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Conformal geometry and (super)conformal higher-spin gauge theoriesFeb 21 2019We develop a manifestly conformal approach to describe linearised (super)conformal higher-spin gauge theories in arbitrary conformally flat backgrounds in three and four spacetime dimensions. Closed-form expressions in terms of gauge prepotentials are ... More
Abstract homomorphisms from locally compact groups to discrete groupsFeb 21 2019We show that every abstract homomorphism $\varphi$ from a locally compact group $L$ to a graph product $G_\Gamma$, endowed with the discrete topology, is either continuous or $\varphi(L)$ lies in a 'small' parabolic subgroup. In particular, every locally ... More
Realizations of groups of piecewise continuous transformations of the circleFeb 19 2019We study the near action of the group PC of piecewise continuous self-transformations of the circle. Elements of this group are only defined modulo indeterminacy on a finite subset, which raises the question of realizability: a subgroup of PC is said ... More
The diameter of products of finite simple groupsFeb 19 2019Following partially a suggestion by Pyber, we prove that the diameter of a product of non-abelian finite simple groups is bounded linearly by the maximum diameter of its factors. For completeness, we include the case of abelian factors and give explicit ... More
Max-Min theorems for weak containment, square summable homoclinic points, and completely positive entropyFeb 18 2019We prove a max-min theorem for weak containment in the context of algebraic actions. Namely, we show that given an algebraic action of $G$ on $X,$ there is a maximal, closed $G$-invariant subgroup $Y$ of $X$ so that the action of $G$ on $Y$ is weakly ... More
The stable category and invertible modules for infinite groupsFeb 18 2019We construct a well-behaved stable category of modules for a large class of infinite groups. We then consider its Picard group, which is the group of invertible (or endotrivial) modules. We show how this group can be calculated when the group acts on ... More
A sufficient condition for a locally compact almost simple group to have open monolithFeb 18 2019We obtain a sufficient condition, given a totally disconnected, locally compact group $G$ with a topologically simple monolith $S$, to ensure that $S$ is open in $G$ and abstractly simple.
Direct limits of regular Lie groupsFeb 17 2019Let G be a regular Lie group which is a directed union of regular Lie groups G_i (all modelled on possibly infinite-dimensional, locally convex spaces). We show that G is the direct limit of the G_i as a regular Lie group whenever G admits a so-called ... More
Growth and expansion in algebraic groups over finite fieldsFeb 17 2019This is a brief introduction to the study of growth in groups of Lie type, with $SL_2(\mathbb{F}_q)$ and some of its subgroups as the key examples. They are an edited version of the notes I distributed at the Arizona Winter School in 2016. Those notes ... More
Plactic monoids satisfy nontrivial identitiesFeb 17 2019It is shown that the plactic monoid P_n of any fixed rank n satisfies a nontrivial identity.
The center of a Green biset functorFeb 17 2019For a Green biset functor $A$, we define the commutant and the center of $A$ and we study some of their properties and their relationship. This leads in particular to the main application of these constructions: the possibility of splitting the category ... More
On Group-Like MagmoidsFeb 16 2019A magmoid is a non-empty set with a partial binary operation; group-like magmoids generalize group-like magmas such as semigroups, monoids and groups. In this article, we first consider the many ways in which the notions of associative multiplication, ... More
The Conjugacy Problem for Higman's GroupFeb 16 2019In 1951, Higman constructed a remarkable group $$H=\left\langle a,b,c,d \, \left| \, b^a = b^2, c^b = c^2, d^c = d^2, a^d = a^2 \right. \right\rangle$$ and used it to produce the first examples of infinite simple groups. By studying fixed points of certain ... More
Normalizers and permutative endomorphisms of the $2$-adic ring $C^*$-algebraFeb 15 2019A complete description is provided for the unitary normalizer of the diagonal Cartan subalgebra $\mathcal{D}_2$ in the $2$-adic ring $C^*$-algebra $\mathcal{Q}_2$, which generalizes and unifies analogous results for Cuntz and Bunce-Deddens algebras. Furthermore, ... More
