This text provides a comprehensive introduction to Berezin-Toeplitz operators on compact Kahler 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.
Yohann Le Floch is maitre de conferences at Universite de Strasbourg, in the Analysis team of the Institut de Recherche Mathematique Avancee. His areas of interest are semiclassical analysis, with a focus on Berezin-Toeplitz operators, and classical and quantum integrable systems.