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.
