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A Brief Introduction to Berezin-Toeplitz Geométrie différentielle
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A Brief Introduction to Berezin-Toeplitz Geométrie différentielle

A Brief Introduction to Berezin-Toeplitz Geométrie différentielle

Yohann Le Floch

140 pages, parution le 16/09/2018

Résumé

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.

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.


Preface.- 1. Introduction.- 2. A short introduction to Kahler manifolds.- 3. Complex line bundles with connections.- 4. Quantization of compact Kahler 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 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.

Caractéristiques techniques

  PAPIER
Éditeur(s) Springer
Auteur(s) Yohann Le Floch
Parution 16/09/2018
Nb. de pages 140
EAN13 9783319946818

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