Related papers: Strongly Minimal Steiner Systems II: Coordinatizat…

We call a metric quasi-Einstein if the $m$-Bakry-Emery Ricci tensor is a constant multiple of the metric tensor. This is a generalization of Einstein metrics, which contains gradient Ricci solitons and is also closely related to the…

We introduce the concept of a type system~$\Part$, that is, a partition on the set of finite words over the alphabet~$\{0,1\}$ compatible with the partial action of Thompson's group~$V$, and associate a subgroup~$\Stab{V}{\Part}$ of~$V$. We…

We use the mathematical structure of group algebras and $H^{+}$-algebras for describing certain problems concerning the quantum dynamics of systems of angular momenta, including also the spin systems. The underlying groups are ${\rm SU}(2)$…

One pillar of quantum magnonics is the exploration of the utilization of the mediation role of magnons in different platforms to develop quantum technologies. The efficient coupling between magnons and various quantum entities is a…

The aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner System $S(t,n,v)$ we associate two ideals, in a suitable polynomial ring, defining a Steiner…

We prove Zilber's Trichotomy Conjecture for strongly minimal expansions of two-dimensional groups, definable in o-minimal structures: Theorem. Let M be an o-minimal expansion of a real closed field, (G;+) a 2-dimensional group definable in…

Let $G$ be a group and $N$ a normal subgroup of $G$. We study the large scale behavior, not the exact values themselves, of the stable mixed commutator length $scl_{G,N}$ on the mixed commutator subgroup $[G,N]$; when $N=G$, $scl_{G,N}$…

A partial Steiner triple system of order $u$ is a pair $(U,\mathcal{A})$ where $U$ is a set of $u$ elements and $\mathcal{A}$ is a set of triples of elements of $U$ such that any two elements of $U$ occur together in at most one triple. If…

We focus on the study of the stability properties of ground-states for the system of $M$ coupled semilinear Schr\"odinger equations with power-type nonlinearities and couplings. Our results are generalizations of the theory for the single…

The quantum orthogonal arrays define remarkable classes of multipartite entangled states called $k$-uniform states whose every reductions to $k$ parties are maximally mixed. We present constructions of quantum orthogonal arrays of strength…

In this article we extend to generic $p$-energy minimizing maps between Riemannian manifolds a regularity result which is known to hold in the case $p=2$. We first show that the set of singular points of such a map can be quantitatively…

A group $G$ is said to have restricted centralizers if for each $g \in G$ the centralizer $C_G(g)$ either is finite or has finite index in $G$. Shalev showed that a profinite group with restricted centralizers is virtually abelian. We take…

We demonstrate that commuting quasilinear systems of Jordan block type are parametrised by solutions of the modified KP hierarchy. Systems of this form naturally occur as hydrodynamic reductions of multi-dimensional linearly degenerate…

Let W be an infinite irreducible Coxeter group with (s_1, ..., s_n) the simple generators. We give a simple proof that the word s_1 s_2 ... s_n s_1 s_2 >... s_n ... s_1 s_2 ... s_n is reduced for any number of repetitions of s_1 s_2 >...…

In this paper, we introduce a quantum version of the wonderful compactification of a group as a certain noncommutative projective scheme. Our approach stems from the fact that the wonderful compactification encodes the asymptotics of matrix…

We show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order $1$),…

We prove, when $S$ is a $2$-group of order at most $2^9$, that each reduced fusion system over $S$ is the fusion system of a finite simple group and is tame. It then follows that each saturated fusion system over a $2$-group of order at…

A classification is given of rank 3 group actions which are quasiprimitive but not primitive. There are two infinite families and a finite number of individual imprimitive examples. When combined with earlier work of Bannai, Kantor,…

We study representations of groups by "affine" automorphisms of compact, convex spaces, with special focus on "irreducible" representations: equivalently "minimal" actions. When the group in question is PSL(2,R), we exhibit a one-one…

We investigate the resilience of spinon quasiparticles in the $J_1$-$J_2$ zig-zag spin chain ($J_2>0$) from the viewpoint of momentum-space entanglement. For small $J_2$, we show that deconfined spinons survive well past the liquid-dimer…