On semilinear sets and asymptotically approximate groupsFeb 15 2019Let $G$ be any group and $A$ be an arbitrary subset of $G$ (not necessarily symmetric and not necessarily containing the identity). The $h$-fold product set of $A$ is defined as $$A^{h} :=\lbrace a_{1}.a_{2}...a_{h} : a_{1},\ldots,a_n \in A \rbrace.$$ ... More
Finite quasiprimitive permutation groups with a metacyclic transitive subgroupFeb 15 2019In this paper, we classify finite quasiprimitive permutation groups with a metacyclic transitive subgroup, solving a problem initiated by Wielandt in 1949. It also involves the classification of factorizations of almost simple groups with a metacyclic ... More
An extension of properties of symmetric group to monoids and a pretorsion theory in the category of mappingsFeb 14 2019Several elementary properties of the symmetric group $S_n$ extend in a nice way to the full transformation monoid $M_n$ of all maps of the set $X:=\{1,2,3,\dots,n\}$ into itself. The group $S_n$ turns out to be in some sense the torsion part of the monoid ... More
A description of automorphism group of power graphs of finite groupsFeb 14 2019The power graph of a group is the graph whose vertex set is the set of nontrivial elements of group, two elements being adjacent if one is a power of the other. We introduce some way for find the automorphism groups of some graphs. As an application We ... More
Reduced thin-sandwich equations on manifolds euclidean at infinity and on closed manifolds: existence and multiplicityFeb 14 2019The reduced thin-sandwich equations (RTSE) appear within Wheeler's thin-sandwich approach towards the Einstein constraint equations (ECE) of general relativity. It is known that these equations cannot be well-posed in general, but, on closed manifolds, ... More
Operational causality in spacetimeFeb 13 2019We consider the general evolution of binary statistics in a, possibly curved, spacetime with the help of the optimal transport theory. It covers a wide range of models including classical statistics, quantum wave-packets and general, possibly non-linear, ... More
Correspondence functors and latticesFeb 13 2019A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commu-tative ring. A main tool for this study is the construction of a correspondence functor associated to any finite ... More
Topological dynamics of Polish group extensionsFeb 13 2019We consider a short exact sequence $1\to H\to G\to K\to 1$ of Polish groups and consider what can be deduced about the dynamics of $G$ given information about the dynamics of $H$ and $K$. We prove that if the respective universal minimal flows $M(H)$ ... More
Correspondence functors and finiteness conditionsFeb 13 2019We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various specific properties ... More
A cubical flat torus theorem and some of its applicationsFeb 13 2019The article is dedicated to the proof of the following cubical version of the flat torus theorem. Let $G$ be a group acting on a CAT(0) cube complex $X$ and $A \leq G$ a normal finitely generated abelian subgroup. Then there exists a median subalgebra ... More
Surface Words are Determined by Word Measures on GroupsFeb 13 2019Every word $w$ in a free group naturally induces a probability measure on every compact group $G$. For example, if $w=\left[x,y\right]$ is the commutator word, a random element sampled by the $w$-measure is given by the commutator $\left[g,h\right]$ of ... More
The algebra of Boolean matrices, correspondence functors, and simplicityFeb 13 2019We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a simple correspondence ... More
Quantum computing, Seifert surfaces and singular fibersFeb 13 2019The fundamental group $\pi_1(L)$ of a knot or link $L$ may be used to generate magic states appropriate for performing universal quantum computation and simultaneously for retrieving complete information about the processed quantum states. In this paper, ... More
Cancellable elements in the lattice of overcommutative semigroup varietiesFeb 12 2019We completely determine all cancellable elements in the lattice of overcommutative semigroup varieties.
Exterior powers of the adjoint representation and the Weyl ring of $E_8$Feb 12 2019I derive explicitly all polynomial relations in the character ring of $E_8$ of the form $\chi_{\wedge^k \mathfrak{e}_8} - \mathfrak{p}_{k} (\chi_{1}, \dots, \chi_{r})=0$, where $\wedge^k \mathfrak{e}_8$ is an arbitrary exterior power of the adjoint representation ... More
On property (T) for automorphism groups of graph productsFeb 12 2019We show that the automorphism group of a graph product of finite groups $Aut(G_\Gamma)$ has Kazhdan's property (T) if and only if $\Gamma$ is a complete graph.
