Related papers: Asymptotically short generalizations of $t$-design…

A $\textit{spherical $t$-design curve}$ was defined by Ehler and Gr\"{o}chenig to be a continuous, piecewise smooth, closed curve on the sphere with finitely many self-intersections whose associated line integral applied to any polynomial…

In analogy to classical spherical t-design points, we introduce the concept of t-design curves on the sphere. This means that the line integral along a t-design curve integrates polynomials of degree t exactly. For low degrees we construct…

Under the Riemann Hypothesis for Dirichlet L-functions, we improve on the error term in a smoothed version of an estimate for the density of elliptic curves with square-free $\Delta=D/16$, where D is the discriminant, by T.D. Browning and…

A spherical $t$-design is a finite subset $X$ of the unit sphere such that every polynomial of degree at most $t$ has the same average over $X$ as it does over the entire sphere. Determining the minimum possible size of spherical designs,…

We report on the problem of the existence of complex and real algebraic curves in the plane with prescribed singularities up to analytic and topological equivalence. The question is whether, for a given positive integer $d$ and a finite…

Given a directed acyclic graph with positive edge-weights, two vertices s and t, and a threshold-weight L, we present a fully-polynomial time approximation-scheme for the problem of counting the s-t paths of length at most L. We extend the…

Spherical $t$-designs are finite point sets on the unit sphere that enable exact integration of polynomials of degree at most $t$ via equal-weight quadrature. This concept has recently been extended to spherical $t$-design curves by the use…

We show that under the action of $\mathrm{diag}(e^{nt},e^{-r_1(t)},\ldots,e^{-r_n(t)})\in\mathrm{SL}(n+1,\mathbb{R})$, where $r_i(t)\to\infty$, on the space of unimodular lattices in $\mathbb{R}^{n+1}$, the translates of any fixed-sized…

We find t-designs on compact algebraic manifolds with a number of points comparable to the dimension of the space of polynomials of degree t on the manifold. This generalizes results on the sphere by Bondarenko, Radchenko and Viazovska. Of…

Consider nonlinear Schr\"odinger equations with small nonlinearities \[\frac{d}{dt}u+i(-\triangle u+V(x)u)=\epsilon \mathcal{P}(\triangle u,u,x),\quad x\in \mathbb{T}^d.\eqno{(*)}\] Let $\{\zeta_1(x),\zeta_2(x),\dots\}$ be the $L_2$-basis…

A Euclidean $t$-design, as introduced by Neumaier and Seidel (1988), is a finite set ${\cal X} \subset \mathbb{R}^n$ with a weight function $w: {\cal X} \rightarrow \mathbb{R}^+$ for which $$\sum_{r \in R} W_r \overline{f}_{S_{r}} =…

This paper focuses on establishing the existence of a class of steady solutions, termed least total curvature solutions, to the incompressible Euler system in a strip. The solutions obtained in this paper complement the least total…

Let $X$ be an infinite hyperbolic surface endowed with an upper bounded geodesic pants decomposition. Alessandrini, Liu, Papadopoulos, Su and Sun \cite{ALPSS}, \cite{ALPS} parametrized the quasiconformal Teichm\"uller space $T_{qc}(X)$ and…

Let $\gamma_0$ be a curve on a surface $\Sigma$ of genus $g$ and with $r$ boundary components and let $\pi_1(\Sigma)\curvearrowright X$ be a discrete and cocompact action on some metric space. We study the asymptotic behavior of the number…

Notions of graph similarity provide alternative perspective on the graph isomorphism problem and vice-versa. In this paper, we consider measures of similarity arising from mismatch norms as studied in Gervens and Grohe: the edit distance…

We study the H^{-1}-norm of the function 1 on tubular neighbourhoods of curves in R^2. We take the limit of small thickness epsilon, and we prove two different asymptotic results. The first is an asymptotic development for a fixed curve in…

We study the problem of the rigorous derivation of one-dimensional models for a thin curved beam starting from three-dimensional nonlinear elasticity. We describe the limiting models obtained for different scalings of the energy. In…

We consider asymptotically autonomous semilinear parabolic equations u_t + Au = f(t,u). Suppose that $f(t,.)\to f^\pm$ as $t\to\pm\infty$, where the semiflows induced by \label{eq:140602-1511} u_t + Au = f^\pm(u) \tag{*} are gradient-like.…

Consider a random regular graph with degree $d$ and of size $n$. Assign to each edge an i.i.d. exponential random variable with mean one. In this paper we establish a precise asymptotic expression for the maximum number of edges on the…

Masur and Minsky showed that the curve graph is quasi-isometric to the Teichm\"uller space electrified along its thin part, and hence the Teichm\"uller space is weakly relatively hyperbolic with respect to the thin part. In this paper, we…