004. Bradd Hart, Thomas G. Kucera, Anand Pillay, Philip J. Hershy Kisilevsky & Eyal Z. Goren (eds.), Number The- Scott & Robert A. G. Seely (eds.), Models, Logics, and ory, vol. 36, 2004. Higher-Dimensional Categories, vol. 53, 2011.

78 Publications

H. E. A. Eddy Campbell & David L. Wehlau (eds.), In- François Lalonde (ed.), Geometry, Topology and Dy- variant Theory in All Characteristics, vol. 35, 2004. namics, vol. 15, 1998. Pavel Winternitz, John Harnad, C. S. Lam & Jiří Pat- John Harnad & Alex Kasman (eds.), The Bispectral Prob- era (eds.), Symmetry in Physics, vol. 34, 2004. lem, vol. 14, 1998. André D. Bandrauk, Michel C. Delfour & Claude Michel Delfour (ed.), Boundaries, Interfaces and Transi- Le Bris (eds.), Quantum Control: Mathematical and Nu- tions, vol. 13, 1998. merical Challenges, vol. 33, 2003. Peter G. Greiner, Victor Ivrii, Luis A. Seco & Catherine Vadim B. Kuznetsov (ed.), The Kowalevski Property, Sulem (eds.), Partial Differential Equations and their vol. 32, 2002. Applications, vol. 12, 1997. John Harnad & Alexander R. Its (eds.), Isomonodromic Luc Vinet (ed.), Advances in Mathematical Sciences: Deformations and Applications in Physics, vol. 31, 2002. CRM’s 25 Years, vol. 11, 1997. John McKay & Abdellah Sebbar (eds.), Proceedings on Donald E. Knuth, Stable Marriage and Its Relation to Moonshine and Related Topics, vol. 30, 2001. Other Combinatorial Problems, vol. 10, 1996. Alan Coley, Decio Levi, Robert Milson, Colin Rogers & Decio Levi, Luc Vinet & Pavel Winternitz (eds.), Sym- Pavel Winternitz (eds.), Bäcklund and Darboux Trans- metries and Integrability of Difference Equations, vol. 9, formations, vol. 29, 2001. 1995. John C. Taylor (ed.), Topics in Probability and Lie Joel S. Feldman, Richard Froese & Lon M. Rosen (eds.), Groups: Boundary Theory, vol. 28, 2001. Mathematical Quantum Theory II: Schrödinger Opera- Israel M. Sigal & Catherine Sulem (eds.), Nonlinear Dy- tor, vol. 8, 1995. namics and Renormalization Group, vol. 27, 2001. Joel S. Feldman, Richard Froese & Lon M. Rosen (eds.), John Harnad, Gert Sabidussi & Pavel Winternitz (eds.), Mathematical Quantum Theory I: Field Theory and Integrable Systems: From Classical to Quantum, vol. 26, Many-Body Theory, vol. 7, 1994. 2000. Guido Mislin (ed.), The Hilton Symposium 1993, vol. 6, Decio Levi & Orlando Ragnisco (eds.), SIDE III— 1994. Symmetry and Integrability of Difference Equations, Donald A. Dawson (ed.), Measure-Valued Processes, vol. 25, 2000. Stochastic Partial Differential Equations and Interacting B. Brent Gordon, James D. Lewis, Stefan Müller-Stach, Systems, vol. 5, 1994. Shuji Saito & Noriko Yui (eds.), The Arithmetic and Ge- Hershy Kisilevsky & M. Ram Murty (eds.), Elliptic ometry of Algebraic Cycles, vol. 24, 2000. Curves and Related Topics, vol. 4, 1994. Pierre Hansen & Odile Marcotte (eds.), Graph Colour- Andrei L. Smirnov & Rémi Vaillancourt (eds.), Asymp- ing and Applications, vol. 23, 1999. totic Methods in Mechanics, vol. 3, 1993. Jan Felipe van Diejen & Luc Vinet (eds.), Algebraic Philip D. Loewen, Optimal Control via Nonsmooth Methods and q-Special Functions, vol. 22, 1999. Analysis, vol. 2, 1993. Michel Fortin (ed.), Plates and Shells, vol. 21, 1999. M. Ram Murty (ed.), Theta Functions, vol. 1, 1993. Katie Coughlin (ed.), Semi-Analytic Methods for the Navier–Stokes Equations, vol. 20, 1999. Springer CRM Series in Mathematical Physics Rajiv Gupta & Kenneth S. Williams (eds.), Number The- ory, vol. 19, 1999. André D. Bandrauk & Misha Ivanov (eds.), Quantum Serge Dubuc & Gilles Deslauriers (eds.), Spline Func- Dynamic Imaging, 2011. tions and the Theory of Wavelets, vol. 18, 1999. John Harnad (ed.), Random Matrices, Random Processes Olga Kharlampovich (ed.), Summer School in Group and Integrable Systems, 2011. Theory in Banff, 1996, vol. 17, 1998. Marc Thiriet, Biology and Mechanics of Blood Flows, Alain Vincent (ed.), Numerical Methods in Fluid Me- 2008 (2 volumes). chanics, vol. 16, 1998. David Sénéchal, André-Marie Tremblay & Claude Bourbonnais (eds.), Theoretical Methods for Strongly Correlated Electrons, 2003.

