相关论文: Approximating L^2-signatures by their compact anal…

We present, in explicit matrix representation and a modernity befitting the community, the classification of the finite discrete subgroups of G_2 and compute the McKay quivers arising therefrom. Of physical interest are the classes of N=1…

Let $G$ be a finite group. The intersection graph of $G$ is a graph whose vertex set is the set of all proper non-trivial subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $H\cap K \neq \{e\}$, where $e$ is…

We introduce the notion of an \emph{$n$-dimensional mixed dihedral group}, a general class of groups for which we give a graph theoretic characterisation. In particular, if $H$ is an $n$-dimensional mixed dihedral group then the we…

Let $k\geq 2$ and $n\geq 3(k-1)$. Let $\mathcal{F}$ and $\mathcal{G}$ be families of $k$-element subsets of an $n$-element set. Suppose that $|F\cap G|\geq 2$ for all $F\in\mathcal{F}$ and $G\in\mathcal{G}$. We show that…

Let $G$ be a connected and simply connected semisimple algebraic group over $\Bbb Q$ and let $\Gamma\subset G(\Bbb Q)$ be an arithmetic subgroup. Let $K_\infty\subset G(\Bbb R)$ be a maximal compact subgroup and let $d$ be the dimension of…

We consider two $S$-dual hyperspherical varieties of the group $G_2 \times \text{SL}(2)$: an equivariant slice for $G_2$, and the symplectic representation of $G_2 \times \text{SL}_2$ in the odd part of the basic classical Lie superalgebra…

We classify all the $2$-arc-transitive strongly regular graphs, and use this classification to study the family of finite $(G,3)$-geodesic-transitive graphs of girth $4$ or $5$ for some group $G$ of automorphisms. For this application we…

We study discrete group actions on coarse Poincare duality spaces, e.g. acyclic simplicial complexes which admit free cocompact group actions by Poincare duality groups. When G is an (n-1) dimensional duality group and X is a coarse…

Let $(M,g)$ an open and oriented riemannian manifold. The aim of this paper is to study some properties of the two following sequences of $L^2$ cohomology groups: $H^i_{2,m\rightarrow M}(M,g)$ defined as the image…

Let G_2 be the exceptional Lie group of automorphisms of the complex Cayley algebra and C be a generic, smooth, connected, projective curve over $\mathbb{C}$ of genus at least 2. For a complex Lie group G, let H^0(M(G),L^k) be the space of…

We conjecture that if $G$ is a simple compact Lie group with trivial center, then every $d$-variable non-constant word map with coefficients in $G$ defines a non-constant function on $G^d$. We prove the conjecture for $A_r$, $B_r$, $E_6$,…

We prove an analogue statement to an estimate by De Lellis-M\"uller in $\mathbb{R}^3$ on the standard Minkowski lightcone. More precisely, we show that under some additional assumptions, any spacelike cross section of the standard lightcone…

Given a Lie group G, one constructs a principal G-bundle on a manifold X by taking a cover U of X, specifying a transition cocycle on the cover, and descending the trivialized bundle along the cover. We demonstrate the existence of an…

We study geodesics of the form $\gamma(t)=\pi(\exp(tX)\exp(tY))$, $X,Y\in \fr{g}=\operatorname{Lie}(G)$, in homogeneous spaces $G/K$, where $\pi:G\rightarrow G/K$ is the natural projection. These curves naturally generalise homogeneous…

We show that local complete intersection subvarieties of smooth projective varieties, which have partially ample normal bundle, possess the G2-property. This generalizes results of Hartshorne and B\u{a}descu-Schneider.

Suppose that $\tilde{G}$ is a connected reductive group defined over a field $k$, and $\Gamma$ is a finite group acting via $k$-automorphisms of $\tilde{G}$ satisfying a certain quasi-semisimplicity condition. Then the connected part of the…

We study the closed group of homeomorphisms of the boundary of real hyperbolic space generated by a cocompact Kleinian group $G_1$ and a quasiconformal conjugate $h^{-1}G_2 h$ of a cocompact group $G_2$. We show that if the conjugacy $h$ is…

The normal covering number $\gamma(G)$ of a finite, non-cyclic group $G$ is the least number of proper subgroups such that each element of $G$ lies in some conjugate of one of these subgroups. We prove that there is a positive constant $c$…

We prove that the action of any non-trivial normal subgroup of the mapping class group of a surface of genus $g\geqslant 2$ is almost minimal on the character variety $X(\pi_1\Sigma_g,{\rm SU}_2)$: the orbit of almost every point is dense.

Let $G$ be a finite group and let $(P_i)_{i=1}^n$ be Sylow subgroups for distinct primes $p_1,\ldots,p_n$. We conjecture that there exists $x \in G$ such that $P_i \cap P_i^x$ is inclusion-minimal in $\{ P_i \cap P_i^g : g \in G\}$ for all…