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Rapportannuel 2005 2006 Rapportannuel 2005 2006 Rapportannuel 2005 2006 Centre de recherches mathématiques Université de Montréal C.P. 6128, succ. Centre-ville Montréal, QC H3C 3J7 Canada Le rapport annuel est également disponible sur le site web du CRM www.crm.umontreal.ca c Centre de recherches mathématiques Université de Montréal, 2006 ISBN 2-921120-43-7 CENTRE DE RECHERCHES MATHÉMATIQUES Présentation du rapport annuel 5 Une année cruciale pour les mathématiques au Canada . 6 Programme thématique 9 Thème de l’année 2005-2006 : Analyse en théorie des nombres . 10 Titulaires des chaires Aisenstadt 2005-2006 : M. Bhargava, K. Soundararajan et T. Tao . 10 Activités de l’année thématique . 13 Programmes thématiques antérieurs . 23 Programme général 24 Activités du CRM . 25 Les colloques CRM-ISM . 34 Programme multidisciplinaire et industriel 37 Activités du CRM du programme multidisciplinaire et industriel . 38 Prix du CRM 45 Le prix CRM-Fields-PIMS décerné à Nicole Tomczak-Jaegermann . 46 Le prix André-Aisenstadt 2006 décerné conjointement à Iosif Polterovich et Tai-Peng Tsai . 47 Le prix ACP-CRM 2006 décerné à John Harnad . 48 Le prix CRM-SSC 2006 décerné à Jeffrey Rosenthal . 49 Grandes Conférences du CRM 50 Jean-Marie De Koninck . 51 Ivar Ekeland . 52 Partenariats du CRM 54 Partenaires du CRM . 55 Initiatives conjointes . 59 Éducation et formation 63 Institut des sciences mathématiques (ISM) . 64 Autres initiatives conjointes . 66 Laboratoires de recherche 68 Laboratoire d’analyse mathématique . 69 CICMA................................................. 72 CIRGET . 75 LaCIM ................................................. 77 Laboratoire de mathématiques appliquées . 80 Laboratoire de physique mathématique . 83 PhysNum . 87 Laboratoire de statistique . 90 Publications 94 Parutions récentes . 95 Parutions antérieures . 95 Prépublications du CRM . 98 Personnel scientifique 100 Membres du CRM en 2005-2006 . 101 Stagiaires postdoctoraux . 103 Visiteurs à long terme . 103 Visiteurs à court terme . 105 Comités à la tête du CRM 107 Bureau de direction . 108 Comité consultatif scientifique . 108 3 CENTRE DE RECHERCHES MATHÉMATIQUES Personnel administratif 111 Direction . 112 Administration et soutien à la recherche . 112 Activités scientifiques . 112 Informatique . 112 Publications . 112 Communications . 112 État des revenus et dépenses de l’exercice financier se terminant le 31 mai 2006 113 Mandat du CRM 116 4 Présentation du rapport annuel CENTRE DE RECHERCHES MATHÉMATIQUES Une année cruciale pour les mathématiques au Canada L’année 2005-2006 au boratoires. De la théorie des nombres, la géomé- CRM fut l’une des an- trie et la topologie jusqu’à l’imagerie cérébrale nées les plus profondes et l’informatique quantique, en passant par les et les plus marquantes groupes de recherche en statistiques et en mathé- de la vie des instituts matiques appliquées, la vitalité du CRM repose, canadiens de mathé- en fin de compte, sur ses laboratoires. matiques. Avec pour Le CRM est en train de mettre sur pied deux organisateurs Andrew nouveaux laboratoires, le laboratoire d’informa- Granville (Université de tique quantique INTRIQ (Institut transdiscipli- Montréal), Chantal Da- naire en informatique quantique) et un autre la- vid (Université Concor- boratoire. L’équipe du CRM a également trans- dia) et Henri Darmon formé son site web, qui comprend 80 000 pages (Université McGill), l’année thématique en ana- dynamiques mises à jour quotidiennement et lyse et théorie des nombres fut une année splen- 7 500 pages produites manuellement, en français dide et merveilleusement remplie de créativité, et en anglais. Ce site web est le résultat d’un long de collaboration et de découvertes. Les trois titu- effort pour diffuser le plus largement et complè- laires de chaires Aisenstadt, approchés au début tement possible tout ce qui peut intéresser les de l’année 2004 par les organisateurs, donnèrent chercheurs travaillant dans les sciences mathé- de magnifiques conférences et passèrent plu- matiques. Le site web reçoit ses informations du sieurs mois au CRM. Il s’agit de M. Bhargava, de « Monstre », une des plus grandes bases de don- Princeton University (invité à donner une confé- nées du monde dans le domaine mathématique. rence plénière au congrès ICM 2006), K. Sounda- Allez à l’adresse www.crm.umontreal.ca et choi- rarajan, de Stanford University, et Terence Tao, sissez votre langue (le choix est restreint, mais de UCLA (qui a reçu la médaille Fields en 2006). c’est quand même un choix !). À la source des innovations et de l’effervescence Le CRM fut le premier institut canadien à sol- du CRM, on trouve les scientifiques qui lui sont liciter des fonds à la fois de la NSF, de l’OTAN attachés et dont le travail attire naturellement et du Clay Institute, et à recevoir de généreuses les mathématiciens éminents du monde entier. subventions de ces organismes : toutes nos de- Alors qu’il est relativement facile pour un insti- mandes furent