Masaki Kashiwara

Takahiro Kawai

William Casper Graustein Professor of Mathematics and Former Chairman of Mathematics Department Shing-Tung Yau

A Great Japanese Mathematician of the Twentieth Century

Mikio Sato

The original title of this work translated as "Foundation of Algebraic Analysis." Kashiwara (Kyoto U., Japan) changed the title to more precisely reflect the nature of the text's contents and to signal his belief that "the microlocal point of view helps concrete calculations, as powerfully as the Cauchy integral formula provides the values of many definite integrals." Chapters cover basic properties of D-modules, characteristic varieties, construction of D-modules, their functorial properties, regular holonomic systems, b-functions, ring of formal microdifferential operators, microlocal analysis of holonomic systems, and microlocal calculus of b-functions. Translated from the Japanese work Daisu Kaiseki Gairon (2000). Annotation copyrighted by Book News, Inc., Portland, OR

D-modules and Microlocal Calculus

Tetsuji Miwa

This work is concerned with combinatorial aspects arising in the theory of exactly solvable models and representation theory. Developments in integrable models reveal an unexpected link between representation theory and statistical mechanics through combinatorics. For example, Young tableaux, which describe the basis of irreducible representations, appear in the Bethe Ansatz method in quantum spin chains as labels for the eigenstates of Hamiltonians. this text presents results and ideas from three viewpoints: representation theory; integrable models; and combinatorics.

Physical Combinatorics

Pierre Schapira

Teresa Monteiro Fernandes

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Proceedings of the International Conference on D-Modules and Microlocal Geometry held at the University of Lisbon (Portugal), October 29-November 2, 1990

D-Modules and Microlocal Geometry

Microlocal Study of Sheaves

A. Kashiwara

A. Matsuo

K. Saito

I. Satake

Ikuo Satake

As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely. This book centers around the theory of primitive forms which currently plays an active and key role in topological field theory (theoretical physics), but was originally developed as a mathematical notion to define a "good period mapping" for a family of analytic structures. The invited papers in this volume are expository in nature by participants of the Taniguchi Symposium on "Topological Field Theory, Primitive Forms and Related Topics" and the RIMS Symposium bearing the same title, both held in Kyoto. The papers reflect the broad research of some of the world's leading mathematical physicists, and should serve as an excellent resource for researchers as well as graduate students of both disciplines.

Topological Field Theory, Primitive Forms and Related Topics

'MathPhys Odyssey 2001' will serve as an excellent reference text for mathematical physicists and graduate students in a number of areas.; Kashiwara/Miwa have a good track record with both SV and Birkhauser.

Integrable Models and Beyond In Honor of Barry M. McCoy

MathPhys Odyssey 2001

D-module theory is essentially the algebraic study of systems of linear partial differential equations. This book, the first devoted specifically to holonomic D-modules, provides a unified treatment of both regular and irregular D-modules. The authors begin by recalling the main results of the theory of indsheaves and subanalytic sheaves, explaining in detail the operations on D-modules and their tempered holomorphic solutions. As an application, they obtain the Riemann-Hilbert correspondence for regular holonomic D-modules. In the second part of the book the authors do the same for the sheaf of enhanced tempered solutions of (not necessarily regular) holonomic D-modules. Originating from a series of lectures given at the Institut des Hautes Études Scientifiques in Paris, this book is addressed to graduate students and researchers familiar with the language of sheaves and D-modules, in the derived sense.

Regular and Irregular Holonomic D-Modules

Edward Frenkel

Alain Valette

Nolan R. Wallach

Michael Cowling

David A. Vogan

Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability. They further illustrate how representation theory is related to quantum computing; and much more. Taken together, this volume provides both a solid reference and deep insights on current research activity.

Lectures given at the C.I.M.E. Summer School held in Venice, Italy, June 10-17, 2004

Representation Theory and Complex Analysis

Sheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. This volume offers a comprehensive and self-contained treatment of Sheaf Theory from the basis up, with emphasis on the microlocal point of view. From the reviews: "Clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics." –Bulletin of the L.M.S.

With a Short History. «Les débuts de la théorie des faisceaux». By Christian Houzel

Sheaves on Manifolds

Lectures Given at the C.I.M.E. Summer School Held in Venice, Italy, June 10-17, 2004

Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.

Masaki Kashiwara

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