Masaki Kashiwara – författare

Based on a seminar sponsored by the Institute for Advanced Study in 1977-1978, this set of papers introduces micro-local analysis concisely and clearly to mathematicians with an analytical background. The papers treat the theory of microfunctions and applications such as boundary values of elliptic partial differential equations, propagation of singularities in the vicinity of degenerate characteristics, holonomic systems, Feynman integrals from the hyperfunction point of view, and harmonic analysis on Lie groups.

The use of algebraic methods for studying analysts is an important theme in modern mathematics. The most significant development in this field is microlocal analysis, that is, the local study of differential equations on cotangent bundles. This treatise provides a thorough description of microlocal analysis starting from its foundations. The book begins with the definition of a hyperfunction. It then carefully develops the microfunction theory and its applications to differential equations and theoretical physics. It also provides a description of microdifferential equations, the microlocalization of linear differential equations. Finally, the authors present the structure theorems for systems of microdifferential equations, where the quantized contact transformations are used as a fundamental device.The microfunction theory, together with the quantized contact transformation theory, constitutes a valuable new viewpoint in linear partial differential equations.Originally published in 1986.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Categories and sheaves, which emerged in the middle of the last century as an enrichment for the concepts of sets and functions, appear almost everywhere in mathematics nowadays.

This book covers categories, homological algebra and sheaves in a systematic and exhaustive manner starting from scratch, and continues with full proofs to an exposition of the most recent results in the literature, and sometimes beyond.

The authors present the general theory of categories and functors, emphasising inductive and projective limits, tensor categories, representable functors, ind-objects and localization. Then they study homological algebra including additive, abelian, triangulated categories and also unbounded derived categories using transfinite induction and accessible objects. Finally, sheaf theory as well as twisted sheaves and stacks appear in the framework of Grothendieck topologies.

Six leading experts lecture on a wide spectrum of recent results on the subject of the title, providing both a solid reference and deep insights on current research activity. Michael Cowling presents a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces. Alain Valette recalls the concept of amenability and shows how it is used in the proof of rigidity results for lattices of semisimple Lie groups. Edward Frenkel describes the geometric Langlands correspondence for complex algebraic curves, concentrating on the ramified case where a finite number of regular singular points is allowed. Masaki Kashiwara studies the relationship between the representation theory of real semisimple Lie groups and the geometry of the flag manifolds associated with the corresponding complex algebraic groups. David Vogan deals with the problem of getting unitary representations out of those arising from complex analysis, such as minimal globalizations realized on Dolbeault cohomology with compact support. Nolan Wallach illustrates how representation theory is related to quantum computing, focusing on the study of qubit entanglement.