ﻻ يوجد ملخص باللغة العربية
Let $X$ be a compact Kahler manifold and $Lto X$ a quantizing holomorphic Hermitian line bundle. To immersed Lagrangian submanifolds $Lambda$ of $X$ satisfying a Bohr-Sommerfeld condition we associate sequences ${ |Lambda, krangle }_{k=1}^infty$, where $forall k$ $|Lambda, krangle$ is a holomorphic section of $L^{otimes k}$. The terms in each sequence concentrate on $Lambda$, and a sequence itself has a symbol which is a half-form, $sigma$, on $Lambda$. We prove estimates, as $ktoinfty$, of the norm squares $langle Lambda, k|Lambda, krangle$ in terms of $int_Lambda sigmaoverline{sigma}$. More generally, we show that if $Lambda_1$ and $Lambda_2$ are two Bohr-Sommerfeld Lagrangian submanifolds intersecting cleanly, the inner products $langleLambda_1, k|Lambda_2, krangle$ have an asymptotic expansion as $ktoinfty$, the leading coefficient being an integral over the intersection $Lambda_1capLambda_2$. Our construction is a quantization scheme of Bohr-Sommerfeld Lagrangian submanifolds of $X$. We prove that the Poincare series on hyperbolic surfaces are a particular case, and therefore obtain estimates of their norms and inner products.
Modular invariance strongly constrains the spectrum of states of two dimensional conformal field theories. By summing over the images of the modular group, we construct candidate CFT partition functions that are modular invariant and have positive sp
We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors predict embedding weights in projective space to ${sim}1$ mean absolute error, whilst classifiers predict dimension and Gor
We investigate unpolarized and polarized gluon distributions and their applications to the Ioffe-time distributions, which are related to lattice QCD calculations of parton distribution functions. Guided by the counting rules based on the perturbativ
We derive new Poincare-series representations for infinite families of non-holomorphic modular invariant functions that include modular graph forms as they appear in the low-energy expansion of closed-string scattering amplitudes at genus one. The Po
We continue the analysis of modular invariant functions, subject to inhomogeneous Laplace eigenvalue equations, that were determined in terms of Poincare series in a companion paper. The source term of the Laplace equation is a product of (derivative