79 Centre de recherches mathématiqes

*Roman Jackiw, Lectures on Fluid Dynamics, 2002. Michael Barr & Charles Wells, Category Theory for Yvan Saint-Aubin & Luc Vinet (eds.), Theoretical Computing Science, 1999. Physics at the End of the Twentieth Century, 2001. Maximilian Ya. Antimirov, Andrei A. Kolyshkin & Yvan Saint-Aubin & Luc Vinet (eds.), Algebraic Meth- Rémi Vaillancourt, Mathematical Models for Eddy Cur- ods in Physics, 2000. rent Testing, 1998. Jan Felipe van Diejen & Luc Vinet (eds.), Calogero– Xavier Fernique, Fonctions aléatoires gaussiennes, vec- Moser–Sutherland Models, 1999. teurs aléatoires gaussiens, 1997. Robert Conte (ed.), The Painlevé Property, 1999. Faqir Khanna & Luc Vinet (eds.), Field Theory, Inte- grable Systems and Symmetries, 1997. Richard MacKenzie, Manu B. Paranjape & Woj- ciech J. M. Zakrzewski (eds.), Solitons, 1999. Paul Koosis, Leçons sur le théorème de Beurling et Mal- liavin, 1996. Luc Vinet & Gordon Semenoff (eds.), Particles and Fields, 1998. David W. Rand, Concorder Version Three, 1996 (software and user guide). Séminaires de mathématiques supérieures Jacques Gauvin, Theory of Nonconvex Programming, Vašek Chvátal (ed.), Combinatorial Optimization: Meth- 1994. ods and Applications, NATO Science for Peace and Se- Decio Levi, Curtis R. Menyuk & Pavel Winter- curity Series - D: Information and Communication Se- nitz (eds.), Self-Similarity in Stimulated Raman Scatter- curity, vol. 31, IOS Press, 2011. ing, 1994. Decio Levi, Peter Olver, Zora Thomova & Pavel Win- Rémi Vaillancourt, Compléments de mathématiques ternitz (eds.), Symmetries and Integrability of Difference pour ingénieurs, 1993. Equations, London Mathematical Society Lecture Note Robert P. Langlands & Dinakar Ramakrishnan (eds.), Series, vol. 381, Cambridge University Press, 2011. The Zeta Functions of Picard Modular Surfaces, 1992. Florin N. Diacu, Singularities of the N-Body Problem, Springer 1992. Lecture Notes in Statistics (subseries CRM) Jacques Gauvin, Théorie de la programmation mathé- Marc Moore (ed.), Spatial Statistics: Methodological As- matique non convexe, 1992. pects and Applications, vol. 159, 2001. Pierre Ferland, Claude Tricot & Axel van de Walle, S. Ejaz Ahmed & Nancy Reid (eds.), Empirical Bayes Analyse fractale, 1992 (software and user guide). and Likelihood Inference, vol. 148, 2001. Stéphane Baldo, Introduction à la topologie des en- sembles fractals, 1991. Les Publications CRM Robert Bédard, Groupes linéaires algébriques, 1991. Laurent Guieu & Claude Roger, L’Algèbre et le Groupe Rudolf Beran & Gilles R. Ducharme, Asymptotic Theory de Virasoro, 2007. for Bootstrap Methods in Statistics, 1991. Luc Lapointe, Ge Mo-Lin, Yvan Saint-Aubin & Luc James D. Lewis, A Survey of the Hodge Conjecture, 1991. Vinet, Proceedings of the Canada–China Meeting on David W. Rand & Tatiana Patera, Concorder, 1991 (soft- Theoretical Physics, 2003. ware and user guide). Armel Mercier, Fonctions de plusieurs variables : Diffé- David W. Rand & Tatiana Patera, Le Concordeur, 1991 rentiation, 2002. (software and user guide). Nadia El-Mabrouk, Thomas Lengauer & David Véronique Hussin (ed.), Lie Theory, Differential Equa- Sankoff (eds.), Currents in Computational Molecular tions and Representation Theory, 1990. Biology, 2001. John Harnad & Jerrold E. Marsden (eds.), Hamiltonian James G. Huard & Kenneth S. Williams (eds.), The Col- Systems, Transformation Groups and Spectral Trans- lected Papers of Sarvadaman Chowla. Volume I: 1925– form Methods, 1990. 1935; Volume II: 1936–1961; Volume III: 1962–1986, 2000. M. Ram Murty (ed.), Automorphic Forms and Analytic Number Theory, 1990.

80 Publications

Wendy G. McKay, Jiří Patera & David W. Rand, Tables *Mark Kac, Quelques problèmes mathématiques en phy- of Representations of Simple Lie Algebras. Volume I: Ex- sique statistique, 1974. ceptional Simple Lie Algebras, 1990. *Sybreen de Groot, La transformation de Weyl et la Anthony W. Knapp, Representations of Real Reductive fonction de Wigner : une forme alternative de la méca- Groups, 1990. nique quantique, 1974. Wendy G. McKay, Jiří Patera & David W. Rand, Sim- pLie, 1990 (software and user guide). Other Collaborations with Publishers Francis H. Clarke, Optimization and Nonsmooth Anal- Marc Moore, Sorana Froda & Christian Léger (eds.), ysis, Montréal, 1989. Mathematical Statistics and Applications: Festschrift for Samuel Zaidman, Une Introduction à la théorie des équa- Constance van Eeden, Lecture Notes–Monograph Se- tions aux dérivées partielles, 1989. ries, vol. 42, 2003 (a collaboration with the Institute of Mathematical Statistics). *Yuri I. Manin, Quantum Groups and Noncommutative Geometry, 1988. Duong H. Phong, Luc Vinet & Shing-Tung Yau (eds.), Mirror Manifolds and Geometry, AMS/IP Studies in Ad- Lucien Le Cam, Notes on Asymptotic Methods in Statis- vanced Mathematics, vol. 10, 1998 (a collaboration with tical Decision Theory, 1974. the AMS and International Press). Les Presses de l’Université de Montréal Pierre Ferland, Claude Tricot & Axel van de Walle, Chaire Aisenstadt Fractal Analysis User’s Guide, 1994 (a collaboration with the AMS). *Laurent Schwartz, Semimartingales and their Stochas- Hedy Attouch, Jean-Pierre Aubin, Francis Clarke & tic Calculus on Manifolds, 1984. ′ Ivar Ekeland (eds.), Analyse non linéaire, 1989 (a col- *Yuval Ne eman, Symétries, jauges et variétés de groupe, laboration with Gauthier-Villars). 1979. *R. Tyrrell Rockafellar, La théorie des sous-gradients et Videos ses applications à l’optimisation, fonctions convexes et Efim Zelmanov, Abstract Algebra in the 20th Century, non convexes, 1979. 1997. *Jacques-Louis Lions, Sur quelques questions d’analyse, Serge Lang, Les grands courants, 1991. de mécanique et de contrôle optimal, 1976. Robert Bédard, Brouiller les cartes, 1991. *Donald E. Knuth, Mariages stables et leurs relations avec d’autres problèmes combinatoires, 1976. Serge Lang, Les équations diophantiennes, 1991. *Robert Hermann, Physical Aspects of Lie Group Theory, Laurent Schwartz, Le mouvement brownien, 1990. 1974. Laurent Schwartz, Une vie de mathématicien, 1989.

