New Trends in Mathematical Physics

Vladas Sidoraviciusˇ

Editor

New Trends

in Mathematical Physics

Selected Contributions

of the XVth International Congress on Mathematical Physics

Vladas Sidoraviciusˇ

Instituto de Matemática Pura e Aplicada (IMPA) Estrada Dona Castorina 110

Rio de Janeiro, RJ Brazil zeitouni@math.umn.edu

ISBN 978-90-481-2809-9 e-ISBN 978-90-481-2810-5 DOI 10.1007/978-90-481-2810-5

Springer Dordrecht Heidelberg London New York

Library of Congress Control Number: 2009932135

©Springer Science+Business Media B.V. 2009

No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

The editor acknowledges that part of the elements used in the cover design (including the logo of the ICMP 2006 meeting) were created by Sergio Vaz.

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)

after the Congress in Rio, Wendelin Werner, the plenary speaker of the XVth ICMP, was awarded the Fields medal for his contribution to this field. And in the spring of 2007 Srinivasa Raghu Varadhan, the chair of the International Scientific Committee of the XV ICMP, was awarded the Abel Prize. I believe this speaks not only about the recognition of the increasing role of Probability Theory and appreciation of its mathematical depth, but also about importance of all our community, since research performed by W. Werner and S.R. Varadhan, and the origins of questions they answer, are deeply rooted in the fields of Mathematical Physics.

However it was also the time when with great sadness we learned in September 2008 about the untimely death of Oded Schramm, the inventor of SLE and the 2003 Poincaré Prize recipient.

The preparation of the Congress as usual has taken a huge amount of work. On the scientific side I must thank all the members of the International Scientific Committee. I would like also to express my deep gratitude and affection to David Brydges, the President of International Association of Mathematical Physics during the period 2003–2005, who was the visionary, driving force and first aid help at all occasions. Among the local organizers I have to single out first of all Prof. J.F. Perez and Profs. C. Camacho, J. Palis and M. Viana who were pivotal for the success of the meeting. And last but no least, all my thanks and appreciation to the whole team of logistic and administrative support of DAC, masterfully conducted by Mme. S. Lima.

The Congress could not have happened without the generous support of numerous sponsors and efforts of many individuals, who are listed on the homepage of the congress (http://www.iamp.org/). I’m most grateful to them all. The reader also will find there the list of participants of the meeting.

Finally a few words on the organization of the book. We were not seeking to produce a standard “Proceedings” book. To document the content of the plenary talks and invited talks in all specialized sessions, in the Appendix to the book we include the abstracts of the meeting as they stood in August 2006, so that the interested reader can trace back the contents of all talks. As for the main part of the book, we invited all plenary speakers and invited speakers of specialized sessions to contribute with articles that they find appropriate for this volume, reflecting the current state of the art in Mathematical Physics, and which are written according to their own vision of the development of their fields. Thus, as a result, the reader will find here the original research articles, extensive reviews, as well as extended versions of talks.

Vladas Sidoraviciusˇ

mechanics in equilibrium (classical and quantum) and nonequilibrium fluctuations, to dynamical systems, to symmetries, to PDE’s . . . .

The three Henri Poincaré prizes, that the Iagolnitzer Foundation sponsors and the IAMP awards, recognize exceptional contributions and honor three colleagues, for their great contributions to Physics and for providing examples that we will try to imitate on how to look at problems that we cherish.

We think that the wide variety of session and plenary talks will provide, through the publication of the present proceedings, inspiration for new challenging problems, and confidence, to the many young colleagues who want to continue the exciting experience of those of us who have followed the developments from the early ‘960’s and can feel the immense difference between what was known at the time and today.

Finally IAMP thanks the local organizers of the meeting in Rio for the effort they made to make easy and agreeable participation by our colleagues, particularly those who undertook a long journey to attend our meeting.

It has been decided that ICMP09 will be held in Prague and we are sure that it will continue the tradition of excellence that this and earlier ICMP meetings have bequeathed to us.

Giovanni Gallavotti

IAMP President 2006–2008

x

National Organizing Committee

ICMP 2006—International Advisory Committee

xi

The XV International Congress on Mathematical Physics was organized by the International Association of Mathematical Physics (IAMP), in association with Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, Instituto do Milênio (IM-AGIMB) and Petrobras (Brazil).

Past Congresses