A Brief Introduction to Berezin¿Toeplitz Operators on Compact Kähler Manifolds (CRM Short Courses) - Hardcover

Le Floch, Yohann

Hardcover

ISBN 10: 3319946811 ISBN 13: 9783319946818

Verlag: Springer International Publishing AG, 2018

Inhaltsangabe

<P>THIS TEXT PROVIDES A COMPREHENSIVE INTRODUCTION TO BEREZIN–TOEPLITZ OPERATORS ON COMPACT KÄHLER MANIFOLDS. THE HEART OF THE BOOK IS DEVOTED TO A PROOF OF THE MAIN PROPERTIES OF THESE OPERATORS WHICH HAVE BEEN PLAYING A SIGNIFICANT ROLE IN VARIOUS AREAS OF MATHEMATICS SUCH AS COMPLEX GEOMETRY, TOPOLOGICAL QUANTUM FIELD THEORY, INTEGRABLE SYSTEMS, AND THE STUDY OF LINKS BETWEEN SYMPLECTIC TOPOLOGY AND QUANTUM MECHANICS. THE BOOK IS CAREFULLY DESIGNED TO SUPPLY GRADUATE STUDENTS WITH A UNIQUE ACCESSIBILITY TO THE SUBJECT. THE FIRST PART CONTAINS A REVIEW OF RELEVANT MATERIAL FROM COMPLEX GEOMETRY. EXAMPLES ARE PRESENTED WITH EXPLICIT DETAIL AND COMPUTATION; PREREQUISITES HAVE BEEN KEPT TO A MINIMUM. READERS ARE ENCOURAGED TO ENHANCE THEIR UNDERSTANDING OF THE MATERIAL BY WORKING THROUGH THE MANY STRAIGHTFORWARD EXERCISES. </P><BR>

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Reseña del editor

This text provides a comprehensive introduction to Berezin–Toeplitz operators on compact Kähler manifolds. The heart of the book is devoted to a proof of the main properties of these operators which have been playing a significant role in various areas of mathematics such as complex geometry, topological quantum field theory, integrable systems, and the study of links between symplectic topology and quantum mechanics. The book is carefully designed to supply graduate students with a unique accessibility to the subject. The first part contains a review of relevant material from complex geometry. Examples are presented with explicit detail and computation; prerequisites have been kept to a minimum. Readers are encouraged to enhance their understanding of the material by working through the many straightforward exercises.

Biografía del autor

Yohann Le Floch is maître de conférences at Université de Strasbourg, in the Analysis team of the Institut de Recherche Mathématique Avancée. His areas of interest are semiclassical analysis, with a focus on Berezin-Toeplitz operators, and classical and quantum integrable systems.

Details zur Ausgabe

• Verlag: Springer International Publishing AG
• Erscheinungsdatum: 2018
• ISBN 10: 3319946811
• ISBN 13: 9783319946818
• Einband: Tapa dura
• Sprache: Englisch
• Auflage: 1
• Anzahl der Seiten: 140