Berezin-Toeplitz quantization on Kaehler manifolds

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 operators, and of the composition of two Berezin-Toeplitz operators. As application we estimate the norm of Donaldson's Q-operator.Comment: 45 pages, footnote at page 3 and Remark 0.5 added; v.3 is a final update to agree with the published pape

Berezin-Toeplitz quantization and its kernel expansion

We survey recent results about the asymptotic expansion of Toeplitz operators and their kernels, as well as Berezin-Toeplitz quantization. We deal in particular with calculation of the first coefficients of these expansions.Comment: 34 page

Nano-mineralogy Studies by Advanced Electron Microscopy

Extended abstract of a paper presented at Microscopy and Microanalysis 2007 in Ft. Lauderdale, Florida, USA, August 5 – August 9, 2007

Davisite, CaScAlSiO_6, a new pyroxene from the Allende meteorite

Davisite, ideally CaScAlSiO_6, is a new member of the Ca clinopyroxene group, where Sc^(3+) is dominant in the M1 site. It occurs as micro-sized crystals along with perovskite and spinel in an ultra-refractory inclusion from the Allende meteorite. The mean chemical composition determined by electron microprobe analysis is (wt%) SiO_2 26.24, CaO 23.55, Al_2O_3 21.05, Sc_2O_3 14.70, TiO_2 (total) 8.66, MgO 2.82, ZrO_2 2.00, Y_2O_3 0.56, V_2O_3 0.55, FeO 0.30, Dy_2O_3 0.27, Gd_2O_3 0.13, Er_2O_3 0.08, sum 100.91. Its empirical formula calculated on the basis of 6 O atoms is Ca_(0.99)(Sc_(0.50)Ti^(3+)0.16^(Mg)0.16Ti^(4+)0.10 Zr_(0.04)V^(3+)_(0.02)Fe^(2+)_(0.01)Y_(0.01))_(∑1.00)(Si_(1.03)Al_(0.97))_(∑2).00O_6. Davisite is monoclinic, C2/c; a = 9.884 Å, b = 8.988 Å, c = 5.446 Å, β =105.86°, V = 465.39 Å^3, and Z = 4. Its electron back-scattered diffraction pattern is an excellent match to that of synthetic CaScAlSiO6 with the C2/c structure. The strongest calculated X-ray powder diffraction lines are [d spacing in Å (I) (hkl)]: 3.039 (100) (221), 2.989 (31) (310), 2.943 (18) (311), 2.619 (40) (002), 2.600 (26) (131), 2.564 (47) (221), 2.159 (18) (331), 2.137 (15) (421), 1.676 (20) (223), and 1.444 (18) (531). The name is for Andrew M. Davis, a cosmochemist at the University of Chicago, Illinois

Equidistribution and convergence speed for zeros of holomorphic sections of singular Hermitian line bundles

We establish the equidistribution of zeros of random holomorphic sections of powers of a semipositive singular Hermitian line bundle, with an estimate of the convergence speed.Comment: 23pages. Final version in Journal of Functional Analysis, (2016

Generalized Bergman kernels on symplectic manifolds of bounded geometry

We study the asymptotic behavior of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle on a symplectic manifold of bounded geometry. First, we establish the off-diagonal exponential estimate for the generalized Bergman kernel. As an application, we obtain the relation between the generalized Bergman kernel on a Galois covering of a compact symplectic manifold and the generalized Bergman kernel on the base. Then we state the full off-diagonal asymptotic expansion of the generalized Bergman kernel, improving the remainder estimate known in the compact case to an exponential decay. Finally, we establish the theory of Berezin-Toeplitz quantization on symplectic orbifolds associated with the renormalized Bochner-Laplacian.Comment: 33 pages, v.2 is a final update to agree with the published pape