Related papers: On a formula of Gammelgaard for Berezin-Toeplitz q…

The notion of a local line bundle on a manifold, classified by 2-cohomology with real coefficients, is introduced. The twisting of pseudodifferential operators by such a line bundle leads to an algebroid with elliptic elements with…

We introduce new tools for analytic microlocal analysis on K\"ahler manifolds. As an application, we prove that the space of Berezin-Toeplitz operators with analytic contravariant symbol is an algebra. We also give a short proof of the…

We study the Berezin-Toeplitz quantization on Kaehler manifolds. We explain first how to compute various associated asymptotic expansions, then we compute explicitly the first terms of the expansion of the kernel of the Berezin-Toeplitz…

In this article we show that a Berezin-type quantization can be achieved on a compact even dimensional manifold $M^{2d}$ by removing a skeleton $M_0$ of lower dimension such that what remains is diffeomorphic to $R^{2d}$ (cell…

We derive algebraic recurrence relations to obtain a deformation quantization with separation of variables for a locally symmetric K\"ahler manifold. This quantization method is one of the ways to perform a deformation quantization of…

We develop Berezin-Toeplitz quantization in a non-compact complex geometric setting. Let $(X,\Theta)$ be a Hermitian manifold, $(L,h^L)$ a positive holomorphic line bundle, and $(E,h^E)$ a holomorphic Hermitian vector bundle. Assuming that…

We prove that Toeplitz operators associated with a Bernstein-Markov measure on a compact complex manifold endowed with a big line bundle form an algebra under composition. As an application, we derive a Szeg\H{o}-type spectral…

We establish the theory of Berezin-Toeplitz quantization on symplectic manifolds of bounded geometry. The quantum space of this quantization is the spectral subspace of the renormalized Bochner Laplacian associated with some interval near…

In this note known formulas for the product of Toeplitz operators are revisited in the context of their applications to the study of Fredholmness, boundedness of Toeplitz products, and the Berezin-Toeplitz quantization. A few open problems…

Let $M$ be an arbitrary complex manifold and let $L$ be a Hermitian holomorphic line bundle over $M$. We introduce the Berezin-Toeplitz quantization of the open set of $M$ where the curvature on $L$ is non-degenerate. The quantum spaces are…

Recently M. Kontsevich found a combinatorial formula defining a star-product of deformation quantization for any Poisson manifold. Kontsevich's formula has been reinterpreted physically as quantum correlation functions of a topological…

We study quantization schemes on a K\"ahler manifold and relate several interesting structures. We first construct Fedosov's star products on a K\"ahler manifold $X$ as quantizations of Kapranov's $L_\infty$-algebra structure. Then we…

We investigate a class of operators resulting from a quantization scheme attributed to Berezin. These so-called Berezin-Toeplitz operators are defined on a Hilbert space of square-integrable holomorphic sections in a line bundle over the…

We use operator algebras and operator theory to obtain new result concerning Berezin quantization of compact K\"ahler manifolds. Our main tool is the notion of subproduct systems of finite-dimensional Hilbert spaces, which enables all…

In this paper, we construct a family of Berezin-Toeplitz type quantizations of a compact symplectic manifold. For this, we choose a Riemannian metric on the manifold such that the associated Bochner Laplacian has the same local model at…

We survey geometric quantization of finite dimensional affine Kahler manifolds. Its corresponding prequantization and the Berezin's deformation quantization formulation, as proposed by Cahen et al., is used to quantize their corresponding…

We use Toeplitz operators to define a star-product on Poisson manifolds whose Poisson structure is induced by a symplectic Lie algebroid. The Toeplitz operators we consider are defined on groupoids whose algebroid can be endowed with a…

The standard (Berezin-Toeplitz) geometric quantization of a compact Kaehler manifold is restricted by integrality conditions. These restrictions can be circumvented by passing to the universal covering space, provided that the lift of the…

Universal solutions to deformation quantization problems can be conveniently classified by the cohomology of suitable graph complexes. In particular, the deformation quantizations of (finite-dimensional) Poisson manifolds and Lie bialgebras…

Let $G$ be a finite pseudoreflection group and $\Omega\subseteq \mathbb C^d$ be a bounded domain which is a $G$-space. We establish identities involving Toeplitz operators on the weighted Bergman spaces of $\Omega$ and $\Omega/G$ using…