We study the low-frequency properties of the bulk photovoltaic effect in topological
semimetals. The bulk photovoltaic effect is a nonlinear optical effect that generates dc …

This work reviews the classical Darboux theorem for symplectic, presymplectic, and
cosymplectic manifolds (which are used to describe mechanical systems), as well as certain …

We give a proof of Kontsevich's formality theorem for a general manifold using Fedosov
resolutions of algebras of polydifferential operators and polyvector fields. The main …

This article is an overview of the results obtained in recent years on symplectic connections.
We present what is known about preferred connections (critical points of a variational …

One of the basic ideas in differential geometry is that the study of analytic properties of
certain differential operators acting on sections of vector bundles yields geometric and …

In the last decade, the development of new ideas in quantum theory, including geometric
and deformation quantization, the non-Abelian Berry''s geometric factor, super-and BRST …

We study Codazzi couplings of an affine connection ∇∇ with a pseudo-Riemannian metric
g, a nondegenerate 2-form ω ω, and a tangent bundle isomorphism L on smooth manifolds …

This is a survey on bi-Lagrangian manifolds, which are symplectic manifolds endowed with
two transversal Lagrangian foliations. We also study the non-integrable case (ie, a …

We provide a deformation quantization, in the sense of Rieffel, for all globally hyperbolic
spacetimes with a Poisson structure. The Poisson structures have to satisfy Fedosov type …

We semiclassicalise the standard notion of differential calculus in noncommutative geometry
on algebras and quantum groups. We show in the symplectic case that the infinitesimal data …