A Brief Introduction to Berezin–Toeplitz Operators on Compact Kähler Manifolds

Yohann Le Floch

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English

Springer Nature Switzerland AG
30 January 2019

Complex analysis, complex variables; Differential & Riemannian geometry

Series: CRM Short Courses

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.

By: Yohann Le Floch
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: Softcover reprint of the original 1st ed. 2018
Dimensions: Height: 235mm, Width: 155mm, Spine: 8mm
Weight: 454g
ISBN: 9783030068981
ISBN 10: 3030068986
Series: CRM Short Courses
Pages: 140
Publication Date: 30 January 2019
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Preface.- 1. Introduction.- 2. A short introduction to Kähler manifolds.- 3. Complex line bundles with connections.- 4. Quantization of compact Kähler manifolds.- 5. Berezin–Toeplitz operators.- 6. Schwartz kernels.- 7. Asymptotics of the projector Pi_k.- 8. Proof of product and commutator estimates.- 9. Coherent states and norm correspondence.- A. The circle bundle point of view.- Bibliography.

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.

Reviews for A Brief Introduction to Berezin–Toeplitz Operators on Compact Kähler Manifolds

The book ... represents an essential prerequisite for anyone who wants to work in the field. The author have managed to make it readable by non-specialists. (Bechir Dali, zbMATH 1452.32002, 2021)