81 Scientific Personnel Scientific Personnel

CRM Members in 2012–2013

In contrast with most other mathematics institutes around the world, the CRM can count on the solid foundation of regular, associate, and invited members. Most regular members are also professors at one of the partner institutions: Montréal, Concordia, McGill, UQAM, Laval, Sherbrooke, and Ottawa. Other members are researchers affiliated with the CRM in 2012–2013 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 national program of theCRMis greatly facilitated by having on hand a large reserve of willing organizers, who even contribute financially to the organization of activities. The largest partnership is with the Université de Montréal, which grants the equivalent of five full-time teaching positions in release time to the CRM. Release agreements with the other Montréal area universities afford the equivalent of two more full-time positions to the CRM. Facilities are alsoprovided to researchers affiliated with junior colleges. Several members are affiliated with the CRM through industrial agreements.

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

83 Centre de recherches mathématiqes

Jacques Hurtubise, McGill François Perron, Montréal Véronique Hussin, Montréal Mikaël Pichot, McGill Adrian Iovita, Concordia Iosif Polterovich, Montréal Dmitry Jakobson, McGill Lea Popovic, Concordia Vojkan Jakšić, McGill James O. Ramsay, McGill Tomasz Kaczynski, Sherbrooke Thomas J. Ransford, Laval Niky Kamran, McGill Bruno Rémillard, HEC Montréal Olga Kharlampovich, McGill Christophe Reutenauer, UQAM Hershy Kisilevsky, Concordia Louis-Paul Rivest, Laval Paul Koosis, McGill Frédéric Rochon, UQAM Dmitry Korotkin, Concordia Ivo G. Rosenberg, Montréal Gilbert Labelle, UQAM Christiane Rousseau, Montréal John Labute, McGill Damien Roy, Ottawa Matilde Lalín, Montréal Peter Russell, McGill François Lalonde, Montréal Yvan Saint-Aubin, Montréal Benoît Larose, Champlain St-Lambert & Concordia David Sankoff, Ottawa Michael Lau, Laval Dana Schlomiuk, Montréal Christian Léger, Montréal Robert Seiringer, McGill Frédéric Lesage, Polytechnique Montréal Alexander Shnirelman, Concordia Jean-Philippe Lessard, Laval Vasilisa Shramchenko, Sherbrooke Sabin Lessard, Montréal Alina Stancu, Concordia Claude Levesque, Laval Ron J. Stern, Concordia Jean-Marc Lina, ÉTS Alain Tapp, Montréal Shiping Liu, Sherbrooke Francisco Thaine, Concordia Emmanuel Lorin de la Grandmaison, Carleton John A. Toth, McGill Steven Lu, UQAM Lennaert van Veen, UOIT Brenda MacGibbon, UQAM Roger Villemaire, UQAM Michael C. Mackey, McGill Luc Vinet, Montréal Vladimir Makarenkov, UQAM Johannes Walcher, McGill Michael Makkai, McGill Timothy R. S. Walsh, UQAM Javad Mashreghi, Laval Pavel Winternitz, Montréal Sherwin A. Maslowe, McGill Daniel T. Wise, McGill Pierre Mathieu, Laval Xiaowen Zhou, Concordia John McKay, Concordia Associate members Manuel Morales, Montréal M. Ram Murty, Queen’s Nantel Bergeron, York Fahima Nekka, Montréal Robert Conte, CEA/Saclay Adam M. Oberman, McGill Stéphane Durand, Édouard-Montpetit Robert G. Owens, Montréal Bertrand Eynard, CEA/Saclay Manu Paranjape, Montréal Martin J. Gander, Genève Jiří Patera, Montréal Pierre Ille, CNRS & Aix-Marseille

84 Scientific Personnel

Marc Laforest, Polytechnique Montréal Jean-Paul Zolésio, INRIA Sophia Antipolis Decio Levi, Roma Tre Invited members Jun Li, Pharsight Emmanuel Lorin de la Grandmaison, Carleton Mylène Bédard, Montréal Yiannis N. Petridis, Univ. Coll. London Louis G. Doray, Montréal Elisa Shahbazian, OODA Technologies Laurent Habsieger, CNRS & Lyon 1 Marc Thiriet, CNRS, UPMC & INRIA Rocquencourt Pierre Lafaye de Micheaux, Montréal Pierre Valin, Defence R&D Canada Sheila Sandon, Nantes Carolyne M. Van Vliet, Montréal & Miami Yuanli Zhang

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 research laboratories, and individual research grants from CRM members. The list below includes postdoctoral fellows in residence at the CRM and those cofunded bytheCRM. Some of the fellows were in residence at the CRM for only part of the year. The affiliation given is the institution where the doctorate was obtained.

Elif Fidan Acar, Toronto Nabil Kahouadji, Paris Diderot Shabnam Akhtari, UBC Caroline Kalla, Bourgogne Ferenc Balogh, Concordia Abdoulaye Sabou Kane, Laval Jessica Banks, Oxford Ilya Karzhemanov, Edinburgh Sandro Bettin, Bristol Leila Kheibarshekan, Gent Alexander Bihlo, Wien Dmitry Kolomenskiy, Provence Cameron Brown, Florida Dimitris Koukoulopoulos, UI Urbana-Champaign Renato Calleja, UT Austin Eunghyun Lee, UC Davis Vorrapan Chandee, Stanford Antonio Lei, Cambridge Adam Clay, UBC Alejandro Morales, MIT Tiago Dinis da Fonseca, UPMC Guyslain Naves, Joseph Fourier Fabrizio Donzelli, Miami Sarah Post, Minnesota Abdelkrim El Basraoui, Ottawa Stamatis Pouliasis, Aristotle Suresh Eswarathasan, Rochester Danilo Riglioni, Roma Tre Renjie Feng, Northwestern Vivien Ripoll, Paris Diderot François Fillion-Gourdeau, McGill Matthew Roberts, Bath Ke Gong, Henan Mathew D. Rogers, UBC Philip Grech, ETH Zürich Yakov Savelyev, Stony Brook Melita Hadzagic, McGill Jihye Seo, Harvard Mariah E. Hamel, UBC Egor Shelukhin, Tel Aviv Adam J. Harper, Cambridge David Sher, Stanford Azadeh Jafari, EPFL Ethan C. Smith, Clemson Gwenaël Joret, ULB Marzena Szajewska, Bialystok

85 Centre de recherches mathématiqes

Agnieszka Tereszkiewicz, Bialystok Mark Wilde, Southern California Carl Tipler, Nantes Driss Yacoubi, UPMC Ihsan Ata Topaloglu, IU Bloomington Guofu Yu, Shanghai Jiao Tong Pascal Turbis, Montréal Yuxiang Zhang, Memorial Matthias Westrich, Aarhus

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 2012–2013 there were 10 activities in the thematic program and 557 researchers took part in these activities, 9 of which were held at the CRM itself. There were also 14 activities in the general program, 7 of which were held at the CRM; altogether 386 participants took part in these activities. Finally the multidisciplinary and industrial program featured 2 activities, one of which took place at the CRM; 58 researchers participated in the activity held at the CRM.

