Related papers: A brief introduction to approximate groups
In his article "Arithmetic Fujita Approximations", Huayi Chen introduces the notion of an approximable graded algebra and asks if any such algebra is a subalgebra of the graded section ring of a big line bundle on an algebraic variety. We…
In this paper we first introduce the unified definition of the sharp constant that includes constants in three major problems of approximation theory, such as, inequalities for approximating elements, approximation of individual elements,…
We survey the classical results of the Dirichlet Approximation Theorem.
Near-openly generated groups are introduced. It is a topological and multiplicative subclass of $\mathbb R$-factorizable groups. Dense and open subgroups, quotients and Raikov completion of a near-openly generated group are near-openly…
In this paper we study categorical properties of the category of abelian hypergroups that leads to the notion of hyper (almost) preadditive and hyper (almost) abelian categories. Our goal is to create a path towards a general theory of…
We initiate the study of $\lambda$-fold near-factorizations of groups with $\lambda > 1$. While $\lambda$-fold near-factorizations of groups with $\lambda = 1$ have been studied in numerous papers, this is the first detailed treatment for…
In this short note we give a proof of the refined version of the uniform invariant approximation property for compact (non-commutative) groups following the Bourgain's approach.
Motivated by appearance of multisemigroups in the study of additive $2$-categories, we define and investigate the notion of a multisemigroup with multiplicities. This notion seems to be better suitable for applications in higher…
Expanded lecture notes. Preliminary version, comments are welcome.
These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.
The structure of groups for which certain sets of commutator subgroups are finite is investigated, with a particular focus on the relationship between these groups and those with finite derived subgroup.
Recently, right-angled Artin groups have attracted much attention in geometric group theory. They have a rich structure of subgroups and nice algorithmic properties, and they give rise to cubical complexes with a variety of applications.…
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…
This is an introduction to the Atlas of Lie Groups and Representations software, for computing representation and structure theory of real reductive groups. The user is led through the basic commands of the software, via numerous examples.…
This paper uses category theory to develop an entirely new approach to approximate game theory. Game theory is the study of how different agents within a multi-agent system take decisions. At its core, game theory asks what an optimal…
Having a function $f$ and a set of functionals $\{\mathcal{C}_{n}\}$, $c_n^f \equiv \mathcal{C}_n \left(f\right)$, one can interpret function approximation very generally as a construction of some function $\mathcal{A}_{N}^{f}$ such that…
This is a sequel to arXiv:1308.3604. We study applications to limit multiplicity generalizing the results of arXiv:1208.2257.
We give an overview of various prolongations of quasigroups. Two step prolongation procedure is proposed.
This is a survey article on selected topics in approximation theory. The topics either use techniques from the theory of several complex variables or arise in the study of the subject. The survey is aimed at readers having an acquaintance…
We use quasi-orders to describe the structure of C-groups. We do this by associating a quasi-order to each compatible C-relation of a group, and then give the structure of such quasi-ordered groups. We also reformulate in terms of…