Masaki Kashiwara Livres

Focusing on the study of sheaves through microlocal methods, this book serves both as a reference and a textbook for this emerging field. It includes a historical overview of sheaf theory, highlighting significant developments that will benefit students and engage specialists. The blend of accessible explanations and in-depth analysis makes it an enjoyable read for those interested in the evolution of this mathematical concept.

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.

This book presents a comprehensive exploration of the Riemann-Hilbert correspondence, focusing on holonomic D-modules, including those that are not necessarily regular. It utilizes the framework of indsheaves to provide a unified approach, making it suitable for advanced readers interested in modern mathematical theories and applications. The text delves into the intricate relationships between algebraic geometry and differential equations, offering a valuable resource for researchers and students in the field.

Taking into account the various criss-crossing among mathematical subject, Physical Combinatorics presents new results and exciting ideas from three viewpoints; representation theory, integrable models, and combinatorics. 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.

Focusing on microlocal analysis, this treatise delves into the local study of differential equations on cotangent bundles, offering a comprehensive exploration from foundational concepts. It introduces hyperfunctions and develops microfunction theory, highlighting its applications in differential equations and theoretical physics. The text also covers microdifferential equations and the microlocalization of linear differential equations, culminating in structure theorems for systems of microdifferential equations, utilizing quantized contact transformations as a key tool.

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.