Related papers: Quasisymmetric geometry of low-dimensional random …
How are the symmetries encoded in quasicrystals? As a compensation for the lack of translational symmetry, quasicrystals admit non-crystallographic symmetries such as 5- and 8-fold rotations in two-dimensional space. It is originated from…
We look for minimal conditions on a two-dimensional metric surface $X$ of locally finite Hausdorff $2$-measure under which $X$ admits an (almost) parametrization with good geometric and analytic properties. Only assuming that $X$ is locally…
We introduce Schottky maps-conformal maps between relative Schottky sets, and study their local rigidity properties. This continues the investigations of relative Schottky sets initiated in [S. Merenkov, "Planar relative Schottky sets and…
This is a final step in a local classification of pseudo-Riemannian manifolds with parallel Weyl tensor that are not conformally flat or locally symmetric.
We investigate a quasisymmetrically invariant counterpart of the topological Hausdorff dimension of a metric space. This invariant, called the topological conformal dimension, gives a lower bound on the topological Hausdorff dimension of…
We generalize the notion of quasirandom which concerns a class of equivalent properties that random graphs satisfy. We show that the convergence of a graph sequence under the spectral distance is equivalent to the convergence using the…
To prove presence of chaos for fractals, a new mathematical concept of abstract similarity is introduced. As an example, the space of symbolic strings on a finite number of symbols is proved to possess the property. Moreover, Sierpinski…
We provide complete structural theorems for the so-called quasiasymptotic behavior of non-quasianalytic ultradistributions. As an application of these results, we obtain descriptions of quasiasymptotic properties of regularizations at the…
In this paper we study quasiconformal curves which are a special case of quasiregular curves. Namely embeddings $\Omega\rightarrow\mathbb{R}^m$ from some domain $\Omega\subset\mathbb{R}^n$ to $\mathbb{R}^m$, where $n\leq m$, which belong in…
We demonstrate existence of a tile assembly system that self-assembles the statistically self-similar Sierpinski Triangle in the Winfree-Rothemund Tile Assembly Model. This appears to be the first paper that considers self-assembly of a…
We investigate asymptotic symmetries in flat backgrounds of dimension higher than or equal to four. For spin two we provide the counterpart of the extended BMS transformations found by Campiglia and Laddha in four-dimensional Minkowski…
Random walks on a graph reflect many of its topological and spectral properties, such as connectedness, bipartiteness and spectral gap magnitude. In the first part of this paper we define a stochastic process on simplicial complexes of…
Though the uniformization theorem guarantees an equivalence of Riemann surfaces and smooth algebraic curves, moving between analytic and algebraic representations is inherently transcendental. Our analytic curves identify pairs of circles…
We study the almost Kaehler geometry of adjoint orbits of non-compact real semisimple Lie groups endowed with the Kirillov-Kostant-Souriau symplectic form and a canonically defined almost complex structure. We give explicit formulas for the…
An algebraic subvariety Z of A_g is totally geodesic if it is the image via the natural projection map of some totally geodesic submanifold X of the Siegel space. We say that X is the symmetric space uniformizing Z. In this paper we…
We derive a local limit theorem for normal, moderate, and large deviations for symmetric simple random walk on the square lattice in dimensions one and two that is an improvement of existing results for points that are particularly distant…
This article presents a systematic study of a class of maps between quasi-metric spaces that preserve left K-Cauchy sequences. We call such maps left K-Cauchy regular maps. Several characterizations of these maps have been given in terms of…
We discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms, in the framework of compact quantum group theory and…
Random operators constitute fundamental building blocks of models of complex systems yet are far from fully understood. Here, we explain an asymmetry emerging upon repeating identical isotropic (uniformly random) operations. Specifically,…
Divided into three parts, the first marks out enormous geometric issues with the notion of quasi-freenss of an algebra and seeks to replace this notion of formal smoothness with an approximation by means of a minimal unital commutative…