This volume mainly summarizes the invited talks presented at the 5th Asia-Pacific Workshop on Quantum Information Science (APWQIS) in conjunction with a Festschrift in honor of Professor Vladimir Korepin's 60th birthday. In this Festschrift, we have assembled a medley of interesting articles from some of his friends, well-wishers and collaborators. Comprising both reviews of the state-of-the-art and the latest results, this book covers various aspects of quantum information science, including topics like quantum discord, quantum computing, quantum entanglement, etc.

Ludwig Eduard Boltzmann (1844-1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. He was one of the most important advocates for atomic theory when that scientific model was still highly controversial. To commemorate the 100th anniversary of his death in Duino, the International Symposium ``Boltzmann's Legacy'' was held at the Erwin Schrodinger International Institute for Mathematical Physics in June 2006. This text covers a broad spectrum of topics ranging from equilibrium statistical and nonequilibrium statistical physics, ergodic theory and chaos to basic questions of biology and historical accounts of Boltzmann's work. Besides the lectures presented at the symposium the volume also contains contributions specially written for this occasion. The articles give a broad overview of Boltzmann's legacy to the sciences from the standpoint of some of today's leading scholars in the field. The book addresses students and researchers in mathematics, physics, and the history of science.

By studying algebraic varieties over a field, this book demonstrates how the notion of schemes is necessary in algebraic geometry. It gives a definition of schemes and describes some of their elementary properties.

Proceedings of the NATO Advanced Study Institute and Séminaire de mathématiques supérieures, Montréal, Canada, July 26--August 6, 1993

Based on courses given by the author at MIT and at Rome University in spring 1997, this book presents an introduction to algebraic aspects of conformal field theory. It includes material on the foundations of a rapidly growing area of algebraic conformal theory.