Related papers: Intersections of diagonal orbits

Let $G$ be a connected Lie group and $\Gamma \subset G$ a lattice. Connection curves of the homogeneous space $M=G/\Gamma$ are the orbits of one parameter subgroups of $G$. To \textit{block} a pair of points $m_1,m_2 \in M$ is to find a…

We define and study preorderings and orderings on rings of the form $M_n(R)$ where $R$ is a commutative unital ring. We extend the Artin-Lang theorem and Krivine-Stengle Stellens\"atze (both abstract and geometric) from $R$ to $M_n(R)$.…

We derive a necessary condition for the existence of marginally stable circular orbits of test particles in stationary axisymmetric spacetimes which possess a refection symmetry with respect to the equatorial plane; photon orbits are also…

Let $X/K$ be a smooth projective variety defined over a number field, and let $f:X\to{X}$ be a morphism defined over $K$. We formulate a number of statements of varying strengths asserting, roughly, that if there is at least one point…

We give two sufficient conditions for the lattice Co(R^n,X) of relatively convex sets of n-dimensional real space R^n to be join-semidistributive, where X is a finite union of segments. We also prove that every finite lower bounded lattice…

We study integrable non-diagonal open boundary conditions for spin chains arising from holographic gauge theories. Their dual description is in terms of open strings stretching between giant gravitons intersecting at arbitrary angles inside…

In this paper, we provide an algebraic condition on any $2n \times 2n$ real symmetric positive definite matrix which is necessary and sufficient for the matrix to be diagonalized by an orthosymplectic matrix in the sense of Williamson's…

Let S(n) be the symmetric group on n points. A subset S of S(n) is intersecting if for any pair of permutations \pi, \sigma in S there is a point i in {1,...,n} such that \pi(i)=\sigma(i). Deza and Frankl \cite{MR0439648} proved that if S a…

We prove a general likely intersections theorem, a counterpart to the Zilber-Pink conjectures, under the assumption that the Ax-Schanuel property and some mild additional conditions are known to hold for a given category of complex quotient…

A set of permutations $I \subset S_n$ is said to be {\em k-intersecting} if any two permutations in $I$ agree on at least $k$ points. We show that for any $k \in \mathbb{N}$, if $n$ is sufficiently large depending on $k$, then the largest…

Suppose $M_{1}$ and $M_{2}$ are two special Lagrangian submanifolds of $\Rtn$ with boundary that intersect transversally at one point $p$. The set $M_{1} \cup M_{2}$ is a singular special Lagrangian variety with an isolated singularity at…

We give a complete characterisation of the single and double arrow relations of the standard context $K(L_n)$ of the lattice $L_n$ of partitions of any positive integer $n$ under the dominance order, thereby addressing an open question of…

We introduce discrete multivortex solitons in a ring of nonlinear oscillators coupled to a central site. Regular clusters of discrete vortices appear as a result of mode collisions and we show that their stability is determined by global…

We address the issue of mobility of localized modes in two-dimensional nonlinear Schr\"odinger lattices with saturable nonlinearity. This describes e.g. discrete spatial solitons in a tight-binding approximation of two-dimensional optical…

The post-main sequence eclipsing binary NN Serpentis was recently announced as the potential host of at least two massive planetary companions. In that work, the authors put forward two potential architectures that fit the observations of…

Let $G=GL(n)$ be the $n\times n$ complex general linear group and let $\mathcal{B}_{n}$ be its flag variety. The standard Borel subgroup $B$ of upper triangular matrices acts on the product $\mathcal{B}_{n}\times \mathbb{P}^{n-1}$ with…

The Semialgebraic Orbit Problem is a fundamental reachability question that arises in the analysis of discrete-time linear dynamical systems such as automata, Markov chains, recurrence sequences, and linear while loops. An instance of the…

It is shown that, given any $k$-dimensional lattice $\Lambda$, there is a lattice sequence $\Lambda_w$, $w\in \mathbb Z$, with sub-orthogonal lattice $\Lambda_o \subset \Lambda$, converging to $\Lambda$ (unless equivalence), also we discuss…

Little red dots (LRDs) are compact high-redshift objects, newly discovered by the James Webb Space Telescope. Although LRDs exhibit broad Balmer emission lines suggestive of the presence of active galactic nuclei (AGN), their spectral…

The group $G = GL_r(k) \times (k^\times)^n$ acts on $\mathbf{A}^{r \times n}$, the space of $r$-by-$n$ matrices: $GL_r(k)$ acts by row operations and $(k^\times)^n$ scales columns. A matrix orbit closure is the Zariski closure of a point…