Long-term visitors Michael Sullivan, UMass Amherst Marc Thiriet, UPMC The following list only includes visitors who werein Zora Thomova, SUNY IT residence for at least four weeks. Nicolae Vulpe, IMI Moldova Mattia Cafasso, Angers Oleksiy Zhedanov, Donetsk IPE Pierre Cagne, ÉNS Wadim Zudilin, Newcastle, AU Chi-Yun Chuang,NTHU Vladimir Dorodnitsyn, Keldysh Inst. Short-term visitors Gerard Freixas i Montplet, Paris Diderot The following visitors were in residence for less than Alexandre Girouard, Neuchâtel four weeks. Elisa Gouvea Mauricio Ferreira, McGill Sergei Agafonov, João Pessoa Jiří Hrivnák, TU Prague Silvia Anjos, IST Azadeh Jafari, Cardiff Joan Carles Artés, UA Barcelona Can Kozcaz, SISSA Alain Aspect, Inst. d’Optique Decio Levi, Roma Tre Ferenc Balogh, SISSA Xiannan Li, UI Urbana-Champaign Ram Band, Bristol Chunshan Lin, Tokyo Jonathan Bober, Washington Frithjof Lutscher, Ottawa Alina Bucur, UC San Diego Keivan Mallahi Karai, Jacobs Goce Chadzitaskos, Doppler Inst. Luigi Martina, Salento Edmund Yik-Man Chiang, Hong Kong UST Alexi Morin-Duchesne, Montréal Matthias Christandl, ETH Zürich Aïda Ouangraoua, Simon Fraser Robert Conte, CEA/Saclay Lucas Pastor, Savoie Charles Doran, Alberta Claude-Alain Pillet, Toulon Anton Dzhamay, Northern Colorado Raphaël Ponge, Seoul NU Paul D. Embrechts, ETH Zürich Maksym Radziwill, Stanford Mauricio Adrian Escobar Ruiz, UNAM Libor Šnobl, TU Prague Brooke Feigon, East Anglia Aleksander Strasburger, SGGW

86 Scientific Personnel

Rupert L. Frank, Princeton Alexei V. Penskoi, Moscow SU Jürg Fröhlich, ETH Zürich Patrick Peter, IAP Leo Goldmakher, Toronto Anne-Charlotte Philippe, INRIA Sophia Antipolis María del Mar González Nogueras, UPC Martin Pinsonnault, Western Ontario Emir Gumrukcuoglu, Tokyo Sarah Post, UH Mānoa Thomas Hoffmann-Ostenhof, Wien Vincent Rivasseau, Paris-Sud Nail H. Ibragimov, Blekinge IT Jeremy Rouse, Wake Forest Mourad E. H. Ismail, Central Florida Jimena Royo-Letelier, Paris-Dauphine Alexander R. Its,IUPUI Philippe Ruelle, UC Louvain Caroline Kalla, Orléans Detchat Samart, Texas A&M Mikhail Karpukhin, Moscow SU Emmanuel Schertzer, UPMC Takeshi Kobayashi, Toronto Wil H. A. Schilders, TU Eindhoven Nam Le, Courant Inst. Kai Schneider, TU Kaiserslautern Yi-Jen Lee, Chinese U Hong Kong Chunhua Shan, York Frank Lemire, Windsor Suzanne Shontz, Mississippi SU Michael Levitin, Reading Nadia Sidorova, Univ. Coll. London Xiannan Li, UI Urbana-Champaign Mark Siggers, Kyungpook NU Elijah Liflyand, Bar-Ilan Philippe Sosoe, Princeton Jérôme Martin, IAP Phan Thanh Nam, Cergy-Pontoise Hiroshi Miki, Kyoto Alexander Turbiner, UNAM Micah B. Milinovich, Mississippi Daniel Ueltschi, Warwick Willard Miller Jr., Minnesota Vincent Vennin, IAP Robert V. Moody, Alberta Mark A. Walton, Lethbridge Emmy Murphy, MIT Daqing Wan, UC Irvine Aleksander Yu. Orlov, Shirshov Inst. Simone Warzel, TU München Milena Pabiniak, Toronto Hongmei Zhu, York Leonid Parnovski, Univ. Coll. London Peter Zograf, Steklov Inst. Subodh Patil, ÉNS

87 List of Students Having Graduated in 2012–2013 List of Students Having Graduated in 2012–2013

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 2012–2013. 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

Isabelle Ascah-Coallier Thierry Chekouo Tekougang Abraham Broer Alejandro Murua Université de Montréal Université de Montréal Mathematics (pure mathematics option) Statistics Mohammad Bardestani Mohammad Hossein Dehghan Andrew Granville Thierry Duchesne Université de Montréal Université Laval Mathematics (pure mathematics option) Statistics Zied Ben Salah Olivier Delalleau Louis G. Doray; Manuel Morales Yoshua Bengio Université de Montréal Université de Montréal Mathematics (applied mathematics option) Computer science Erwan Biland Alpha Boubacar Diallo Claude Levesque Vladimir Makarenkov Université Laval Université du Québec à Montréal Mathematics Computer science Richard Bois Plamen Dragiev André Fortin; Michel Fortin Vladimir Makarenkov Université Laval Université du Québec à Montréal Mathematics Computer science Yaiza Canzani Peyman Eslami Dmitry Jakobson Pawel Gora; Abraham Boyarsky McGill University Concordia University Mathematics Mathematics Francesc Castella Yasser Farhat Henri Darmon Frédéric Gourdeau; Thomas J. Ransford McGill University Université Laval Mathematics Mathematics Zhuge Chanjing Ionica Groparu-Cojocaru Michael C. Mackey Louis G. Doray; Manuel Morales McGill University Université de Montréal Physiology Mathematics (applied mathematics option) François Charest Lenka Háková François Lalonde; Octav Cornea Jiří Patera Université de Montréal Université de Montréal Mathematics (pure mathematics option) Mathematics (applied mathematics option) François Charette Salima Hassaine Octav Cornea Yann-Gaël Guéhéneuc; Sylvie Hamel Université de Montréal Université de Montréal Mathematics (pure mathematics option) Computer science

