# Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006

Volume I

## Editors

### Marta Sanz-Solé

Universitat de Barcelona, Spain### Javier Soria

Universitat de Barcelona, Spain### Juan L. Varona

Universidad de La Rioja, Logroño, Spain### Joan Verdera

Universitat Autónoma de Barcelona, Spain

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**Note: The ICM2006 Proceedings are available only as a set, individual volumes cannot be ordered.**

The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world, and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outstanding mathematical achievement. At the same time, the International Mathematical Union awards the Nevanlinna Prize for work in the field of theoretical computer science. The proceedings of ICM 2006, published as a three-volume set, present an overview of current research in all areas of mathematics and provide a permanent record the congress.

The first volume features the works of Fields Medallists and the Nevanlinna Prize winner, the plenary lectures, and the speeches and pictures of the opening and closing ceremonies and award sessions. The other two volumes present the invited lectures, arranged according to their mathematical subject.