Related papers: Constructing bounded remainder sets and cut-and-pr…

Following Coxeter we use barycentric coordinates in affine geometry to prove theorems on ratios of areas. In particular, we prove a version of Routh-Steiner theorem for parallelograms.

Quantum toroidal algebras are obtained from quantum affine algebras by a further affinization, and, like the latter, can be used to construct integrable systems. These algebras also describe the symmetries of instanton partition functions…

The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of…

We extend several techniques and theorems from geometric group theory so that they apply to geometric actions on arbitrary proper metric ARs (absolute retracts). A second way that we generalize earlier results is by eliminating freeness…

Basic facts and definitions of conformal moduli of rings and quadrilaterals are recalled. Some computational methods are reviewed. For the case of quadrilaterals with polygonal sides, some recent results are given. Some numerical…

We develop new, easily computable exponential decay bounds for inverses of banded matrices, based on the quasiseparable representation of Green matrices. The bounds rely on a diagonal dominance hypothesis and do not require explicit…

We classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in $d \geq 3$ dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model…

We extend the decoupling results of the first two authors to the case of real analytic surfaces of revolution in $\mathbb{R}^3$. New examples of interest include the torus and the perturbed cone.

We use curvature decompositions to construct generating sets for the space of algebraic curvature tensors and for the space of tensors with the same symmetries as those of a torsion free, Ricci symmetric connection; the latter naturally…

Here I present several theorems about trapezoids tilings. The first one is related to trapezoids with rational base relation, the other ones are related to those with base relation from quadratic number field.

For all classical groups (and for their analogs in infinite dimension or over general base fields or rings) we construct certain contractions, called "homotopes". The construction is geometric, using as ingredient involutions of associative…

For all classical groups (and for their analogs in infinite dimension or over general base fields or rings) we construct certain contractions, called "homotopes". The construction is geometric, using as ingredient involutions of associative…

In this article we develop the theory of residually finite rationally $p$ (RFR$p$) groups, where $p$ is a prime. We first prove a series of results about the structure of finitely generated RFR$p$ groups (either for a single prime $p$, or…

Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among other, but still share many important properties. One may regard homotopy as…

We consider residue structures $R/G$ where $(G,+)$ is an additive subgroup of a ring $(R,+,\cdot)$, not necessarily an ideal. Special instances include Krasner's construction of quotient hyperfields, and Pumpluen's construction of…

We study various aspects of the dynamics induced by integer matrices on the invariant rational lattices of the torus in dimension 2 and greater. Firstly, we investigate the orbit structure when the toral endomorphism is not invertible on…

A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.

We study obstructed deformation problems for two-dimensional residual Galois representations arising from weight~$2$ newforms of level~$N$. Using Poitou-Tate duality, we isolate local and global sources of obstructions and give concrete…

We argue that 2D dodecagonal spherical quasicrystalls (QCs) will be discovered in the nearest future and investigate how the planar QC order becomes compatible with the spherical geometry. We show that the appearance of curvature-induced…

Transversal structures (also known as regular edge labelings) are combinatorial structures defined over 4-connected plane triangulations with quadrangular outer-face. They have been intensively studied and used for many applications…