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Charles Hélou Mohammad Najafi Ivaki Gilles Brassard Alina Stancu Université de Montréal Concordia University Computer science Mathematics Kassem Kalach Guillaume Provencher Gilles Brassard; Louis Salvail Yvan Saint-Aubin Université de Montréal Université de Montréal Computer science Physics Johanna Karouby Yassir Rabhi Robert Brandenberger Masoud Asgharian; Brenda MacGibbon McGill University McGill University Physics Statistics Hamid Khakdaman Hela Romdhani Yves Bourgault; Marten Ternan Lajmi Lakhal-Chaieb; Louis-Paul Rivest University of Ottawa Université Laval Chemical Engineering Statistics Hussein Khreibani Olivier Rouch Vasilisa Shramchenko Madrane Aziz; Paul Arminjon Université de Sherbrooke Université de Montréal Mathematics Mathematics (applied mathematics option) Michelle Larouche Mireille Schnitzer Jiří Patera Erica E. M. Moodie Université de Montréal McGill University Mathematics (applied mathematics option) Biostatistics Nima Lashkari Narinder Sharma Alexander Maloney; Patrick Hayden Dominic Rochon; Kuldeep S. Charak McGill University Université du Québec à Trois-Rivières Mathematics Mathematics Mehdi Layeghifard Karine St-Onge Vladimir Makarenkov François Major; Sylvie Hamel Université du Québec à Montréal Université de Montréal Biology Computer science Adrien Lemaitre Bocar Amadou Wane Gena Hahn; Benoît Larose José Manuel Urquiza; André Fortin Université de Montréal Université Laval Computer science Mathematics Hui Li Liu Alisha Wissanji Xiaowen Zhou Alexander Maloney; Keshav Dasgupta Concordia University Université de Montréal Statistics Physics Amanollah Mehrabian Yongling Xiao David A. Stephens Erica E. M. Moodie; Michal Abrahamowicz McGill University McGill University Statistics Biostatistics Alexi Morin-Duchesne Wei Xue Yvan Saint-Aubin Robert Brandenberger Université de Montréal McGill University Physics Physics

90 List of Students Having Graduated in 2012–2013

M.Sc. Students

Albert Ajonkeu Thanina Berkane Louis-Paul Rivest Christian Léger; Piere Duchesne Université Laval Université de Montréal Statistics Statistics Farid Aouji Valentin Bisson Lajmi Lakhal-Chaieb; Belkacem Abdous Yoshua Bengio Université Laval Université de Montréal Mathematics Computer science Samuel April Timothy Blais Louis-Paul Arguin Alexander Maloney Université de Montréal McGill University Mathematics (applied mathematics option) Mathematics Farzad Aryan Éloïse Boiteau Andrew Granville André Fortin Université de Montréal Université Laval Mathematics (pure mathematics option) Mathematics Adétona O. Paterne Bada Samuel Boucher Louis-Paul Rivest Vestislav Apostolov Université Laval Université du Québec à Montréal Statistics Mathematics Nadia Bahri Catalina Butnariu Qazi Ibadur Rahman David Haziza Université de Montréal Université de Montréal Mathematics (pure mathematics option) Statistics Jean-François Bégin Hassan Choueib Mylène Bédard; Patrice Gaillardetz Michel C. Delfour Université de Montréal Université de Montréal Mathematics (applied mathematics option) Mathematics (applied mathematics option) Latifa Ben Hadj Slimene Paul Robert Chouha Éric Marchand Alain Tapp; Gilles Brassard Université de Sherbrooke Université de Montréal Mathematics Computer science Fabiola Bene Tchaleu Maurice-Étienne Cloutier David Haziza; Pierre Duchesne Jean-Marie De Koninck; Claude Levesque Université de Montréal Université Laval Statistics Mathematics Ryan Benty Marc-Alexandre Côté Alina Stancu Shengrui Wang; Maxime Descoteaux Concordia University Université de Sherbrooke Mathematics Mathematics Francesca Bergamaschi Bianca Côté-Brunet Adrian Iovita Jean-François Angers; Manuel Morales Concordia University Université de Montréal Mathematics Statistics

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Miguel Alfredo Cutimanco Panduro Andrew Fenwick Virginie Charette; Vasilisa Shramchenko Galia Dafni Université de Sherbrooke Concordia University Mathematics Mathematics Pierre-Luc Cyr Heinz Fiedler Jean-François Angers Alain Tapp Université de Montréal Université de Montréal Statistics Computer science Philippe Delorme Iulian Fransinescu Pierre Lafaye de Micheaux René Ferland Université de Montréal Université du Québec à Montréal Statistics Mathematics Marie-Hélène Descary Alexandre Fréchette Fabrice Larribe Bruce Shepherd Université du Québec à Montréal McGill University Mathematics (statistics option) Mathematics Caroline Deschênes Yves Gagnon Christian Léger Nadia El-Mabrouk Université de Montréal Université de Montréal Statistics Bioinformatics Jean-François Désilets Ludovick Gagnon Pavel Winternitz José Manuel Urquiza Université de Montréal Université Laval Physics Mathematics Hugo Drouin-Vaillancourt Shan Gao Alain Tapp Adrian Iovita Université de Montréal Concordia University Computer science Mathematics Yeting Du Gabriel Girard Abbas Khalili; Johanna Nešlehová Maxime Descoteaux McGill University Université de Sherbrooke Statistics Mathematics Mathieu Dupont Mireille Guerrier Fabrice Larribe Louis-Paul Rivest Université du Québec à Montréal Université Laval Mathematics (statistics option) Statistics David Émond Dezhao Han Nadia Ghazzali José Garrido Université Laval Concordia University Mathematics Actuarial science Laura C. Eslava Fernández Julie Héroux Louigi Addario-Berry Erica E. M. Moodie McGill University McGill University Mathematics Biostatistics

