Acknowledgements The ICM 2006 is held under the auspices of the International Mathematical Union and the sponsorship of the following public and academic bodies and private companies and foundations. List of Sponsors Public Bodies Ministerio de Educaci´ony Ciencia Ministerio de Asuntos Exteriores y de Cooperaci´on Agencia Espa˜nolade Cooperaci´onInternacional Ministerio de Cultura Biblioteca Nacional Direcci´onGeneral de Comunicaci´ony Cooperaci´onCultural Sociedad Estatal de Conmemoraciones Culturales Comunidad de Madrid Consejer´ıade Educaci´on Instituto Madrile˜node Desarrollo Ayuntamiento de Madrid Madrid-Convention Bureau Concejal´ıa de las Artes Centro Cultural Conde Duque Consejo Superior de Investigaciones Cient´ıficas Correos Fundaci´onCarolina Fundaci´onEspa˜nola para la Ciencia y la Tecnolog´ıa Academic Bodies Universidad Aut´onomade Madrid Universitat de Barcelona Universitat Aut`onoma de Barcelona Universidad de Castilla-La Mancha Universidad Complutense de Madrid Universidad Nacional de Educaci´ona Distancia Universidad de Sevilla Association for Women in Mathematics Canadian Mathematical Society Real Sociedad Matem´atica Espa˜nola Royal Dutch Mathematical Society Sociedad de Estad´ıstica e Investigaci´onOperativa Sociedad Espa˜nolade Matem´atica Aplicada Societat Catalana de Matem`atiques Soci´et´eMath´ematique de France Irish Mathematical Society Mathematical Society of Japan National Council of Teachers of Mathematics, USA Sociedad Espa˜nolade Investigaci´onen Educaci´onMatem´atica Federaci´onEspa˜nola de Sociedades de Profesores de Matem´aticas Sociedad Espa˜nolade Historia de las Ciencias y de las T´ecnicas Private Companies and Foundations Enterasys Fundaci´onPedro Barri´ede la Maza Fundaci´onRam´onAreces Fundaci´onVodafone Grupo SM, Editorial SM ONCE Springer The King Juan Carlos I of Spain Center of N. Y. University in Madrid International Congress of Mathematicians Madrid, 2006 August 22–30 Welcome to the ICM 2006! Every four years, mathematicians from all over the world gather together for two basic reasons: to debate the most recent results in the discipline and to honor the most outstanding achievements over this period. In no other discipline is a comparable event of this nature held. The fact that mathematicians have been able to maintain this tradition for more than a century is a source of admiration for our colleagues in other fields. The ICM is much more than a congress. Naturally, it involves an important scientific component, for which reason it is a mathematical congress, but there is also a vital social component, which makes it a truly international congress of mathematicians. For Spanish mathematicians, the ICM in Madrid is an important step on the international scene; from a merely testimonial presence in mathematical research 25 years ago, today we have reached really spectacular figures in terms of production. Our aim is also to improve the quality of our research work, and we feel sure that the ICM 2006 will provide us with a basis that will pave the way for better mathematical infrastructures in our country. We are looking forward greatly to the ICM 2006 and trust that all our visitors and guests will take away good memories of Spanish hospitality, in the expectation that the vitality of this culturally complex and varied country will inspire them with the wish to visit us again. The ICM 2006 is a collective undertaking on the part of the whole Spanish mathematical community, to which everyone has contributed in his or her own way. Furthermore, the economic and logistical support provided by the Ministries of Education, Culture and Foreign Affairs, as well as by the Community of Madrid Regional Government and the City of Madrid itself, has been vital for the success of the congress. Private initiative has also played an important part, particularly in opening up new avenues of collaboration for Spanish mathematicians in the future. I would like to express my gratitude to the members of the Organizing Committee for the extraordinary effort they have made; without them this congress would not have been possible. All those involved in the organization of such an outstanding event are aware of the difficulties to be overcome, the moments of excitement and also the moments of discouragement. In the end, however, here we are, and the effort has undoubtedly been worth it. We sincerely hope that you all enjoy these nine days in Madrid to the utmost; we could not wish for a better reward. Welcome to Madrid! Manuel de Le´on President of the ICM 2006 Organizing Committee Contents About this Book and the Schedule 5 A The program day by day 6 Tuesday, August 22 . 6 Wednesday, August 23 . 7 Thursday, August 24 . 15 Friday, August 25 . 24 Saturday, August 26 . 35 Monday, August 28 . 46 Tuesday, August 29 . 57 Wednesday, August 30 . 65 B Plenary Lectures 69 C Schedule of Sections 1-20 71 01: Logic and Foundations . 71 02: Algebra . 73 03: Number Theory . 78 04: Algebraic and Complex Geometry . 82 05: Geometry . 85 06: Topology . 