Related papers: Euclidean Steiner Shallow-Light Trees in Higher Di…
We give constructions of some special cases of $[n,k]$ Reed-Solomon codes over finite fields of size at least $n$ and $n+1$ whose generator matrices have constrained support. Furthermore, we consider a generalisation of the GM-MDS…
We study string theory in supersymmetric time-dependent backgrounds. In the framework of general relativity, supersymmetry for spacetimes without flux implies the existence of a covariantly constant null vector, and a relatively simple form…
Given a set of $n$ points in $R^2$, the Szemer\'edi-Trotter theorem establishes that the number of lines which can be incident to at least $k > 1$ of these points is $O(n^2/k^3 + n/k)$. J.\ Solymosi conjectured that if one requires the…
In 1960, Klee showed that a subset of a Euclidean space must be a singleton provided that each point in the space has a unique farthest point in the set. This classical result has received much attention; in fact, the Hilbert space version…
We set up a connection between the theory of spherical designs and the question of minima of Epstein's zeta function. More precisely, we prove that a Euclidean lattice, all layers of which hold a 4-design, achieves a local minimum of the…
A design is a finite set of points in a space on which every "simple" functions averages to its global mean. Illustrative examples of simple functions are low-degree polynomials on the Euclidean sphere or on the Hamming cube. We prove lower…
This paper studies the regularity of solutions to the Zakharov and Klein-Gordon-Schr\"{o}dinger systems at low regularity levels. The main result is that the nonlinear part of the solution flow falls in a smoother space than the initial…
We consider a (1+1) dimensional scalar field theory that supports oscillons, which are localized, oscillatory, stable solutions to nonlinear equations of motion. We study this theory in an expanding background and show that oscillons now…
Let $\mathcal{P}$ be an $n$-point subset of Euclidean space and $d\geq 3$ be an integer. In this paper we study the following question: What is the smallest (normalized) relative change of the volume of subsets of $\mathcal{P}$ when it is…
Static, cylindrically symmetric solutions to nonlinear scalar-Einstein equations are considered. Regularity conditions on the symmetry axis and flat or string asymptotic conditions are formulated in order to select soliton-like solutions.…
We study configurations of points on the unit sphere that minimize potential energy for a broad class of potential functions (viewed as functions of the squared Euclidean distance between points). Call a configuration sharp if there are m…
Some massless supermultiplets appear as the trivial solution of Kostant's equation, a Dirac-like equation over special cosets. We study two examples; one over the coset SU(3)/SU(2) times U(1) contains the N=2 hypermultiplet in (3+1)…
A classical theorem of Alon and Milman states that any $d$ dimensional centrally symmetric convex body has a projection of dimension $m\geq e^{c\sqrt{\ln{d}}}$ which is either close to the $m$-dimensional Euclidean ball or to the…
A $d$-hypertree on $[n]$ is a maximal acyclic $d$-dimensional simplicial complex with full $(d-1)$-skeleton on the vertex set $[n]$. Alternatively, in the language of algebraic topology, it is a minimal $d$-dimensional simplicial complex…
The KKLT scenario in a warped throat, if consistent, provides a concrete counterexample to both the AdS scale separation and the dS swampland conjectures. First, we define and analyze the relevant effective field theory for the conifold…
We study random unrooted plane trees with $n$ vertices sampled according to the weights corresponding to the vertex-degrees. Our main result shows that if the generating series of the weights has positive radius of convergence, then this…
We establish sharp energy estimates for some solutions, such as global minimizers, monotone solutions and saddle-shaped solutions, of the fractional nonlinear equation $(-\Delta)^{1/2} u=f(u)$ in $\re^n$. Our energy estimates hold for every…
Straight-line (linear) context-free tree (SLT) grammars have been used to compactly represent ordered trees. It is well known that equivalence of SLT grammars is decidable in polynomial time. Here we extend this result and show that…
We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is…
The problem of enumerating spanning trees on graphs and lattices is considered. We obtain bounds on the number of spanning trees $N_{ST}$ and establish inequalities relating the numbers of spanning trees of different graphs or lattices. A…