Separable deformations of the generalized quaternion group algebrasFeb 12 2019The group algebras $kQ_{2^n}$ of the generalized quaternion groups $Q_{2^n}$ over fields $k$ which contain $\mathbb{F}_{2^{n-2}}$, are deformed to separable $k((t))$-algebras $[kQ_{2^n}]_t$. The dimensions of the simple components of $\overline{k((t))}\otimes_{k((t))}[kQ_{2^n}]_t$ ... More
The twisted group ring isomorphism problem over fieldsFeb 12 2019Similarly to how the classical group ring isomorphism problem asks, for a commutative ring $R$, which information about a finite group $G$ is encoded in the group ring $RG$, the twisted group ring isomorphism problem asks which information about $G$ is ... More
Noncommutative invariant theory of symplectic and orthogonal groupsFeb 11 2019We present a method for computing the Hilbert series of the algebra of invariants of the complex symplectic and orthogonal groups acting on graded noncommutative algebras with homogeneous components which are polynomial modules of the general linear group. ... More
On inclusive Racah matrices $\bar S$ for rectangular representationsFeb 11 2019We use the recent observation about the evolution formula for twist knots to provide a nearly explicit answer for Racah matrix $\bar S$ in arbitrary rectangular representation $R=[r^s]$. The answer is expressed through the eigenvectors of a simply-looking ... More
On exclusive Racah matrices $\bar S$ for rectangular representationsFeb 11 2019Feb 15 2019We use the recent observation about the evolution formula for twist knots to provide a nearly explicit answer for Racah matrix $\bar S$ in arbitrary rectangular representation $R=[r^s]$. The answer is expressed through the eigenvectors of a simply-looking ... More
Dynamical alternating groups, stability, property Gamma, and inner amenabilityFeb 11 2019We prove that the alternating group of a topologically free action of a countably infinite group $\Gamma$ on the Cantor set has the property that all of its $\ell^2$-Betti numbers vanish and, in the case that $\Gamma$ is amenable, is stable in the sense ... More
The topology of Baumslag-Solitar representationsFeb 11 2019Let $\Gamma=\langle a,b | a b^{p} a^{-1} = b^{q}\rangle$ be a Baumslag--Solitar group and $G$ be a complex reductive algebraic group with maximal compact subgroup $K<G$. We show that, when $p$ and $q$ are relatively prime with distinct absolute values, ... More
All those EPPA classes (Strengthenings of the Herwig-Lascar theorem)Feb 11 2019In this paper we prove a general theorem showing the extension property for partial automorphisms (EPPA, also called the Hrushovski property) for classes of structures containing relations and unary functions, optionally equipped with a permutation group ... More
The word problem of the Brin-Thompson groups is coNP-completeFeb 11 2019We prove that the word problem of the Brin-Thompson group nV over a finite generating set is coNP-complete for every n \ge 2. It is known that the groups $n V$ are an infinite family of infinite, finitely presented, simple groups. We also prove that the ... More
Undecidability of the word problem for one-relator inverse monoids via right-angled Artin subgroups of one-relator groupsFeb 11 2019We prove the following results: (1) There is a one-relator inverse monoid $\mathrm{Inv}\langle A\:|\:w=1 \rangle$ with undecidable word problem; and (2) There are one-relator groups with undecidable submonoid membership problem. The first of these results ... More
Metric Curvatures and their Applications 2: Metric Ricci Curvature and FlowFeb 09 2019In this second part of our overview of the different metric curvatures and their various applications, we concentrate on the Ricci curvature and flow for polyhedral surfaces and higher dimensional manifolds, and we largely review our previous studies ... More
On dimension of product of groupsFeb 08 2019We prove that for geometrically finite groups cohomological dimension of the direct product of a group with itself equals 2 times the cohomological dimension dimension of the group.
