Related papers: Necessary and sufficient conditions for McShane's …

In this paper we develop in detail the geometric constructions that lead to many uniqueness results for the determination of polyhedral sets, typically scatterers, by a finite minimal number of measurements. We highlight how unique…

For a given finite subset $S$ of a compact Riemannian manifold $(M,g)$ whose Schouten curvature tensor belongs to a given cone, we establish a necessary and sufficient condition for the existence and uniqueness of a conformal metric on $M…

In his seminal paper on complex reflection arrangements, Bessis introduces a Garside structure for the braid group of a well-generated irreducible complex reflection group. Using this Garside structure, he establishes a strong connection…

In this paper a geometric characterization of the unique geodesics in Thompson's metric spaces is presented. This characterization is used to prove a variety of other geometric results. Firstly, it will be shown that there exists a unique…

We describe a class $\mathcal{C}$ of punctured torus bundles such that, for each $M \in \mathcal{C}$, all but finitely many Dehn fillings on $M$ are virtually Haken. We show that $\mathcal{C}$ contains infinitely many commensurability…

We examine the generic local and global rigidity of various graphs in R^d. Bruce Hendrickson showed that some necessary conditions for generic global rigidity are (d+1)-connectedness and generic redundant rigidity and hypothesized that they…

Suppose $G$ is finitely generated group and $\mathcal{C}(G)$ consists of all $\rho:G\to\operatorname{PGL}(n+1,\mathbb{R})$ for which there exists a properly convex set in $\mathbb{R}\mathbb{P}^n$ that is preserved by $\rho(G)$. Then the…

We reformulate and extend the geometric method for proving Kazhdan property T developed by Dymara and Januszkiewicz and used by Ershov and Jaikin. The main result says that a group G, generated by finite subgroups G_i, has property T if the…

We construct polynomial conformal invariants, the vanishing of which is necessary and sufficient for an $n$-dimensional suitably generic (pseudo-)Riemannian manifold to be conformal to an Einstein manifold. We also construct invariants…

We find upper and lower bounds of the multiplicities of irreducible admissible representations $\pi$ of a semisimple Lie group $G$ occurring in the induced representations $Ind_H^G\tau$ from irreducible representations $\tau$ of a closed…

Let $G$ be a reductive affine algebraic group, and let $X$ be an affine algebraic $G$-variety. We establish a (poly)stability criterion for points $x\in X$ in terms of intrinsically defined closed subgroups $H_{x}$ of $G$, and relate it…

The goal of this paper is to establish fundamental properties of the Hochschild, topological Hochschild, and topological cyclic homologies of commutative, Noetherian rings, which are assumed only to be F-finite in the majority of our…

We state conditions for which a definable local homomorphism between two locally definable groups $\mathcal{G}$, $\mathcal{G^{\prime}}$ can be uniquely extended when $\mathcal{G}$ is simply connected (Theorem 2.1). As an application of this…

For every finite quasisimple group of Lie type $G$, every irreducible character $\chi$ of $G$, and every element $g$ of $G$, we give an exponential upper bound for the character ratio $|\chi(g)|/\chi(1)$ with exponent linear in $\log_{|G|}…

Any endomorphism of a finitely generated free group naturally descends to an injective endomorphism of its stable quotient. In this paper, we prove a geometric incarnation of this phenomenon: namely, that every expanding irreducible train…

The main result of this paper gives a topological property satisfied by any homeomorphism of the annulus $\mathbb{A}=\mathbb{S}^1 \times [-1,1]$ isotopic to the identity and with at most one fixed point. This generalizes the classical…

A group $G$ is said to be periodic if for any $g\in G$ there exists a positive integer $n$ with $g^n=id$. We prove that a finitely generated periodic group of homeomorphisms on the 2-torus that preserves a measure $\mu$ is finite. Moreover…

We discuss phases of gauge theories in the holographic context, and formulate a criterion for the existence of a Higgs phase, where the gauge redundancy is "spontaneously broken", in purely bulk language. This condition, the existence of a…

Let $k$ be an algebraically closed field of characteristic 0, $Y=k^{r}\times {(k^{\times})}^{s}$ and let $G$ be an algebraic torus acting diagonally on the ring of differential operators $\cD (Y)^G$. We give necessary and sufficient…

In this paper, we compute the {\Sigma}^n(G) and {\Omega}^n(G) invariants when 1 \rightarrow H \rightarrow G \rightarrow K \rightarrow 1 is a short exact sequence of finitely generated groups with K finite. We also give sufficient conditions…