couronnées de plus de succès que tut d’inviter un récipiendaire de médaille Fields ce à quoi nous nous attendions. Notons que le ou de prix Nobel à donner une conférence, il seul congrès du type « NATO Advanced Study est beaucoup plus difficile et intéressant d’invi- Institute » à recevoir un financement de l’OTAN ter ces récipiendaires et de travailler avec eux chaque année est le « Séminaire de mathéma- pendant plusieurs mois juste avant qu’ils ne re- tiques supérieures », organisé conjointement par çoivent les plus grands honneurs (et la médaille le CRM et le Département de mathématiques et Fields en particulier). C’est ce qui se produi- de statistique de l’Université de Montréal. En sit l’année dernière dans le cas des trois jeunes 2007, le CRM organisera pour la première fois titulaires des chaires Aisenstadt. Pendant l’an- un congrès aux États-Unis. Ce congrès aura lieu née thématique, plus de quarante chercheurs du à Stanford University en juin 2007 et sera le pre- monde entier et de nombreux stagiaires postdoc- mier à réunir la plupart des mathématiciens tra- toraux firent de longs séjours au CRM. Des cen- vaillant en théorie symplectique des champs. À taines de conférenciers invités vinrent au CRM l’heure où nous écrivons ces lignes, nous venons dans le cadre de l’année thématique, y com- tout juste d’apprendre que la NSF nous accordait pris Tim Gowers, de Cambridge University (ré- le montant demandé. cipiendaire d’une médaille Fields), Jean Bour- gain, de l’Institute for Advanced Study (réci- Le CRM a signé cette année de nouveaux ac- piendaire d’une médaille Fields), et Barry Ma- cords internationaux, notamment des accords zur, de Harvard University. avec l’INRIA et l’INSERM (deux instituts fran- çais), et des accords avec l’Amérique Latine et Le CRM est beaucoup plus qu’un centre où ont l’Europe de l’Est (DIMATIA). Des négociations lieu des congrès et des ateliers ; c’est à la fois sont en cours avec le CNRS afin de créer trois un milieu d’incubation pour des progrès fasci- ou quatre GDRI (Groupe de recherche interna- nants qui ont des répercussions dans le monde tional) comprenant une vaste gamme de pro- entier, et un institut comprenant dix grands la- 6 PRÉSENTATION DU RAPPORT ANNUEL jets dans la plupart des domaines des mathéma- Le CRM a aussi lancé cette année le pro- tiques, financés conjointement, pour la première gramme« Grandes conférences du CRM » afin de fois, par des organismes européens et nord- rejoindre le grand public, les professeurs de se- américains. Enfin, le CRM prépare une mission condaire et de collège et leurs étudiants. La qua- scientifique en Inde qui jettera les bases de liens lité et le rayonnement de ces conférences ont été durables entre le Canada et les grands centres tels qu’elles ont touché tous les milieux de la so- scientifiques de ce pays. Cette mission, prépa- ciété, même les universitaires, aussi bien en bio- rée avec le gouvernement du Québec et plu- logie, médecine et philosophie qu’en physique et sieurs vice-recteurs, aura lieu en novembre 2006. informatique. Avec comme conférenciers Jean- Puisque les mathématiques sont l’une des trois Marie De Koninck, choisi scientifique de l’an- disciplines choisies pour cette mission et que le née par Radio-Canada, Ivar Ekeland, directeur congrès ICM aura lieu en Inde en 2010 (après du PIMS et ancien président de l’Université de une lutte serrée avec Montréal), il est naturel de Paris-Dauphine, et en novembre 2006 Bart de créer des liens à la fois avec des centres de ma- Smit, de l’Université de Leyde aux Pays-Bas, thématiques pures et des centres de mathéma- ces conférences ont suscité un engouement re- tiques appliquées. marquable et attiré chaque fois environ 300 per- En collaboration avec l’Institut des sciences ma- sonnes de tous les milieux. thématiques (ISM), son partenaire en enseigne- Les Grandes conférences du CRM ont lieu à tour ment universitaire, le CRM a lancé cette an- de rôle dans les grandes universités québécoises, née la revue Accromαth. Ses textes sont rédi- et pourraient très bien avoir lieu hors campus gés et révisés par la plus belle équipe éditoriale dans de grandes salles de Montréal, Québec, canadienne qui soit, constituée d’André Ross Sherbrooke ou Ottawa. Le CRM veut contribuer (rédacteur en chef), France Caron, Louis Char- (et contribue déjà) au rayonnement intellectuel bonneau, Jocelyn Dagenais, Jean-Marie De Ko- des universités et de ses chercheurs, où que ce ninck, André Deschênes, Christian Genest, Fré- soit, et en tout temps. Nous voulons animer la déric Gourdeau, Bernard Hodgson et Christiane vie intellectuelle de ce pays, la faire entrer dans Rousseau. Tous ses membres s’impliquent dans les moeurs de façon nette et naturelle et faire l’enseignement des mathématiques, que ce soit connaître aux Québécois et aux Canadiens les au niveau secondaire, collégial ou universitaire, plus grands enjeux scientifiques et culturels du et plusieurs d’entre eux sont reconnus pour leurs XXIe siècle.
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