Related papers: String C-group representations of almost simple gr…

We give an explicit description of the set of element orders for every almost simple group with socle $E_7(q)$.

This survey reports on current progress of programs to classify graph C*-algebras and Leavitt path algebras up to Morita equivalence using K-theory. Beginning with an overview and some history, we trace the development of the classification…

The study of word maps on groups has been of deep interest in recent years. This survey focuses on the case of power maps on groups; $viz.$ the map $x\mapsto x^M$ for a group $G$, and an integer $M\geq 2$. Here, we accumulate various…

We show that strong approximate lattices in higher-rank semi-simple algebraic groups are arithmetic.

This paper introduces new structural decompositions for almost symmetric numerical semigroups through the combinatorial lens of Young diagrams. To do that, we use the foundational correspondence between numerical sets and Young diagrams,…

In this survey we describe progress over the last decade or so in understanding the complexity of solving constraint satisfaction problems (CSPs) approximately in the streaming and sketching models of computation. After surveying some of…

This note presents an application of the quasi-conform transformation in surveying.

This survey aims to collect the main results of the theory of the set-theoretical solutions to the pentagon equation obtained up to now in the literature. In particular, we present some classes of solutions and raise some questions.

In the field of mathematics, a purely combinatorial equivalent to a simplicial complex, or more generally, a down-set, is an abstract structure known as a family of sets. This family is closed under the operation of taking subsets, meaning…

Word-representable graphs, which are the same as semi-transitively orientable graphs, generalize several fundamental classes of graphs. In this paper we propose a novel approach to study word-representability of graphs using a technique of…

I review work developing the idea that string is a composite of point-like entities called string bits. Old and new insights this picture brings into the nature of string theory are discussed. This paper summarizes my talk presented to the…

This is a survey article on classical groups (over arbitrary division rings) and their geometries.

We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated to a matrix, the representation theory can be understood in terms of ``loop'' and…

The main purpose of this paper is to investigate $C$-distribution semigroups and $C$-ultradistribution semigroups in the setting of sequentially complete locally convex spaces. There are a few important theoretical novelties in this field…

We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts…

A recent conjecture of the author and Teng Fang states that there are only finitely many finite simple groups with no cubic graphical regular representation. In this paper, we make a crucial progress towards this conjecture by giving an…

We classify the pairs $(C,G)$ where $C$ is a seminormal curve over an arbitrary field $k$ and $G$ is a smooth connected algebraic group acting faithfully on $C$ with a dense orbit, and we determine the equivariant Picard group of $C$. We…

An elementary approach to the construction of Coxeter group representations is presented.

We prove that a countable group with an effective minimal non-elementary convergence group action is a Powers group. More strongly we prove that it is a strongly Powers group and thus its non-trivial subnormal subgroups are $C^*$-simple.

Notes of a 8h course given at the University of G\"oteborg during an Erasmus exchange visit, June 11-15, 2018. It is intended for PhD and graduate students familiar with $C^*$-algebras but not specializing in quantum groups. The proofs, if…