Related papers: Universal Properties of Lens Proxy Pullbacks
The peculiar motion of massive objects across the line of sight imprints a dipolar temperature anisotropy pattern on the cosmic microwave background known as the moving lens effect. This effect provides a unique probe of the transverse…
The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However,…
Lenses have a rich history and have recently received a great deal of attention from applied category theorists. We generalize the notion of lens by defining a category $\mathsf{Lens}_F$ for any category $\mathcal{C}$ and functor $F\colon…
We establish the universal properties of the bicategory of polynomials, considering both cartesian and general morphisms between these polynomials. A direct proof of these universal properties would be impractical due to the complicated…
The analysis of strong lensing images usually involves an external convergence and shear, which are meant to model the effect of perturbations along the line of sight, on top of the main lens. Such a description of line-of-sight…
We characterize the relative prismatic cohomology of Bhatt and Scholze by a universal property by endowing it with the additional structure of a ``derived $\delta$-ring". This involves introducing an analogue of prismatic envelopes in the…
This is a mostly expository paper, intended to explain a very natural relationship between two a priori distinct notions appearing in the literature: Generic Vanishing in the context of vanishing theorems and birational geometry, and…
The classical perspective of a function is a construction which transforms a convex function into one that is jointly convex with respect to an auxiliary scaling variable. Motivated by applications in several areas of applied analysis, we…
Several recent studies show that bright, intermediate and high redshift optically and radio selected QSOs are positively correlated with nearby galaxies on a range of angular scales up to a degree. Obscuration by unevenly distributed…
This paper has two parts. In the first part we recall the important role that weak proregularity of an ideal in a commutative ring has in derived completion and in adic flatness. We also introduce the new concepts of idealistic and…
Given a composition of two commutative squares, one well-known pullback lemma says that if both squares are pullbacks, then their composition is also a pullback; another well-known pullback lemma says that if the composed square is a…
We find that the function that describes the surface of spherical aberration free lenses can be used for both positive and negative refractive index media. With the inclusion of negative index, this function assumes the form of all the…
We present a purely category-theoretic characterization of retracts of Fra\"iss\'e limits. For this aim, we consider a natural version of injectivity with respect to a pair of categories (a category and its subcategory). It turns out that…
We examine additional symmetries of specific refraction index profiles that are used in the well-known phenomena of perfect imaging and cloaking.In the considered cases, the translation generator and the angular momentum are conserved. We…
Gravitational lensing has emerged as a powerful probe of the matter distribution on subgalactic scales, which itself may contain important clues about the fundamental origins and properties of dark matter. Broadly speaking, two different…
Strong gravitational lensing provides a geometric probe of cosmology in a unique manner through distance ratios involving the source and lens. This is well known for the time delay distance derived from measured delays between lightcurves…
Weak gravitational lensing of distant galaxies can probe the total projected mass distribution of foreground gravitational structures on all scales and has been used successfully to map the projected mass distribution of rich intermediate…
Time delays in gravitational lenses can be used to determine the Hubble constant and the lens potential. In future surveys, many gravitational lenses can be discovered, and their time delays and image positions can in principle be measured.…
We prove that stability -- a strong quasiconvexity property -- pulls back under proper actions on proper metric spaces. This result has several applications, including that convex cocompact subgroups of both mapping class groups and outer…
Let $T^n$ be the real $n$-torus group. We give a new definition of lens spaces and study the diffeomorphic classification of lens spaces. We show that any $3$-dimensional lens space $L(p; q)$ is $T^2$-equivariantly cobordant to zero. We…