Begins with a brief review of relativity, relativistic quantum mechanics, and classical gauge theories, emphasizing the basic physical concepts and mathematical foundations. This book offers a precise definition of the fermionic projector and the use of me

In commemoration of the tenth anniversary of the Institute of Mathematics at East China Normal University, an International Conference on complex geometry and related fields convened. This book presents conference highlights, dealing with topics of differe

The International Congress of Mathematicians was an historical event that was held at the Morningside Center of Mathematics of the Chinese Academy of Sciences (Beijing, China). It was the first occasion where Chinese mathematicians from all over the world gathered to present their research. Topics covered in the volume include algebra and representation theory, algebraic geometry, number theory and automorphic forms, Riemannian geometry and geometric analysis, mathematical physics, topology, complex analysis and complex geometry, computational mathematics, and combinatorics.

The collection of articles in this volume are based on lectures presented during the Winter School on Mirror Symmetry held at Harvard University. There are many directions suggested by mirror symmetry which could potentially have very rich connections in physics and mathematics. This book brings together research in a major area of mathematical physics, including the progress in mirror manifolds and Lagrangian submanifolds. In particular, several articles describing homological approach and related topics are included.

Consists of the proceedings of the Third International Congress of Chinese Mathematicians, held at the Chinese University of Hong Kong in December 2004. This book features lectures on topics such as algebra, number theory and cryptography; algebraic geomet

Consists of the proceedings of the Third International Congress of Chinese Mathematicians, held at the Chinese University of Hong Kong in December 2004. This book features lectures on topics such as algebra, number theory and cryptography; algebraic geomet

This volume contains papers presented at the conference Computational Prespectives on Number Theory held at the University of Illinois at Chicago in honour of the retirement of A.O.L. Atkin. In keeping with Atkin's interests and work, the papers cover a range of topics, including algebraic number theory, p-adic modular forms and modular curves. Many of the papers reflect Atkin's particular interest in computational and algorithmic questions.

Based on lectures from a program on integrable systems and differential geometry held at Taiwan's National Center for Theoretical Sciences, this book provides an introduction to integrable systems and their relation to differential geometry. It is suitable

The theory of Dirichlet forms brings together methods and insights from the calculus of variations, stochastic analysis, partial differential and difference equations, potential theory, Riemannian geometry and more.

This volume presents contributions of participants of a workshop held at the Centre de Recherches Mathematiques (CRM), University of Montreal. It can be viewed as a sequel to Mirror Symmetry I (1998), Mirror Symmetry II (1996) and Mirror Symmetry III (1999). The text presents a broad survey of many of the noteworthy developments that have taken place in string theory, geometry and duality since the mid 1990s. Some of the topics emphasized include: integrable models and supersymmetric gauge theories; theory of M- and D-branes and noncommutative geometry; duality between strings and gauge...