Zeros of irreducible characters lying in a normal subgroupFeb 08 2019Let $N$ be a normal subgroup of a finite group $G$. An element $g\in G$ such that $\chi(g)=0$ for some irreducible character $\chi$ of $G$ is called a vanishing element of $G$. The aim of this paper is to analyse the influence of the $\pi$-elements in ... More
On zeros of irreducible characters lying in a normal subgroupFeb 08 2019Feb 13 2019Let $N$ be a normal subgroup of a finite group $G$. An element $g\in G$ such that $\chi(g)=0$ for some irreducible character $\chi$ of $G$ is called a vanishing element of $G$. The aim of this paper is to analyse the influence of the $\pi$-elements in ... More
Regularization by ε-metricFeb 08 2019The regularization of propagators by means of a complex metric is considered. (The paper is an English translation of the first of two articles in Russian published by the author in 1987-88: V.D. Ivashchuk, Regularization by {\epsilon}-metric. I, Izvestiya ... More
Link quandles are residually finiteFeb 08 2019In a recent work [2] we introduced residual finiteness of quandles, and proved that free quandles and knot quandles are residually finite. In this note, we extend these results to show that link quandles are residually finite. This is achieved by showing ... More
An approach to harmonic analysis on non-locally compact groups I: level structures over locally compact groupsFeb 08 2019We define a class of spaces on which one may generalise the notion of compactness following motivating examples from higher-dimensional number theory. We establish analogues of several well-known topological results (such as Tychonoff's Theorem) for such ... More
The non-projective part of the tensor powers of a moduleFeb 08 2019Let $M$ be a finite dimensional modular representation of a finite group $G$. We consider the generating function for the non-projective part of the tensor powers of $M$, and we write $\gamma_G(M)$ for the reciprocal of the radius of convergence of this ... More
Rank, coclass and cohomologyFeb 07 2019We prove that for any prime $p$ the finite $p$-groups of fixed coclass have only finitely many different mod-$p$ cohomology rings between them. This was conjectured by Carlson; we prove it by first proving a stronger version for groups of fixed rank.
Constructive Non-Linear Polynomial Cryptanalysis of a Historical Block CipherFeb 07 2019One of the major open problems in symmetric cryptanalysis is to discover new specif i c types of invariant properties which can hold for a larger number of rounds of a block cipher. We have Generalised Linear Cryptanalysis (GLC) and Partitioning Cryptanalysis ... More
Comments on "Discrete Groups, Expanding Graphs and Invariant Measures", by Alexander LubotzkyFeb 07 2019This document is a collection of comments that I wrote down while reading the first four chapters of the book "Discrete Groups, Expanding Graphs and Invariant Measures" by Alexander Lubotzky. Most of them are more detailed versions of proofs. Some imprecisions ... More
Global evolution of the U(1) Higgs Boson: nonlinear stability and uniform energy boundsFeb 07 2019Relying on the hyperboloidal foliation method, we establish the nonlinear stability of the ground state of the so-called U(1) standard model of electroweak interactions. This amounts to establishing a global-in-time theory for the initial value problem ... More
A short introduction to Monstrous MoonshineFeb 07 2019This paper is an introduction to the Monstrous Moonshine correspondence aiming at an undergraduate level. We review first the classification of finite simple groups and some properties of the monster $\mathbb{M}$, and then the theory of classical modular ... More
A short introduction to Monstrous MoonshineFeb 07 2019Feb 18 2019This paper is an introduction to the Monstrous Moonshine correspondence aiming at an undergraduate level. We review first the classification of finite simple groups and some properties of the monster $\mathbb{M}$, and then the theory of classical modular ... More
Torsion groups do not act on $2$-dimensional $\mathrm{CAT}(0)$ complexesFeb 07 2019We show, under mild hypotheses, that if each element of a finitely generated group acting on a $2$-dimensional $\mathrm{CAT}(0)$ complex has a fixed point, then the action is trivial. In particular all actions of finitely generated torsion groups on such ... More
Retracts of free groups and a question of BergmanFeb 06 2019Let $F_n$ be a free group of finite rank $n \geq 2$. We prove that if $H$ is a subgroup of $F_n$ with $\textrm{rk}(H)=2$ and $R$ is a retract of $F_n$, then $H \cap R$ is a retract of $H$. However, for every $m \geq 3$ and every $1 \leq k \leq n-1$, there ... More
