Brief Introduction to Berezin–Toeplitz Operators on Compact Kähler Manifolds

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.

• 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.

“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)