92 List of Students Having Graduated in 2012–2013

Eliot Hijano Jérémie Mathieu Alexander Maloney Dominic Rochon; Louis Marchildon McGill University Université du Québec à Trois-Rivières Mathematics Physics Zahraa Issa Annaliza McGillivray Matilde Lalín Abbas Khalili Université de Montréal McGill University Mathematics (pure mathematics option) Statistics Samuel Johnson Nassim Mojaverian Marni Mishna Erica E. M. Moodie Simon Fraser University McGill University Mathematics Biostatistics Philip Lagogianis Marcela Molinie Alexander Maloney Jacques Bélair McGill University Université de Montréal Mathematics Mathematics (applied mathematics option) Sandra Larrivée Vanessa W. K. Ng Jean-François Renaud Frédéric Lesage Université du Québec à Montréal École Polytechnique de Montréal Mathematics Electrical Engineering Jean-Sébastien Lechasseur Jean-François Nolet Matilde Lalin Virginie Charette Université de Montréal Université de Sherbrooke Mathematics (pure mathematics option) Mathematics Jean-Sébastien Lévesque Ivo Pendev Robert Guénette Pawel Gora Université Laval Concordia University Mathematics Mathematics Erin Lundy David Olivier Pham David B. Wolfson; David A. Stephens Manuel Morales McGill University Université de Montréal Statistics Statistics Dominique Maheux Marta Pieropan Robert Guénette Adrian Iovita Université Laval Concordia University Mathematics Mathematics Céline Maistret Dany Pilon Hershy Kisilevsky; Adrian Iovita Mathieu Boudreault Concordia University Université du Québec à Montréal Mathematics Mathematics (financial mathematics option) Viktor Marushka Alan Regis Iosif Polterovich Wei Sun Université de Montréal Concordia University Mathematics (pure mathematics option) Statistics

93 Centre de recherches mathématiqes

Reza Sadoughianzadeh Tommy Thomassin Adrian Iovita Geneviève Gauthier; Mathieu Boudreault Concordia University HEC Montréal Mathematics Financial Engineering Becem Saidani Marie-Hélène Toupin Éric Marchand; Maxime Descoteaux Louis-Paul Rivest Université de Sherbrooke Université Laval Mathematics Statistics Etienne Saint-Amant Hugo Tremblay Maxime Descoteaux Gilbert Labelle Université de Sherbrooke Université du Québec à Montréal Mathematics Mathematics Modou Sene Véronique Tremblay Thierry Duchesne Anne-Catherine Favre; Thierry Duchesne Université Laval Université Laval Statistics Statistics David Simonyan Benoit Tricot Thierry Duchesne Maxime Descoteaux Université Laval Université de Sherbrooke Statistics Mathematics Kevin Sookhee Loukia Tsakanikas Wei Sun Lennaert van Veen; Eusebius Doedel Concordia University Concordia University Statistics Mathematics Dong Sun Jean-Philippe Turcotte Yogendra P. Chaubey Éric Marchand Concordia University Université de Sherbrooke Statistics Mathematics Yasmine Tawfik Fan Zhang Robert G. Owens Yogendra P. Chaubey Université de Montréal Concordia University Mathematics (applied mathematics option) Statistics Hervé Tchouake Tchuiguep François Perron Université de Montréal Statistics

94 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 of Laboratories. In 2012–2013 the members of the Local Scientific Committee were Christian Genest (McGill University), Andrew Granville (Université de Montréal), Dmitry Jakobson (McGill University), François Lalonde (Université de Montréal; Director of the CRM), and Lea Popovic (Concordia University). 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 2012–2013. Sophie D’Amours, Vice-Rector (Research) François Lalonde, Director of the CRM Université Laval Université de Montréal Graham Carr, Vice-President (Research) Odile Marcotte, Deputy Director of the CRM Concordia University Université du Québec à Montréal Christian Genest Yves Mauffette, Vice-Rector (Research) McGill University Université du Québec à Montréal Jacques Hurtubise Christiane Rousseau Vice-Principal (Research) Representative Université de Montréal McGill University Geneviève Tanguay, Vice-Rector (Research) John Harnad Université de Montréal Concordia University

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 nine CRMLabora- tories 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:

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

96 Governance and Scientific Guidance

John Harnad (Concordia University) Adam M. Oberman (McGill University) Mathematical Physics Applied Mathematics (from January 8th, 2013) Dmitry Jakobson (McGill University) Robert G. Owens (Université de Montréal) Mathematical Analysis Applied Mathematics (until January 7th, 2013) Jean-Marc Lina (École de technologie supérieure) PhysNum — Medical Imaging and Pharmacometrics

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 un- A specialist of probability the- dergraduate degree from the Uni- ory and its applications, Gérard versity of Cambridge in 1975 and Ben Arous arrived to the Courant completed his doctoral degree with Institute (NYU) as a Professor of David Williams at the University Mathematics in 2002. He was ap- College of Swansea in Wales (1978). pointed Director of the Courant In- Since then he has been a leading stitute and Vice Provost for Science researcher in probability theory, in and Engineering Development in particular diffusion in fractals and other disordered September 2011. A native of France, Professor Ben media. He held a Royal Society University Research Arous studied Mathematics at the École normale su- Fellowship at the University of Cambridge from 1985 périeure and earned his Ph.D. from the Université Pa- to 1992, when he joined the Mathematics Department ris Diderot (1981). He has been a Professor at the Uni- at the University of British Columbia. He is currently versité Paris-Sud, at the École normale supérieure, and Professor of Mathematics at UBC. He has held a num- more recently at the École Polytechnique Fédérale de ber of visiting professorships at leading universities. Lausanne, where he held the Chair of Stochastic Mod- Martin Barlow gave an invited lecture at the 1990 ICM elling. He was Chair of the Department of Mathemat- in Kyoto and was an invited lecturer at the presti- ics at the Université Paris-Sud and the Departments of gious Saint-Flour Summer School in 1995. In 2008 he Mathematics and Computer Science at the École nor- received the Jeffery-Williams Prize of the Canadian male supérieure. He also founded a Mathematics Re- Mathematical Society and in 2009 the CRM –Fields– search Institute in Lausanne, the Bernoulli Center. He PIMS Prize. Other distinctions include the Rollo David- is the managing editor (with Amir Dembo, Stanford) of son Prize from the University of Cambridge and the one of the main journals in his field, Probability Theory Junior Whitehead Prize from the London Mathemati- and Related Fields. cal Society. He has been a leader of the international Professor Ben Arous works on probability theory probability community as a lead organizer of numer- (stochastic analysis, large deviations, random media ous conferences, Associate Editor of all the top prob- and random matrices) and its connections with other ability journals, and Editor-in-Chief of the Electronic domains of mathematics (partial differential equations, Communications in Probability. He has been a Fellow dynamical systems), physics (statistical mechanics of of the Institute of Mathematical Statistics since 1995 disordered media), and industrial applications. He is and of the Royal Society of Canada since 1998. In 2006 mainly interested in the time evolution of complex sys- he was elected Fellow of the Royal Society (London). tems and the universal aspects of their long-time behaviour and of their slow relaxation to equilibrium, in particular how complexity and disorder imply ag- ing. He is a Fellow of the Institute of Mathematical

