The purpose of this Brief is to give a quick practical introduction into the subject of Toeplitz operators on Kähler manifolds, via examples, worked out carefully and in detail. Necessary background is included. Several theorems on asymptotics of Toeplitz operators are reviewed and illustrated by examples, including the case of tori and the 2-dimensional sphere. Applications in the context of multisymplectic and hyperkähler geometry are discussed. The book is suitable for graduate students, advanced undergraduate students, and any researchers.
Introduction.- Preliminaries.- Toeplitz Opreators on the Sphere.- Toeplitz Operators on the Torus.- Toeplitz Operators on Multisymplectic and Hyperkähler Manifolds.