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We show that in high dimensions the set of stable lattices is almost of full measure in the space of unimodular lattices.
A tensor space is a vector space equipped with a finite collection of multilinear forms. The length of a tensor space is its length as a representation of its symmetry group. Infinite dimension tensor spaces of finite length are special,…
A set of lines through the origin in Euclidean space is called equiangular when any pair of lines from the set intersects with each other at a common angle. We study the maximum size of equiangular lines in Euclidean space and use graph…
Over the past few decades, there has been extensive research on scattered subspaces, partly because of their link to MRD codes. These subspaces can be characterized using linearized polynomials over finite fields. Within this context,…
For point $x$ in the inverse limit space $X$ with a single unimodal bonding map we construct, with the use of symbolic dynamics, a planar embedding such that $x$ is accessible. It follows that there are uncountably many non-equivalent…
We solve two related extremal-geometric questions in the $n-$dimensional space $\mathbb{R}^n_{\infty}$ equipped with the maximum metric. First, we prove that the maximum size of a right-equidistant sequence of points in…
Various aspects of Supersymmetry in 1-dimensional systems are analyzed.
We calculate the maximal dimension of linear spaces of symmetric and hermitian matrices with given high rank, generalizing a well-known result of Adams {\em et al.}
This is a complete classification of the complex forms of quaternionic symmetric spaces
We determine the largest size of $3$-uniform set systems on $[n]$ with VC-dimension $2$ for all $n$.
The focus of the paper is on the maximal dimension of affine subspaces of nilpotent $n \times n $ matrices with fixed rank. In particular we obtain two results in the "border" cases rank equal to $n-1$ and rank equal to $1$.
We study the exponential map of connected symmetric spaces and characterize, in terms of midpoints and of infinitesimal conditions, when it is a diffeomorphism, generalizing the Dixmier-Saito theorem for solvable Lie groups. We then give a…
In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…
The structure of $k$-diametral point configurations in Minkowski $d$-space is shown to be closely related to the properties of $k$-antipodal point configurations in $\mathbb{R}^d$. In particular, the maximum size of $k$-diametral point…
The aim of the paper is to present the integrable systems on partial isometries which are related to the restricted Grassmannian in finite dimensional context. Some explicit solutions are obtained.
We establish a characterization of the extraordinary dimension of perfect maps between metrizable spaces.
Partially ordered sets (posets) play a universal role as an abstract structure in many areas of mathematics. For finite posets, an explicit enumeration of distinct partial orders on a set of unlabelled elements is known only up to a…
The aim of this article is to show the existence, and also give an explicit construction, of infinite sets of orthogonal exponentials for certain families of convex polytopes which include simple-rational polytopes and also non simple…
In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.