Related papers: An asymptotically good tower of curves of the fiel…
We obtain explicit formulas for the number of non-isomorphic elliptic curves with a given group structure (considered as an abstract abelian group). Moreover, we give explicit formulas for the number of distinct group structures of all…
We find an upper bound for the asymptotic dimension of a hyperbolic metric space with a set of geodesics satisfying a certain boundedness condition studied by Bowditch. The primary example is a collection of tight geodesics on the curve…
For a Euclidean building $X$ of type $A_{2}$, we classify the 0-dimensional subbuildings $A$ of $\partial_{T}X$ that occur as the asymptotic boundary of closed convex subsets. In particular, we show that triviality of the holonomy of a…
We construct smooth 4-manifolds homeomorphic but not diffeomorphic to CP^2+6CP^2-bar.
We construct symplectic structures on roughly half of all equal rank biquotients of the form $G//T$, where $G$ is a compact simple Lie group and $T$ a torus, and investigate Hamiltonian Lie group actions on them. For the Eschenburg flag,…
There are exactly eight edge-to-edge tilings of the sphere by congruent equilateral pentagons: three pentagonal subdivision tilings with 12, 24, 60 tiles; four earth map tilings with 16, 20, 24, 24 tiles; and one flip modification of the…
The goal of this technical note is to show that the geometry of generalized parabolic towers cannot be essentially bounded. It fills a gap in author's paper "Combinatorics, geomerty and attractors of quasi-quadratic maps", Annals of Math.,…
On a projective surface it is well-known that the set of curves orthogonal to a nef line bundle is either finite or uncountable. We show that this dichotomy fails in higher dimension by constructing a nef line bundle on a threefold which is…
We give optimal lower bounds for the number of sextactic points on a simple closed curve in the real projective plane. Sextactic points are after inflection points the simplest projectively invariant singularities on such curves. Our method…
We associate a tower with an infinitesimal algebraic skeleton to the (2+1)-dimensional (compact and noncompact) Heisenberg spin model. In particular, we construct the absolute parallelism defining the tower and the corresponding extension…
We give a method for constructing Kummer covers with many points over finite fields.
We prove that curves indicated in the title exist. This results answers to a question posed by A.G.Vitushkin about 30 years ago. We also discuss the minimal number of boundary components of a curve in the unit ball passing through the…
We give a general procedure for gluing together possibly noncompact manifolds of constant scalar curvature which satisfy an extra nondegeneracy hypothesis. Our aim is to provide a simple paradigm for making `analytic' connected sums. In…
We conjecture that meanders are governed by the gravitational version of a c=-4 two-dimensional conformal field theory, allowing for exact predictions for the meander configuration exponent \alpha=\sqrt{29}(\sqrt{29}+\sqrt{5})/12, and the…
We provide a given algebraic structure with the structure of an infinitesimal algebraic skeleton. The necessary conditions for integrability of the absolute parallelism of a tower with such a skeleton are dispersive nonlinear models and…
In this article we investigate the automorphism group of an asymptotically optimal tower of function fields introduced by Garcia and Stichtenoth. In particular we provide a detailed description of the decomposition group of some rational…
In this note we construct a flag simplicial $3$-sphere $\Delta$ with the following properties: - $\Delta$ is not a suspension; - $\Delta$ has no edge that can be contracted to obtain another flag sphere; - The only equators (induced…
We propose and analyze a class of particle methods for the Vlasov equation with a strong external magnetic field in a torus configuration. In this regime, the time step can be subject to stability constraints related to the smallness of…
Let X be a curve over the finite field of q elements and let N(X), g(X) be its number of rational points and genus respectively. The Ihara constant A(q) is defined by the limit superior of N(X)/g(X) as the genus of X goes to infinity. In…
The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such…