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We find a set of generators for the automorphism group of a graph product of finitely generated abelian groups entirely from a certain labeled graph. In addition, we find generators for the important subgroup of star-automorphisms defined…
This survey offers an overview of an on-going project on uniform symmetries in abstract stable homotopy theories. This project has calculational, foundational, and representation-theoretic aspects, and key features of this emerging field on…
Symmetric mass generation is the name given to a mechanism for gapping fermions while preserving a chiral, but necessarily non-anomalous, symmetry. In this paper we describe how symmetric mass generation for continuous symmetries can be…
In this paper we develop in detail the geometric constructions that lead to many uniqueness results for the determination of polyhedral sets, typically scatterers, by a finite minimal number of measurements. We highlight how unique…
This is a research monograph on constructions of and group actions on countable homogeneous graphs, concentrating particularly on the simple random graph and its edge-coloured variants. We study various aspects of the graphs, but the…
We initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain…
Centrality metrics have become a popular concept in network science and optimization. Over the years, centrality has been used to assign importance and identify influential elements in various settings, including transportation,…
We show the existence of regular combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, t-designs, and t-wise…
We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a…
For each family of finite classical groups, and their associated simple quotients, we provide an explicit presentation on a specific generating set of size at most 8. Since there exist efficient algorithms to construct this generating set…
We study social networks and focus on covert (also known as hidden) networks, such as terrorist or criminal networks. Their structures, memberships and activities are illegal. Thus, data about covert networks is often incomplete and…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
Methods from additive number theory are applied to construct families of finitely generated linear semigroups with intermediate growth.
Mixture models are often used to identify meaningful subpopulations (i.e., clusters) in observed data such that the subpopulations have a real-world interpretation (e.g., as cell types). However, when used for subpopulation discovery,…
Normal subgroups and there properties for finite and infinite iterated wreath products $S_{n_1}\wr \ldots \wr S_{n_m}$, $n, m \in \mathbb{N}$ are founded. The special classes of normal subgroups and there orders are investigated. Special…
As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…
We use algebraic arc complexes to prove a homological stability result for symplectic groups with slope 2/3 for rings with finite unitary stable rank. Symplectic groups are here interpreted as the automorphism groups of formed spaces with…
The generation of synthetic data is an essential tool to study complex systems, allowing for example to test models of these in precisely controlled settings, or to parametrize simulation models when data is missing. This paper focuses on…
The abundance of interconnected data has fueled the design and implementation of graph generators reproducing real-world linking properties, or gauging the effectiveness of graph algorithms, techniques and applications manipulating these…
This paper presents the foundational ideas for a new way of modeling social aggregation. Traditional approaches have been using network theory, and the theory of random networks. Under that paradigm, every social agent is represented by a…