97 Centre de recherches mathématiqes

Statistics (as of August 2011) and an elected member of and as Vice President for Academic Affairs at York Uni- the International Statistical Institute. He was a plenary versity, in Toronto, as well as on the faculties of the speaker at the European Congress of Mathematics, an University of Chicago and the University of Minnesota. invited speaker at the International Congress of Math- He has been a founding editor of a number of statistical ematicians, received a senior Lady Davis Fellowship journals. He has been Vice President of the American (Israel), the Rollo Davidson Prize (Imperial College, Statistical Association and President of the Institute of London), and the Montyon Prize (French Academy of Mathematical Statistics and the International Society Sciences). for Bayesian Analysis. Allan Borodin received his B.A. in Fienberg’s research includes the development of statis- Mathematics in 1963 (from Rutgers tical methods, especially tools for categorical data anal- University), his M.Sc. in Electrical ysis and the analysis of network data, algebraic statis- Engineering and Computer Science tics, causal inference, statistics and the law, machine in 1966 (from Stevens Institute of learning, and the history of statistics. Technology), and his Ph.D. in Com- Fienberg is a member of the U.S. National Academy of puter Science in 1969 (from Cornell Sciences, and a fellow of the Royal Society of Canada, University). He was a systems pro- the American Academy of Arts and Sciences, and the grammer at Bell Laboratories in New Jersey from 1963 American Academy of Political and Social Science, as to 1966 and a Research Fellow at Cornell from 1966 well as a fellow of the American Association for the to 1969. Since 1969, he has been a professor in the Advancement of Science, the American Statistical As- Department of Computer Science at the University of sociation, the Institute of Mathematical Statistics, and Toronto, where he became a full professor in 1977. an elected member of the International Statistical In- He was department chair from 1980 to 1985. Professor stitute. Borodin is a world leader in the mathematical foundations of computer science and has made fundamental Edward Frenkel grew up in Rus- contributions to many areas, including algebraic com- sia and then moved to the US. He putations, resource tradeoffs, routing in interconnec- received his Ph.D. in Mathemat- tion networks, parallel algorithms, on-line algorithms, ics from Harvard University at the and adversarial queuing theory. Professor Borodin has age of 23 after one year of study. been the editor of many journals, including the SIAM He stayed on at Harvard, first as Journal on Computing. He has held positions on, or a Junior Fellow at the prestigious been active in, dozens of committees and organiza- Harvard Society of Fellows, and tions, both inside and outside the University, and has then as an Associate Professor. He was offered a Full held several visiting professorships internationally. In Professorship at the University of California, Berkeley 1991 Professor Borodin was elected a Fellow of the at the age of 28 (one of the youngest ever), and he has Royal Society of Canada and in 2008 he received the been Professor of Mathematics at Berkeley since then. CRM –Fields–PIMS Prize. In 2008 he received the first Chaire d’Excellence award from the Fondation Sciences Mathématiques de Paris. Stephen E. Fienberg is Mau- rice Falk University Professor of Frenkel has authored two books and about 80 articles Statistics and Social Science at in mathematical journals, and he has lectured on his Carnegie Mellon University. He is work around the world. Among his other awards are the Carnegie Mellon codirector of the Hermann Weyl Prize and the Packard Fellowship the Living Analytics Research Cen- in Science and Engineering. tre. Fienberg received his hon. B.Sc. Susan Friedlander is currently in Mathematics and Statistics from Director of the Center for Applied the University of Toronto (1964) and his A.M. and Ph.D. Mathematical Sciences and Pro- degrees in Statistics from Harvard University (1965, fessor of Mathematics at the Uni- 1968). versity of Southern California. She Professor Fienberg has served as Dean of the College obtained her Doctoral degree at of Humanities and Social Sciences at Carnegie Mellon Princeton University in 1972. She

98 Governance and Scientific Guidance has published extensively in the areas of differential ical Sciences and a member of the Board of Directors equations and fluid mechanics. She has been very ac- of the Center for Mathematics and Teaching. Profes- tive on numerous committees and evaluation panels, sor Green also served on the NSERC Major Resources including the Council of the American Mathematical Support Committee and was the editor of the Journal Society and the Board on Mathematical Sciences and of Algebraic Geometry. His research interests are in Their Applications of the National Academies. She has commutative algebra, algebraic geometry, and applied also been involved continuously in the organization mathematics. of conferences and workshops; in particular she was Laurent Habsieger has been a se- a member of the AMS-Shanghai Joint Meeting Pro- nior researcher at the Centre na- gram Committee. She has served on numerous AMS tional de la recherche scientifique editorial boards and university committees. She has (CNRS) since 2002. A former student been honoured with several academic awards, includ- at the École Normale Supérieure ing the Institut Henri-Poincaré Medal, the Gauthier- (ENS), he completed his Ph.D. in Villars Prize for Nonlinear Analysis, and the Univer- Strasbourg before spending one year sity of Illinois Scholar Award (in 2003). Over the years, at the IMA (Minneapolis) as a post- she has been a frequent invited lecturer in the United doctoral fellow. He was then a professor at the Univer- States and around the world. sité du Québec à Montréal (UQAM) for two years. In Mark Goresky has been a member 1990 he joined the CNRS as a junior researcher in Bor- of the Institute for Advanced Study in deaux and in 2002 he accepted a position as senior re- Princeton since 1994. He received his searcher in Lyon. Laurent Habsieger then managed the B.Sc. from the University of British national research group in number theory for 8 years. Columbia in 1971 and a Ph.D. from He was deputy director of his laboratory for 5 years Brown University in 1976. In 1986 he and supervised three Franco-Hungarian research pro- was elected to the Royal Society of grams. In 2011 the CNRS launched the UMI CRM and Canada. He was awarded the Jeffery- he was appointed co-director of the UMI with François Williams Prize of the Canadian Mathematical Society Lalonde, director of the CRM. in 1996 and the Steele Prize of the American Mathe- Having completed his thesis in combinatorics, Laurent matical Society in 2002 (jointly with R. MacPherson). Habsieger broadened its expertise to number theory. He was a member of the editorial board of the Cana- He is the author of around 40 scientific articles in many dian Journal of Mathematics from 1997 to 2000 and is areas of mathematics: combinatorics, arithmetic, spe- currently a member of the editorial board of the Bul- cial functions, coding theory, analysis, etc. letin of the American Mathematical Society. He is a world expert in geometric representation theory. Barbara Lee Keyfitz has been a professor at the Ohio State Univer- Mark L. Green has been a pro- sity since January 2009. She served fessor in the UCLA Department as Director of the Fields Institute of Mathematics since 1982. He re- for Research in Mathematical Sci- ceived his Ph.D. from Princeton ences from 2004 to 2008. From 2000 University in 1972 and was Direc- to 2008, she was John and Rebecca tor of the Institute for Pure and Moores Professor of Mathematics at Applied Mathematics from 2001 to the University of Houston, which she joined in 1987, 2008. Mark Green has received nu- following appointments at Columbia, Princeton, and merous honours during his career. In particular, he Arizona State University. She studied at the University was an invited speaker at the International Congress of Toronto and obtained her Ph.D. at the Courant In- of Mathematicians in Berlin in 1998. He was a plenary stitute (NYU). Barbara Keyfitz is a Fellow of the Amer- speaker at the Abel Centennial held in Oslo in 2002 ican Association for the Advancement of Science and and the Hodge Centennial held in Edinburgh in 2003. the recipient of the 2005 Krieger–Nelson Prize of the Professor Green’s services to the mathematical com- Canadian Mathematical Society. She serves as Trea- munity are extensive. He was a member of the Board surer of the International Council of Industrial and Ap- of Trustees at the Claremont Center for the Mathemat- plied Mathematics and has been a member of several

