Related papers: Three Generalizations Regarding Limit Sets for Com…

Consider a general circle packing $\mathcal{P}$ in the complex plane $\mathbb{C}$ invariant under a Kleinian group $\Gamma$. When $\Gamma$ is convex-cocompact or its critical exponent is greater than 1, we obtain an effective…

Using the rings of Lipschitz and Hurwitz integers $\mathbb{H}(\mathbb{Z})$ and $\mathbb{H}ur(\mathbb{Z})$ in the quaternion division algebra $\mathbb{H}$, we define several Kleinian discrete subgroups of $PSL(2,\mathbb{H})$

It is well known that $n$-dimensional projective group gives rise to a non-homogenous representation of the Lie algebra $sl(n+1)$ on the polynomial functions of the projective space. Using Shen's mixed product for Witt algebras (also known…

This article is concerned with the analysis of the one-dimensional compressible Euler equations with a singular pressure law, the so-called hard sphere equation of state. The result is twofold. First, we establish the existence of bounded…

In this article we introduce and study uniform and non-uniform approximate lattices in locally compact second countable (lcsc) groups. These are approximate subgroups (in the sense of Tao) which simultaneously generalize lattices in lcsc…

For a convex set (K) of the (n)-dimensional Euclidean space, the Steiner-Minkowski polynomial (M_K(t)) is defined as the (n)-dimensional Euclidean volume of the neighborhood of the radius (t). Being defined for positive (t), the…

The goal of this paper is to propose an approach to the formulation of dynamics for causal sets and coupled matter fields. We start from the continuum version of the action for a Klein-Gordon field coupled to gravity, and rewrite it first…

Let $\mathcal{C}(n,k)$ be the set of $k$-dimensional simplicial complexes $C$ over a fixed set of $n$ vertices such that: (1) $C$ has a complete $k-1$-skeleton; (2) $C$ has precisely ${{n-1}\choose {k}}$ $k$-faces; (3) the homology group…

We study sets of local dimensions for self-similar measures in $\mathbb{R}$ satisfying the finite neighbour condition, which is formally stronger than the weak separation condition but satisfied in all known examples. Under a mild technical…

We define eventually symmetric functions to be those power series of bounded degree in infinitely many variables that are invariant under interchanging all the variables with large enough indices. We show how this ring $\tilde{\Lambda}$ is…

We describe the spaces of stability conditions on certain triangulated categories associated to Dynkin diagrams. These categories can be defined either algebraically via module categories of preprojective algebras, or geometrically via…

Kobayashi [Duke Math. J. (1992)] gave a necessary condition for the existence of compact Clifford-Klein forms in terms of Cartan projections and non-compact dimensions of reductive subgroups. We extend his method to non-reductive subgroups,…

In this paper we derive new upper bounds for the densities of measurable sets in R^n which avoid a finite set of prescribed distances. The new bounds come from the solution of a linear programming problem. We apply this method to obtain new…

We solve exactly the general one-dimensional $O(N)$-invariant spin model taking values in the sphere $S^{N-1}$, with nearest-neighbor interactions, in finite volume with periodic boundary conditions, by an expansion in hyperspherical…

Let X be a finite set of cardinality n. The Kalmanson complex K_n is the simplicial complex whose vertices are non-trivial X-splits, and whose facets are maximal circular split systems over X. In this paper we examine K_n from three…

We analyse the complexity of the computation of the class group structure, regulator, and a system of fundamental units of a certain class of number fields. Our approach differs from Buchmann's, who proved a complexity bound of L(1/2,O(1))…

The present work stemmed from the study of the problem of harmonic analysis on the infinite-dimensional unitary group U(\infty). That problem consisted in the decomposition of a certain 4-parameter family of unitary representations, which…

We develop a theory of limits for sequences of dense abstract simplicial complexes, where a sequence is considered convergent if its homomorphism densities converge. The limiting objects are represented by stacks of measurable [0,1]-valued…

Possible short and semi-short positive energy, unitary representations of the Osp(2N|4) superconformal group in three dimensions are discussed. Corresponding character formulae are obtained, consistent with character formulae for the…

In this paper, we prove a generalization of a discreteness criteria for a large class of subgroups of PSL$_2(\mathbb{C})$. In particular, we show that for a given finitely generated, purely loxodromic, free Kleinian group…