Related papers: Higher internal covers
We study groups definable in existentially closed geometric fields with commuting derivations. Our main result is that such a group can be definably embedded in a group interpretable in the underlying geometric field. Compared to earlier…
We develop some aspects of the model theory of additive structures, with particular emphasis on the abelian category of pp-imaginaries.
In this work we deal with coverings and actions of Lie group- groupoids being a sort of the structured Lie groupoids. Firstly, we define an action of a Lie group-groupoid on some Lie group and the smooth coverings of Lie group-groupoids.…
The success of neural networks builds to a large extent on their ability to create internal knowledge representations from real-world high-dimensional data, such as images, sound, or text. Approaches to extract and present these…
An observable for nonabelian, higher-dimensional forms is introduced, its properties are discussed and its expectation value in BF theory is described. This is shown to produce potential and genuine invariants of higher-dimensional knots.
A higher dimensional lattice space can be decomposed into a number of four-dimensional lattices called as layers. The higher dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer…
Since its foundations, more than one hundred years ago, the field of structural biology has strived to understand and analyze the properties of molecules and their interactions by studying the structure that they take in 3D space. However,…
Master's thesis. We present a study of the BMS Group is higher space-time dimensions, and the extension of this group to non-relativistic systems.
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
We investigate higher-dimensional $\Delta$-systems indexed by finite sets of ordinals, isolating a particular definition thereof and proving a higher-dimensional version of the classical $\Delta$-system lemma. We focus in particular on…
We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.
The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, ``conformal'' (multicomponent) and Kontsevich models are considered in some detail, together with the…
We examine configurations of finite subsets of manifolds within the homotopy-theoretic context of $\infty$-categories by way of stratified spaces. Through these higher categorical means, we identify the homotopy types of such configuration…
We study Lie rings definable in a finite-dimensional theory, extending the results for the finite Morley rank case. In particular, we prove a classification of Lie rings of dimension up to four in the NIP or connected case. In…
We define a higher-order generalisation of the CPM construction based on arbitrary finite abelian group symmetries of symmetric monoidal categories. We show that our new construction is functorial, and that its closure under iteration can…
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep…
Different group structures which underline the integrable systems are considered. In some cases, the quantization of the integrable system can be provided with substituting groups by their quantum counterparts. However, some other group…
Higher structures - infinity algebras and other objects up to homotopy, categorified algebras, `oidified' concepts, operads, higher categories, higher Lie theory, higher gauge theory... - are currently intensively investigated in…
Based on the notion of a $\Delta$-group(oid), ring-valued invariants of pairs of topological spaces can be defined in intrinsic topological terms.
We construct higher-dimensional Calabi-Yau varieties defined over a given number field with Zariski dense sets of rational points. We give two elementary constructions in arbitrary dimensions as well as another construction in dimension…