This volume is the outcome of a CIRM Workshop on Renormalization and Galois Theories held in Luminy, France, in March 2006. The subject of this workshop was the

This book tells mathematicians about an amazing subject invented by physicists and it tells physicists how a master mathematician must proceed in order to under

And God said, Let there be light; and there was light. Genesis 1,3 Light is not only the basis of our biological existence, but also an essential source of our

The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces whe

This book contains carefully revised and expanded versions of eight courses that were presented at the University of Strasbourg during two geometry master class