Splitting groups with cubic Cayley graphs of connectivity twoFeb 06 2019Feb 07 2019A group $G$ splits over a subgroup $C$ if $G$ is either a free product with amalgamation $A \underset{C}{\ast} B$ or an HNN-extension $G=A \underset{C}{\ast} (t)$. We invoke Bass-Serre theory and classify all infinite groups which admit cubic Cayley graphs ... More
On the evolution of the spacetime Bartnik massFeb 06 2019It is conjectured that the full (spacetime) Bartnik mass of a surface $\Sigma$ is realised as the ADM mass of some stationary asymptotically flat manifold with boundary data prescribed by $\Sigma$. Assuming this holds true for a 1-parameter family of ... More
On embeddings of quandles into groupsFeb 06 2019In the present paper, we introduce the new construction of quandles. For a group $G$ and its subset $A$ we construct a quandle $Q(G,A)$ which is called the $(G,A)$-quandle and study properties of this quandle. In particular, we prove that if $Q$ is a ... More
The Isoperimetric Problem in Riemannian Optical GeometryFeb 05 2019In general relativity, spatial light rays of static spherically symmetric spacetimes are geodesics of surfaces in Riemannian optical geometry. In this paper, we apply results on the isoperimetric problem to show that length-minimizing curves subject to ... More
Conformal wave equations for the Einstein-tracefree matter systemFeb 05 2019Inspired by a similar analysis for the vacuum conformal Einstein field equations by Paetz [Ann. H. Poincar\'e 16, 2059 (2015)], in this article we show how to construct a system of quasilinear wave equations for the geometric fields associated to the ... More
Ideal zeta functions associated to a family of class-2-nilpotent Lie ringsFeb 05 2019We produce explicit formulae for various ideal zeta functions associated to the members of an infinite family of class-$2$-nilpotent Lie rings, introduced in [8], in terms of Igusa functions. As corollaries we obtain information about analytic properties ... More
Optimal bounds for ancient caloric functionsFeb 05 2019For any manifold with polynomial volume growth, we show: The dimension of the space of ancient caloric functions with polynomial growth is bounded by the degree of growth times the dimension of harmonic functions with the same growth. As a consequence, ... More
Hyperballeans of groupsFeb 04 2019In this paper we define some ballean structure on the power set of a group and, in particular, we study the subballean with support the lattice of all its subgroups. If $G$ is a group, we denote by $L(G)$ the family of all subgroups of $G$. For two groups ... More
Outer automorphism groups of graph products: subgroups and quotientsFeb 04 2019Feb 12 2019We show that the outer automorphism groups of graph products of finitely generated abelian groups satisfy the Tits alternative, are residually finite, their so-called Torelli subgroups are finitely generated, and they satisfy a dichotomy between being ... More
Outer automorphism groups of graph products: subgroups and quotientsFeb 04 2019We show that the outer automorphism groups of graph products of finitely generated abelian groups satisfy the Tits alternative, are residually finite, their so-called Torelli subgroups are finitely generated, and they satisfy a dichotomy between being ... More
Uniqueness of minimal loop quantum cosmology dynamicsFeb 04 2019Feb 11 2019We show that the standard Hamiltonian of isotropic loop quantum cosmology is selected by physical criteria plus one choice: that it have a `minimal' number of terms. We also show the freedom, and boundedness of energy density, even when this choice is ... More
Stability in Bounded Cohomology for Classical Groups, I: The Symplectic CaseFeb 04 2019We show that continuous bounded group cohomology stabilizes along the sequences of real or complex symplectic Lie groups, and deduce that bounded group cohomology stabilizes along sequences of lattices in them, such as $(\mathrm{Sp}_{2r}(\mathbb{Z}))_{r ... More
Minimal additive complements in finitely generated abelian groupsFeb 04 2019Given two non-empty subsets $W,W'\subseteq G$ in an arbitrary abelian group $G$, $W'$ is said to be an additive complement to $W$ if $W + W'=G$ and it is minimal if no proper subset of $W'$ is a complement to $W$. The notion was introduced by Nathanson ... More
La cosmología y los matemáticos (Cosmology and mathematicians)Feb 04 2019Free translation of the original abstract in Spanish: Some of the most relevant milestones due to, or instigated by, mathematicians concerning the creation, development and advances of Cosmology as a scientific discipline are presented and discussed. ... More
Conformality for a robust class of non-conformal attractorsFeb 04 2019In this paper we investigate the Hausdorff dimension of limit sets of Anosov representations. In this context we revisit and extend the framework of hyperconvex representations and establish a convergence property for them, analogue to a differentiability ... More
