The book contains research papers on Diophantine Geometry, written by participants to a related workshop held at the Centro De Giorgi of the Scuola Normale of Pisa during the period April-July 2005. The authors are eminent experts in the field; actually, several interacting subfields of the main topic are represented here, which is particularly useful to get a broad overview of recent research developments.

This book contains papers presented by leading experts at the "Interdisciplinary Workshop on Mathematical Methods in Biomedical Imaging and Intensity-Modulated Radiation Therapy (IMRT)" held at the Centro di Ricerca Matematica (CRM) Ennio De Giorgi at Pisa, Italy, from October 15 to 19, 2007. The book consists of research and review papers by leading experts and practitioners in biomedical imaging and intensity-modulated radiation therapy (IMRT). The topics include mathematical aspects and practical problems in current major and emerging technologies for the diagnostic and therapeutic medicine and biology research. The contributed work signifies the interdisciplinary cooperation between mathematicians and scientists from medical physics, engineering, clinical medicine and biology, that leads to mathematically-based better solutions of practical problems in biomedical imaging and IMRT. This book is also a survey of important research directions and opportunities in mathematics induced by problems in biomedical imaging and radiation planning applications.

In the most recent years growing attention has been dedicated to many body quantum systems from the point of view of quantum information. Indeed, after the initial investigation of simple systems as single or two qubits, the need for understanding the characteristics of a realistic quantum information device necessarily leads to the study of many body quantum systems. These studies are also driven by the very fast development of experiments which in recent years have reached the goal of coherent control of a few qubits with a roadmap for further scaling and improvement of coherent control and manipulation techniques. This book gives a selection of the current research topics in the field of quantum information for many body quantum systems together with open problems.