90 07: Lie Groups and Lie Algebras . 93 08: Analysis . 96 09: Operator Algebras and Functional Analysis . 101 10: Ordinary Differential Equations and Dynamical Systems . 104 11: Partial Differential Equations . 109 12: Mathematical Physics . 115 13: Probability and Statistics . 119 14: Combinatorics . 123 15: Mathematical Aspects of Computer Science . 127 16: Numerical Analysis and Scientific Computing . 130 17: Control Theory and Optimization . 134 18: Applications of Mathematics in the Sciences . 138 19: Mathematics Education and Popularization of Mathematics . 143 20: History of Mathematics . 147 D Mathematical Software 149 E Special Activities 151 F Other Activities 154 G Cultural Activities 156 H Social Activities 159 H.1 Opening Ceremony and Reception . 159 H.2 ICM 2006 Party . 159 H.3 Tourist Program . 160 H.4 Congress Excursions . 161 H.5 Activities for Accompanying Persons . 162 I Program Changes and Informal Seminars 163 J Practical Information 164 K Committees 169 K.1 Organizing Committees . 169 K.2 IMU Committees . 172 ICM 2006 – Program iii L List of Speakers 174 L.1 Plenary Speakers . 174 L.2 Invited Speakers . 174 L.3 Short Communications . 176 L.4 Posters . 184 L.5 Mathematical Software . 187 L.6 Special Activities: Organizers, Panelists and Speakers . 188 L.7 Other Activities: Organizers, Panelists and Speakers . 188 M Chairpersons 189 N Contributions referees 192 O Volunteers 194 P Donators 200 Q List of Exhibitors 202 R Structure of the Conference Building and Room Index 205 Map of the Building 206 iv ICM 2006 – Program About this Book and the Schedule We invite you to enjoy the many activities of the ICM 2006 throughout eight intensive days. We have organized the timetable into four parts: • Morning sessions, going from 9:00 to 12:45, devoted exclusively to plenary lectures. • Midday special lectures, devoted to awardees and some special lectures. • Afternoon sessions, starting at 15:00 and ending either at 17:45 or at 18:45, devoted to invited lectures running in seven or eight parallel sessions. • Evening sessions, from 18:00 to 20:00, for panel discussions on important issues for mathematics and mathematicians and presentations of a great variety of interesting projects related with mathematics (see sections E, F and G). Mathematical contributions of participants are scheduled in the afternoon and evening sessions. The book that you have in your hands intends to help you with your daily searching of the most interesting activities according to your interests and taste. If you do not mind to miss some updates, this is enough. However, we recommend consultation of the on-line companion of this book: the on-line program accessible through the website of the congress http://www.icm2006.org/ and continually updated during the congress. Notice that accepted abstracts by participants at the ICM 2006 who have registered later than June 13, 2006, are not included in this book. Following the wise tradition of the (at least) three last ICM’s, the schedule is presented in two different forms: day by day and by sections. We devote a separate section to the contributions on mathematical software, because of their special character and scheduling. Notice that for the non-invited sessions, we have only listed the name of the author of the presentation. For poster sessions, authors are listed in alphabetical order. Activities of the evening sessions are gathered in three different sections, according to their character. They are listed in alphabetical order. The entries on practical information are also listed in alphabetical order. In spite of their universal flavour, the names of the rooms of the congress venue —Palacio Municipal de Congresos de Madrid— have been modified, for the sake of simplicity. The name of the room for each activity appears listed on the right hand side with a short code. For decoding, please consult section R. Using our logical renaming (R for right wing and L for left wing) plus the map of the building, we very much hope you will not be lost. The first day, you will probably feel like in a maze, but very soon you will admire the grandiose, clever structure of one of the samples of modern architecture in Madrid. Marta Sanz-Sol´e Chair of the Local Program Committee Credits • Layout and typesetting: Maria Juli`a • Programming and database management: Rafael Serra Fuster, Agilgrup • Technical secretariat: Unicongress • LATEX macros adapted from ICM’98 Berlin, kindly handed over by Martin Gr¨otschel, President of the Organizing Committee ICM 2006 – Program 5 Tuesday, August 22 A The program day by day Tuesday, August 22 Opening Ceremony 10:30 – 12:30 Auditorium A∗ Video Film Opening of the Congress Sir John Ball, President of the International Mathematical Union Manuel de Le´on, President of the ICM 2006 Organizing Committee Musical Interlude Welcome Addresses by Public Authorities Musical Interlude Presentation of the Fields Medals Sir John Ball, Chair of the Fields Medal Committee for 2006 Presentation of the Rolf Nevanlinna Prize Margaret H.