Normal distributions of finite Markov chainsFeb 04 2019We show that the stationary distribution of a finite Markov chain can be expressed as the sum of certain normal distributions. These normal distributions are associated to planar graphs consisting of a straight line with attached loops. The loops touch ... More
Right-angled Coxeter groups with non-planar boundaryFeb 04 2019We investigate the planarity of the boundaries of right-angled Coxeter groups. We show that non-planarity of the defining graph does not necessarily imply non-planarity of every boundary of the associated right-angled Coxeter group, although it does in ... More
Galois groups of symmetric sextic trinomialsFeb 03 2019We compute the Galois group of the splitting field $ F$ of any irreducible and separable polynomial $f(x)=x^6+ax^3+b$ with $a,b\in K$, a field with characteristic different from two. The proofs require to distinguish between two cases: whether or not ... More
Cube complexes and abelian subgroups of automorphism groups of RAAGsFeb 03 2019We construct free abelian subgroups of the group $U(A_\Gamma)$ of untwisted outer automorphisms of a right-angled Artin group, thus giving lower bounds on the virtual cohomological dimension. The group $U(A_\Gamma)$ was previously studied by Charney, ... More
Group-theoretic remarks on Goldbach's conjectureFeb 03 2019The famous strongly binary Goldbach's conjecture asserts that every even number $2n \geq 8$ can always be expressible as the sum of two distinct odd prime numbers. We use a new approach to dealing with this conjecture. Specifically, we apply the element ... More
SSGP topologies on free groups of infinite rankFeb 03 2019We prove that every free group G with infinitely many generators admits a Hausdorff group topology T with the following property: for every T-open neighbourhood U of the identity of G, each element g in G can be represented as a product g=g_1 g_2 ... ... More
CMC foliations of open spacetimes asymptotic to open Robertson-Walker spacetimesFeb 03 2019We consider open globally hyperbolic spacetimes $N$ of dimension $n+1$, $n\ge 3$, which are spatially asymptotic to a Robertson-Walker spacetime or an open Friedmann universe with spatial curvature $\tilde\kappa = 0,-1$ and prove, under reasonable assumptions, ... More
The energy and spectrum of non commuting graphFeb 02 2019Let G be a non-abelian group and Z(G) be the center of G. The non-commuting graph {\Gamma}(G) of G is a graph with vertex set is non central elements of G and two vertices x, y are adjacent if and only if they are commute. In this paper we calculate the ... More
The distance formula in algebraic spacetime theoriesFeb 01 2019The Lorentzian distance formula, conjectured several years ago by Parfionov and Zapatrin, has been recently proved by the second author. In this work we focus on the derivation of an equivalent expression in terms of the geometry of 2-spinors by using ... More
Asymptotic Behavior of Cosmologies with $Λ>0$ in 2+1 DimensionsFeb 01 2019We study, using Mean Curvature Flow methods, 2+1 dimensional cosmologies with a positive cosmological constant and matter satisfying the dominant and the strong energy conditions. If the spatial slices are compact with non-positive Euler characteristic ... More
Subgroups of arbitrary even ordinary depthFeb 01 2019We show that for each positive integer $n$, there are a group $G$ and a subgroup $H$ such that the ordinary depth is $d(H, G) = 2n$. This answers the question posed by Lars Kadison (see [10]) whether even ordinary depth larger than $6$ can occur.
Trigonometric series and self-similar setsFeb 01 2019Feb 06 2019Let $F$ be a self-similar set on $\mathbb{R}$ associated to contractions $f_j(x) = r_j x + b_j$, $j \in \mathcal{A}$, for some finite $\mathcal{A}$, such that $F$ is not a singleton. We prove that if $\log r_i / \log r_j$ is irrational for some $i \neq ... More
Polysymplectic formulation for BF gravity with Immirzi parameterJan 31 2019The polysymplectic formulation of the CMPR action, which is a BF-type formulation of General Relativity that involves an arbitrary Immirzi parameter, is performed. We implement a particular scheme within this covariant Hamiltonian approach to analyze ... More
The completion of the $3$-modular character table of the Chevalley group $F_4(2)$ and its covering groupJan 31 2019Using computational methods, we complete the determination of the $3$-modular character table of the Chevalley group $F_4(2)$ and its covering group.
A family of non-FSZ finite symplectic groupsJan 31 2019Let $p$ be an odd prime with $p\equiv1\bmod 4$. Then for any odd power $q$ of $p$ and a positive integer $j$ we show that the groups $\text{Sp}_{p^j+1}(q),\text{PSp}_{p^j+1}(q)$, and their Sylow $p$-subgroups are non-$FSZ_{p^j}$.
