Related papers: Circular planar nearrings: geometrical and combina…
Let G be a reductive p-adic group. Let $\Phi$ be an invariant distribution on G lying in the Bernstein center Z(G). We prove that $\Phi$ is supported on compact elements in G if and only if it defines a constant function on every component…
We give a geometric interpretation of cluster varieties in terms of blowups of toric varieties. This enables us to provide, among other results, an elementary geometric proof of the Laurent phenomenon for cluster algebras (of geometric…
A classical combinatorial fact is that the simplicial complex consisting of disjointly embedded chords in a convex planar polygon is a sphere. For any surface F with non-empty boundary, there is an analogous complex Arc(F) consisting of…
Two vertex-labelled polygons are \emph{compatible} if they have the same clockwise cyclic ordering of vertices. The definition extends to polygonal regions (polygons with holes) and to triangulations---for every face, the clockwise cyclic…
Consider the $2n$-dimensional closed ball $B$ of radius 1 in the $2n$-dimensional symplectic cylinder $Z = D \times R^{2n-2}$ over the closed disc $D$ of radius 1. We construct for each $\epsilon >0$ a Hamiltonian deformation $\phi$ of $B$…
Let $\mathcal{D}=\{D_0,\ldots,D_{n-1}\}$ be a set of $n$ topological disks in the plane and let $\mathcal{A} := \mathcal{A}(\mathcal{D})$ be the arrangement induced by $\mathcal{D}$. For two disks $D_i,D_j\in\mathcal{D}$, let $\Delta_{ij}$…
This article is a gentle introduction to the mathematical area known as circle packing, the study of the kinds of patterns that can be formed by configurations of non-overlapping circles. The first half of the article is an exposition of…
In Euclidean 3-space endowed with a Cartesian reference system we consider a class of surfaces, called Delaunay tori, constructed by bending segments of Delaunay cylinders with neck-size $a$ and $n$ lobes along circumferences centered at…
The nonrelativistic many-electron system in the forward, exchange and BCS approximation is considered. In this approximation, which is still quartic in the annihilation and creation operators, the model is explicitly solvable for arbitrary…
We complete the analysis on the birational rigidity of quasismooth Fano 3-fold deformation families appearing in the Graded Ring Database as a complete intersection. When such a deformation family $X$ has Fano index at least 2 and is…
Points of an orbit of a finite Coxeter group G, generated by n reflections starting from a single seed point, are considered as vertices of a polytope (G-polytope) centered at the origin of a real n-dimensional Euclidean space. A general…
We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool…
An intriguing correspondence between certain finite planar tessellations and the Descartes circle arrangements is presented. This correspondence may be viewed as a visualization of the spinor structure underlying Descartes circles.
A polygonal complex in euclidean 3-space is a discrete polyhedron-like structure with finite or infinite polygons as faces and finite graphs as vertex-figures, such that a fixed number r of faces surround each edge. It is said to be regular…
It is shown theoretically that a nonchiral, two-dimensional array of metallic spheres exhibits optical activity as manifested in calculations of circular dichroism. The metallic spheres occupy the sites of a rectangular lattice and for…
From the point of view of optimization, a critical issue is relating the combinatorial diameter of a polyhedron to its number of facets $f$ and dimension $d$. In the seminal paper of Klee and Walkup [KW67], the Hirsch conjecture of an upper…
Consider $2n$ points on the unit circle and a reference dissection $\mathrm{D}_\circ$ of the convex hull of the odd points. The accordion complex of $\mathrm{D}_\circ$ is the simplicial complex of non-crossing subsets of the diagonals with…
We study the orbit of $\mathbb{R}$ under the Bianchi group $\operatorname{PSL}_2(\mathcal{O}_K)$, where $K$ is an imaginary quadratic field. The orbit, called a Schmidt arrangement $\mathcal{S}_K$, is a geometric realisation, as an…
The relationship between spinors and Clifford (or geometric) algebra has long been studied, but little consistency may be found between the various approaches. However, when spinors are defined to be elements of the even subalgebra of some…
This work is based on the approach developed by J.~Dorfmeister, F.~Pedit and H.~Wu [GANG and KITCS preprint, Report KITCS94-4-1] to construct maps $\Phi:D\rightarrow R^3$, $D$ being the unit disk in $C$, whose images are surfaces of…