29 mai 2017 à 2 juin 2017
TOULOUSE
Fuseau horaire Europe/Paris

Bergman kernels on symplectic manifolds and applications.

1 juin 2017, 14:00
45m
Amphi Schwartz IMT building 1R3 (TOULOUSE)

Amphi Schwartz IMT building 1R3

TOULOUSE

Paul Sabatier University

Orateur

M. Xiaonan Ma

Description

A suitable notion of ``holomorphic section'' of a prequantum line bundle on a compact symplectic manifold is the eigensections of low energy of the Bochner Laplacian acting on high $p$-tensor powers of the prequantum line bundle. We explain the asymptotic expansion of the corresponding kernel of the orthogonal projection as the power p tends to infinity. This implies the compact symplectic manifold can be embedded in the corresponding projective space. With extra effort, we show the Fubini-Study metrics induced by these embeddings converge at speed rate $1/p^{2}$ to the symplectic form. We explain also its implication on Bezerin-Toeplitz quantizations.

Documents de présentation

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