A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Constructing brane quantization for -resolutions using SYZ mirror symmetry.
This paper is devoted to rigidity of smooth bundles which are equipped with fiberwise geometric or dynamical structure. We show that the fiberwise associated sphere bundle to a bundle whose leaves are equipped with (continuously varying) metrics of negative curvature is a topologically trivial bundle when either the ba…
The study uses symplectic capacities to bound the systole on the sphere.
The book is devoted to constructing embedding finite-dimensional maps into trivial bundles and investigating the corresponding general position properties.
Paper compares higher torsions and removes fiberwise Morse function assumption.
9We consider complex structures with totally real zero section of the tangent bundle. We assume that the complex structure tensor is real-analytic along the fibers of the tangent bundle. This assumption is quite natural in view of a well known existence result by Bruhat and Whitney. We provide explicit integrability eq…
Survey on quantization methods on Kähler manifolds.
Geometric quantization of a Poisson manifold need not imply quantization of its symplectic leaves. We provide the leafwise geometric quantization of a Poisson manifold, seen as a foliated one, whose quantum algebra restricted to each leaf is quantized.
The paper classifies quantizable functions and explores symmetry in quantization methods.
Introduces sheaf quantization, a topological approach to geometric quantization.
Geometric quantization for specific symplectic structures proved.
The construction of a linear connection on a pullback bundle from a connection on a vector bundle is explained in terms of fiberwise linear approximation. This procedure clarifies the geometric meaning of the linearized connection as well as the associated parallel transport and curvature.
The paper studies quantization on symplectic manifolds with real polarizations, comparing different quantization methods.
We define a bordism invariant for the fiberwise intersection theory. Under some certain conditions, this invariant is an obstruction for the theory.
We study a notion of pre-quantization for -symplectic manifolds. We use it to construct a formal geometric quantization of -symplectic manifolds equipped with Hamiltonian torus actions with nonzero modular weight. We show that these quantizations are finite dimensional -modules.
New method for quantizing symplectic manifolds with Lagrangian bundles.
A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kaehler structure is proposed. The Hilbert space of states is realized via the Bott-Borel-Weil theorem in the sheaf cohomology of the geometric quantization line bundle. The correspondin…
An analogue of geometric quantization of Poisson algebras obtained by algebraic reduction of symmetries is developed. Interpretation of the obtained results and their application to the problem of commutativity of quantization and reduction are given
Extends geometric quantization to singular spaces.
We construct Hermitian representations of Lie algebroids and associated unitary representations of Lie groupoids by a geometric quantization procedure. For this purpose we introduce a new notion of Hamiltonian Lie algebroid actions. The first step of our procedure consists of the construction of a prequantization line …
Geometric quantization shows compatibility of symmetries on coadjoint orbits and Kähler-Einstein manifolds.
Study geometric quantization on K3 surfaces, showing spectral convergence.
Using geometric quantization procedure, the quantization of algebra of observables for physical system with Ricci-flat phase space is obtained. In the classical case the appointed physical system is reduced to harmonic oscillator when the one real parameter is vanished.
Study finds lower bounds for energy on fibred manifolds using fiberwise symmetrization.
A fibration of a Riemannian manifold is fiberwise homogeneous if there are isometries of the manifold onto itself, taking any given fiber to any other one, and preserving fibers. Examples are fibrations of Euclidean n-space by parallel n-planes, and the Hopf fibrations of the round n-sphere by great n-spheres. In this …
In this paper we pursue the study of formal geometric quantization of non-compact Hamiltonian manifolds. Our main result is the proof that two quantization process coincide. This fact was obtained by Ma and Zhang in the preprint arXiv:0812.3989 by completely different means.
In this paper, we prove a functorial aspect of the formal geometric quantization procedure of non-compact spin-c manifolds.
In this paper, Hamiltonian monodromy is studied from the point of view of geometric quantization abd theta functions, and various differential geometric aspects thereof are dealt with, all related to holonomies of suitable flat connections.
Quantizes Kähler-Ricci flow for Fano manifolds.
Study on Mabuchi functional's convexity using ε-geodesics.
We establish a geometric quantization formula for a Hamiltonian action of a compact Lie group acting on a noncompact symplectic manifold with proper moment map.
Study continuity of Bergman kernels on degenerating varieties.
By the quantization condition compact quantizable Kaehler manifolds can be embedded into projective space. In this way they become projective varieties. The quantum Hilbert space of the Berezin-Toeplitz quantization (and of the geometric quantization) is the projective coordinate ring of the embedded manifold. This all…
The paper presents an extension of the geometric quantization procedure to integrable, big-isotropic structures. We obtain a generalization of the cohomology integrality condition, we discuss geometric structures on the total space of the corresponding principal circle bundle and we extend the notion of a polarization.
Quantization-aware training can recover accuracy lost by post-training quantization.
We study the geometric quantization process for twisted Poisson manifolds. First, we introduce the notion of Lichnerowicz-twisted Poisson cohomology for twisted Poisson manifolds and we use it in order to characterize their prequantization bundles and to establish their prequantization condition. Next, we introduce a p…
We describe three perspectives on higher quantization, using the example of magnetic Poisson structures which embody recent discussions of nonassociativity in quantum mechanics with magnetic monopoles and string theory with non-geometric fluxes. We survey approaches based on deformation quantization of twisted Poisson …
We prove that the boundary distance map of a smooth compact Finsler manifold with smooth boundary determines its topological and differentiable structures. We construct the optimal fiberwise open subset of its tangent bundle and show that the boundary distance map determines the Finsler function in this set but not in …
Geometric quantization extended to big line bundles.
The article defines and compares two types of quantizations on compact manifolds.
Construct geometric interpretation of Heston model using group quantization.
Geometric quantization on hyperKähler manifolds via brane quantization.
Defines spectral sequences for fiberwise Dirac operators and proves adiabatic limit formula.
A geometric quantization of a Kähler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat co…
In this article we develop tools to compute the Geometric Quantization of a symplectic manifold with respect to a regular Lagrangian foliation via sheaf cohomology and obtain important new applications in the case of real polarizations. The starting point is the definition of representation spaces due to Kostant. Besid…
The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the polarization bundle. The existence of reducible quantum structures leads to considering the…
Formally equates two quantization methods and constructs non-commutative algebras.
For arbitrary compact quantizable Kaehler manifolds it is shown how a natural formal deformation quantization (star product) can be obtained via Berezin-Toeplitz operators. Results on their semi-classical behaviour (their asymptotic expansion) due to Bordemann, Meinrenken and Schlichenmaier are used in an essential man…