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We explain some simple methods to establish the property of Rapid Decay for a number of groups arising geometrically. We also give new examples of groups with the property of Rapid Decay. In particular we establish the property of Rapid…
Nature is a blossoming of regular structures, signature of self-organization of the underlying microscopic interacting agents. Turing theory of pattern formation is one of the most studied mechanisms to address such phenomena and has been…
We introduce so-called cone topologies of paratopological groups, which are a wide way to construct counterexamples, especially of examples of compact-like paratopological groups with discontinuous inversion. We found a simple interplay…
A staged tree model is a discrete statistical model encoding relationships between events. These models are realised by directed trees with coloured vertices. In algebro-geometric terms, the model consists of points inside a toric variety.…
Respecting deformational constraints and predeformations poses a substantial challenge in the description of nonlinear elasticity. We here outline how group theory can play a beneficial role to overcome this challenge. Specifically, group…
A class of groups is investigated, each of which has a fairly simple presentation . For example the group $R = (a, b, c, d | a^3 = b^3 = c^3 = d^3 = 1, ba^{-1} =dc^{-1}, ca^{-1} = db^{-1}) $ is in the class. Such a group does not have as a…
We explore the idea of using automatic and similar kind of presentations of structures to deal with the conceptual problem of natural proof-theoretic ordinal notations. We conclude that this approach still does not meet the goals.
Coherence theorems for covariant structures carried by a category have traditionally relied on the underlying term rewriting system of the structure being terminating and confluent. While this holds in a variety of cases, it is not a…
This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…
As a model of temporally evolving networks, we consider a globally coupled logistic map with variable connection weights. The model exhibits self-organization of network structure, reflected by the collective behavior of units. Structural…
We investigate how often geodesics have homology in a fixed set of the homology lattice of a compact Riemann surface. We prove that closed geodesics are equidistributed on any sets with asymptotic density with respect to a specific norm. We…
We study the notion of geometric structures for toposes: This generalizes the notion of (X,G) manifolds. We give some applications to algebraic geometry
We describe a technique to determine the automorphism group of a geometrically represented graph, by understanding the structure of the induced action on all geometric representations. Using this, we characterize automorphism groups of…
This book provides a self-contained introduction to geometric group theory. The topics range from an introduction of Cayley and Schreier graphs to Gromov's theorem on groups of polynomial growth and amenability. We discuss the ping-pong…
First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful.…
We extend our generic rigidity theory for periodic frameworks in the plane to frameworks with a broader class of crystallographic symmetry. Along the way we introduce a new class of combinatorial matroids and associated linear…
We study the homotopy theory of locally ordered spaces, that is manifolds with boundary whose charts are partially ordered in a compatible way. Their category is not particularly well-behaved with respect to colimits. However, this category…
We study quasiminimal classes, i.e. abstract elementary classes (AECs) that arise from a quasiminimal pregeometry structure. For these classes, we develop an independence notion, and in particular, a theory of independence in $\M^{eq}$. We…
This paper is devoted to a study of mathematical structures arising from choice functions satisfying the path independence property (Plott functions). We broaden the notion of a choice function by allowing of empty choice. This enables us…
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…