Related papers: Expanders and box spaces

The Cohn-Umans group-theoretic approach to matrix multiplication suggests embedding matrix multiplication into group algebra multiplication, and bounding $\omega$ in terms of the representation theory of the host group. This framework is…

We study the dual relationship between quantum group convolution maps $L^1(\mathbb{G})\rightarrow L^{\infty}(\mathbb{G})$ and completely bounded multipliers of $\widehat{\mathbb{G}}$. For a large class of locally compact quantum groups…

We prove that all finitely generated fully residually free groups (limit groups) have a sequence of finite dimensional unitary representations that `strongly converge' to the regular representation of the group. The corresponding statement…

First we give a new proof of Goto's theorem for Lie algebras of compact semisimple Lie groups using Coxeter transformations. Namely, every $x$ in $L = \operatorname{Lie}(G)$ can be written as $x =[a, b]$ for some $a$, $b$ in $L$. By using…

We discuss the structure of microcanonical ensembles in inertial and non-inertial frames attached to a confined system of positive energy particles in curved spacetime. Under certain physically reasonable assumptions that ensure the…

Nonabelian simply connected nilpotent Lie groups and not virtually abelian finitely generated groups of polynomial growth do not quasi-isometrically embed into uniformly convex Banach spaces. We quantify this fact by showing that a ball of…

We prove symplectic non-squeezing (in the sense of Gromov) for the cubic nonlinear Schr\"odinger equation on $\R^2$. This is the first symplectic non-squeezing result for a Hamiltonian PDE in infinite volume. As the underlying symplectic…

We give examples of closed, oriented 3-manifolds whose fundamental groups are not isomorphic, but yet have the same sets of finite quotient groups; hence the same profinite completions. We also give examples of compact, oriented 3-manifolds…

We determine the representations of the ``conformal'' group ${\bar{SO}}_0(2, n)$, the restriction of which on the ``Poincar\'e'' subgroup ${\bar{SO}}_0(1, n-1).T_n$ are unitary irreducible. We study their restrictions to the ``De Sitter''…

Given two real numbers, the $L^2$ functions whose Fourier transforms vanish with a certain rapidity near the given numbers are characterised as those that are expressible as the sum of a certain number of generalised finite differences that…

In this paper, we discuss the fixed point property for an infinite family of order-preserving mappings which satisfy the Lipschitzian condition on comparable pairs. The underlying framework of our main results is a metric space of any…

We study systems $(V,T,U_1,U_2)$ consisting of a finite dimensional vector space $V$, a nilpotent $k$-linear operator $T:V\to V$ and two $T$-invariant subspaces $U_1\subset U_2\subset V$. Let $\mathcal S(n)$ be the category of such systems…

We generalize the result of our recent paper on the massless single off-shell scalar box integral to the case of two non-adjacent end points off the light cone. An analytic result in $d=4-2\varepsilon$ dimensions is established in terms of…

We show that some classical results on expander graphs imply growth results on normal subsets in finite simple groups. As one application, it is shown that given a nontrivial normal subset $ A $ of a finite simple group $ G $ of Lie type of…

Philip Hall raised around 1965 the following question which is stated in the Kourovka Notebook: Is there a non-trivial group which is isomorphic with every proper extension of itself by itself? We will decompose the problem into two parts:…

Consider an arithmetic group $\mathbf{G}(O_S)$, where $\mathbf{G}$ is an affine group scheme with connected, simply connected absolutely almost simple generic fiber, defined over the ring of $S$-integers $O_S$ of a number field $K$ with…

We construct an extension of the Poincare group which involves a mixture of internal and space-time supersymmetries. The resulting group is an extension of the superPoincare group with infinitely many generators which carry internal and…

An axis-parallel $d$-dimensional box is a cartesian product $I_1\times I_2\times \dots \times I_b$ where $I_i$ is a closed sub-interval of the real line. For a graph $G = (V,E)$, the $boxicity \ of \ G$, denoted by $\text{box}(G)$, is the…

We consider properties of the box polynomials, a one variable polynomial defined over all integer partitions $\lambda$ whose Young diagrams fit in an $m$ by $n$ box. We show that these polynomials can be expressed by the finite difference…

Let $T$ be a finitely branching rooted tree such that any node has at least two successors. The path space $[T]$ is an ultrametric space: for distinct paths $f,g$ let $d(f,g)= 1/|T_n|$, where $T_n$ denotes the $n$-th level of the tree, and…