© 2018

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


Part of the CRM Short Courses book series (CRMSC)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Yohann Le Floch
    Pages 1-6
  3. Yohann Le Floch
    Pages 7-21
  4. Yohann Le Floch
    Pages 23-36
  5. Yohann Le Floch
    Pages 55-62
  6. Yohann Le Floch
    Pages 63-73
  7. Yohann Le Floch
    Pages 75-96
  8. Yohann Le Floch
    Pages 97-113
  9. Yohann Le Floch
    Pages 115-123
  10. Back Matter
    Pages 125-140

About this book


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.


Kahler manifolds complexified tangent bundle complex line bundles quantization compact Kahler manifolds Berezin-Toeplitz operator Schwartz kernels Kostant-Souriau operators coherent states norm correspondence Szego projector Kaehler manifolds graduate text semiclassical analysis graduate text quantization geometric quantization circle bundle Berezin–Toeplitz operators course Tel-Aviv

Authors and affiliations

  1. 1.IRMAUniversité de StrasbourgStrasbourgFrance

About the authors

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.

Bibliographic information


“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.” (Béchir Dali, zbMATH 1452.32002, 2021)