In this snapshot, we will first give an introduction to hyperbolic geometry and we will then show how certain matrix groups of a number-theoretic origin give rise to a large variety of interesting tessellations of 3-dimensional ...

We use Constraint Satisfaction Methods to construct and enumerate finite L-algebras up to isomorphism. These objects were recently introduced by Rump and appear in Garside theory, algebraic logic, and the study of the ...

We study the homotopy type of the space $\mathcal{E}(L)$ of unparametrised embeddings of a split link $L=L_1\sqcup \ldots \sqcup L_n$ in $\mathbb{R}^3$. Inspired by work of Brendle and Hatcher, we introduce a semi-simplicial ...

The goal of this paper is to study convergence and error estimates of the Monte Carlo method for the Navier-Stokes equations with random data. To discretize in space and time, the Monte Carlo method is combined with a ...

For an element $w$ of a Coxeter group $W$ there are two important attributes, namely its length, and its expression as a product of disjoint cycles in its action on $\Phi$, the root system of $W$. This paper investigates ...

The advances in biomedical imaging techniques have enabled us to access the 3D shapes of a variety of structures: organs, cells, proteins. Since biological shapes are related to physiological functions, shape data may hold ...

Pattern is ubiquitous and seems totally familiar. Yet if we ask what it is, we find a bewildering collection of answers. Here we suggest that there is a common thread, and it revolves around dynamics.

Consider a population of $N$ individuals, each of them carrying a type in $\mathbb N_0$. The population evolves according to a Moran dynamics with selection and mutation, where an individual of type $k$ has the same selective ...

We consider surfaces of three types: the sphere, the torus, and many-holed tori. These surfaces naturally admit geometries of positive, zero, and negative curvature, respectively. It is interesting to study straight line ...

We find the intervals $[\alpha, \beta (\alpha)]$ such that if a univariate real polynomial or entire function $f(z) = a_0 + a_1 z + a_2 z^2 + \cdots $ with positive coefficients satisfy the conditions $ \frac{a_{k-1}^2}{ ...