Related papers: An introduction to Bousfield localization
The purpose of this survey is to describe how locally compact groups can be studied as geometric objects. We will emphasize the main ideas and skip or just sketch most proofs, often referring the reader to our much more detailed book…
We investigate the notions of \emph{localization} and \emph{filtration} in the context of extended affine Lie algebras. Our primary objective is to develop a localization theory that facilitates the construction of meaningful local…
This file proves the properties of the angle constraints and shows how to construct displacement constraints by various kinds of relative measurements.
The Bayesian approach to the prediction of particle type given measurements of particle location is explored, using a parametric model whose prior is based on the transformation group. Two types of particle are considered, and locations are…
Surprisingly, the issue of events localization in spacetime is poorly understood and a fortiori realized even in the context of Einstein's relativity. Accordingly, a comparison between observational data and theoretical expectations might…
Some early chapters of the upcoming book "Polyfold Constructions: Tools, Techniques, and Functors"
Factorization algebras are local-to-global objects living on manifolds, and they arise naturally in mathematics and physics. Their local structure encompasses examples like associative algebras and vertex algebras; in these examples, their…
In this paper, we explore the virtual technique that is very useful in studying moduli problem from differential geometric point of view. We introduce a class of new objects "virtual manifolds/orbifolds", on which we develop the integration…
Localization methods are ubiquitous in cyclic homology theory, but vary in detail and are used in different scenarios. In this paper we will elaborate on a common feature of localization methods in noncommutative geometry, namely…
In this paper, we define locally matchable subsets of a group which is extracted from the concept of matchings in groups and used as a tool to give alternative proofs for existing results in matching theory. We also give the linear analogue…
Building on progress in feature representations for image retrieval, image-based localization has seen a surge of research interest. Image-based localization has the advantage of being inexpensive and efficient, often avoiding the use of 3D…
For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.
We give characterizations, for various fragments of geometric logic, of the class of theories classified by a locally connected (resp. connected and locally connected, atomic, compact, presheaf) topos, and exploit the existence of multiple…
Given subsets $\mathcal{C},\mathcal{F}$ of a preorder $\mathcal{A}$, we give necessary and sufficient conditions for $\mathcal{A}$ to admit the structure of a model category whose cofibrant objects are $\mathcal{C}$ and whose fibrant…
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…
In this article we investigate the so-called Bilateral Small Lebesgue Spaces: prove that they are associated to the Grand Lebesgue spaces, calculate its fundamental functions and Boyd's indices find its dual spaces etc.
These notes are an introduction to higher dimensional local fields and higher dimensional adeles. As well as the foundational theory, we summarise the theory of topologies on higher dimensional local fields and higher dimensional local…
The fundamental bigroupoid of a topological space is one way of capturing its homotopy 2-type. When the space is semilocally 2-connected, one can lift the construction to a bigroupoid internal to the category of topological spaces, as Brown…
Exploiting the properties of the Jost-Lehmann-Dyson representation, it is shown that in 1+2 or more spacetime dimensions, a nonempty smallest localization region can be associated with each local observable (except for the c-numbers) in a…
We survey different perspectives on the stochastic localization process of Eldan, a powerful construction that has had many exciting recent applications in high-dimensional probability and algorithm design. Unlike prior surveys on this…