99 Centre de recherches mathématiqes editorial boards. Her research interests are in the field ceedings. He has given 90 invited lectures at interna- of nonlinear partial differential equations. tional conferences and a series of Aisenstadt lectures A mathematician and physicist by at the CRM (in the fall of 2009). training, François Lalonde holds Claus Michael Ringel received a Doctorat d’État (1985) from the the Diplom (1968) and Ph.D. in Université Paris-Sud in the field of Mathematics from the Goethe- differential topology. His fields of Universität Frankfurt am Main in interest include symplectic topol- 1969 and the Habilitation from ogy, Hamiltonian dynamics, and the Eberhard Karls Universität Tü- the study of infinite-dimensional bingen in 1972. He taught briefly groups of transformations. He has been a member of at Carleton University in Ottawa the Royal Society of Canada since 1997 and was a Kil- (1970–1972). From 1978 to 2010 he was Professor of lam Research Fellowship recipient in 2000–2002. He Mathematics at the Universität Bielefeld in Germany, holds the Canada Research Chair in the field of Sym- where he is now Professor Emeritus. He is in addition plectic Geometry and Topology at the Department of Visiting Chair Professor at Shanghai Jiao Tong Uni- Mathematics and Statistics of the Université de Mont- versity in China. Claus Ringel’s research is in Repre- réal. François Lalonde was a plenary speaker at the sentation Theory, the study of concrete realizations of First Canada–China congress in 1997; part of his work abstract algebraic structures. His work has been pro- in collaboration with Dusa McDuff was presented in foundly influential in the development of the theory of her plenary address at the ICM 1998 in Berlin. He was representations of finite-dimensional algebras, in par- also an invited speaker at the ICM 2006 in Madrid. ticular quivers, hereditary algebras, Ringel–Hall alge- Claude Le Bris obtained his doc- bras, and quantum groups. He has had, and continues torate from the École Polytech- to have, a leading role in a number of SFB (Sonder- nique in France and his accredi- forschungsbereich: Collaborative Research Centre) in tation to supervise research from Germany in the area of representation theory. the Université Paris Dauphine in Since 2003 Keith F. Taylor has 1997. His research interests include been teaching at Dalhousie Uni- mathematical analysis and numer- versity where he notably held the ical methods for partial differen- position of dean at the Faculty tial equations and their applications to molecular sim- of Science from 2003 to 2008. ulation, multiscale problems, materials science, and He is currently Associate Vice- continuum mechanics. He is a world-renowned ex- President Academic for the Out- pert in the mathematics of quantum chemistry and reach and International Programs. the computation of the electronic structure in quan- After obtaining his Ph.D. (1976) at the University of tum physics. Claude Le Bris received the Blaise Pascal Alberta, he became Assistant Professor and Associate Prize from the Académie des Sciences in 1999, the “CS Professor at the University of Saskatchewan. In 1996– 2002 Prize in Scientific Computing,” and the Giovanni 1997, Professor Taylor won the Student Union Teach- Sacchi-Landriani Prize from the Istituto Lombardo in ing Excellence Award, followed by the Master Teacher 2002. He was Civil Engineer-in-Chief and Research Award in 2001. He finds his primary research interests Scientist at the École Nationale des Ponts et Chaussées in Abstract Harmonic Analysis and Wavelet Analysis, and scientific leader of the MICMAC project at INRIA. Spectral Problems Arising in Chemistry and Technol- Claude Le Bris has been a member of several program ogy Enhanced Pedagogy. He has supervised five Ph.D. committees of international conferences and thematic theses and nine M.Sc. theses and is still the founding years organized by research centres. He was co-editor director of the Math Readiness Summer Camps created of Mathematical Modelling and Numerical Analysis and in 1996. editor of the Applied Mathematics Research eXpress. He 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-

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Akshay Venkatesh has been Fellowship (2007), the Salem Prize (2007), the David a professor at Stanford Univer- and Lucile Packard Foundation Fellowship (2007– sity since September 2008. He 2012), and the SASTRA Ramanujan Prize (2008). In obtained his Ph.D. from Prince- 2010 he was Aisenstadt Chair lecturer at the CRM, ton University in 2002, was within the framework of the thematic semester on C.L.E. Moore Instructor at MIT Number Theory as Experimental and Applied Science. from 2002 to 2004, and a pro- His research interests are in number theory and au- fessor at the Courant Institute tomorphic forms, including representation theory, dy- (NYU) from 2004 to 2008. Akshay Venkatesh has re- namics on homogeneous spaces, and arithmetic alge- ceived many prizes and fellowships since the begin- braic geometry. ning of his career, in particular the Sloan Foundation

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.

101 CRM Administrative and Support Staff CRM Administrative and Support Staff

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 Julie Labbé Diane Brulé-De Filippis Secretary Administrative Assistant

Scientific Activities

Louis Pelletier Sakina Benhima 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

103 Mandate of the CRM Mandate of the CRM

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 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

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

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