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 ...
Developments in mathematical physics during the second half of the 20th century influenced a number of mathematical areas, among the more significant being representation theory, differential equations, combinatorics, and algebraic geometry. In all of them, the dynamic role of integrable models has been central, largely due to two essential ...
The first series of lectures in this volume are an introductory account of the theory of microfunctions. This parallels somewhat the account in (SKK); however, here the cohomological aspects of the subject are somewhat suppressed in order to make these lectures more accessible to an audience of analysts. The subsequent lectures in this volume are ...
This work is concerned with combinatorial aspects arising in the theory of exactly solvable models and representation theory. Recent 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 ...
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 ...
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 ...
From the reviews: This book is devoted to the study of sheaves by microlocal methods..(it) may serve as a reference source as well as a textbook on this new subject. Houzel's historical overview of the development of sheaf theory will identify important landmarks for students and will be a pleasure to read for specialists. - "Math. Reviews 92a ...
Masaki Kashiwara is undoubtedly one of the masters of the theory of $D$-modules, and he has created a good, accessible entry point to the subject. The theory of $D$-modules is a very powerful point of view, bringing ideas from algebra and algebraic geometry to the analysis of systems of differential equations. It is often used in conjunction with ...
After three introductory volumes on the classification of the finite simple groups, ("Mathematical Surveys and Monographs, Volumes 40.1, 40.2, and 40.3"), the authors now start the proof of the classification theorem: They begin the analysis of a minimal counterexample $G$ to the theorem. Two fundamental and powerful theorems in finite group ...
The focus of this work is the strong interaction between mathematics and theoretical physics. Theories developed in maths are being applied to physics, and conversely. It centres around the theory of primitive forms which plays an active role in topological field theory (theoretical physics).
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