On the space of ends of infinitely generated groupsJan 30 2019We study the space of ends of groups. For a finitely generated group, this is a Cantor space as soon as it is infinite. In contrast, we show that for infinitely generated countable groups, it exhibits several behaviors. For instance, we show that for ... More
The finite volume method on a Schwarzschild backgroundJan 30 2019We introduce a class of nonlinear hyperbolic conservation laws on a Schwarzschild black hole background and derive several properties satisfied by (possibly weak) solutions. Next, we formulate a numerical approximation scheme which is based on the finite ... More
Topological boundaries of unitary representationsJan 30 2019We introduce and study a generalization of the notion of the Furstenberg boundary of a discrete group $\Gamma$ to the setting of a general unitary representation $\pi: \Gamma \to B(\mathcal H_\pi)$. This space, which we call the "Furstenberg-Hamana boundary" ... More
An exotic presentation of Q_28Jan 30 2019We introduce a new family of presentations for the quaternion groups and show that for the quaternion group of order 28, one of these presentations has non-standard second homotopy group.
On an idea of Michael AtiyahJan 30 2019In this note we investigate the idea of Michael Atiyah of using, as a possible approach to the Theorem of Feit-Thompson on the solvability of finite groups of odd order, the iterations of the transformation which replaces a representation of a finite ... More
Banalytic spaces and characterization of Polish groupsJan 30 2019A topological space is defined to be banalytic (resp. analytic) if it is the image of a Polish space under a Borel (resp. continuous) map. A regular topological space is analytic if and only if it is banalytic and cosmic. Each (regular) banalytic space ... More
On the spread of topological groups containing subsets of the Sorgenfrey lineJan 30 2019We prove that any topological group $G$ containing a subspace $X$ of the Sorgenfrey line has spread $s(G)\ge s(X\times X)$. Under OCA, each topological group containing an uncountable subspace of the Sorgenfrey line has uncountable spread. This implies ... More
2- and 3-Covariant Equiangular Tight FramesJan 29 2019Equiangular tight frames (ETFs) are configurations of vectors which are optimally geometrically spread apart and provide resolutions of the identity. Many known constructions of ETFs are group covariant, meaning they result from the action of a group ... More
Jones representations of Thompson's group $F$ arising from Temperley-Lieb-Jones algebrasJan 29 2019Following a procedure due to V. Jones, using suitably normalized elements in a Temperley-Lieb-Jones (planar) algebra we introduce a 3-parametric family of unitary representations of the Thompson's group $F$ equipped with canonical (vacuum) vectors and ... More
Attractors of the Einstein-Klein Gordon systemJan 29 2019It is shown that negative Einstein metrics are attractors of the Einstein-Klein-Gordon system. As an essential part of the proof we upgrade a technique that uses the continuity equation complementary to $L^2$-estimates to control massive matter fields. ... More
A note on growth of hyperbolic groupsJan 29 2019The following short note provides an alternative proof of a result of Coornaert: namely, that given a non-elementary word-hyperbolic group $G$ with a finite generating set $X$, there exist constants $\lambda,D > 1$ such that \[ D^{-1}\lambda^n \leq |B_{G,X}(n)| ... More
A note on growth of hyperbolic groupsJan 29 2019Feb 14 2019The following short note provides an alternative proof of a result of Coornaert: namely, that given a non-elementary word-hyperbolic group $G$ with a finite generating set $X$, there exist constants $\lambda,D > 1$ such that \[ D^{-1}\lambda^n \leq |B_{G,X}(n)| ... More
On conjugacy of stabilizers of reductive group actionsJan 29 2019It is shown that the main result of N. R. Wallach, Principal orbit type theorems for reductive algebraic group actions and the Kempf--Ness Theorem, arXiv:1811.07195v1 (17 Nov 2018) is a special case of a more general statement, which can be deduced, using ... More
A note on cellular automataJan 29 2019For an arbitrary group $G$ and arbitrary set $A$, we define a monoid structure on the set of all uniformly continuous functions $A^G\to A$ and then we show that it is naturally isomorphic to the monoid of cellular automata $\mathrm{CA}(G, A)$. This gives ... More