Related papers: Random triangular groups at density 1/3

This paper gives a free entropy theoretic perspective on amenable absorption results for free products of tracial von Neumann algebras. In particular, we give the first free entropy proof of Popa's famous result that the generator MASA in a…

It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform stability with respect to the family of unitary operators on…

The p-variate gamma distribution in the sense of Krishnamoorthy and Parthasarathy exists for all positive integer degrees of freedom d and at least for all real values d > p-2, p > 1. For special structures of the "associated" covariance…

Recently there has been much interest in studying random graph analogues of well known classical results in extremal graph theory. Here we follow this trend and investigate the structure of triangle-free subgraphs of $G(n,p)$ with high…

If a group $\Gamma$ acts geometrically on a CAT(0) space $X$ without 3-flats, then either $X$ contains a $\Gamma$-periodic geodesic which does not bound a flat half-plane, or else $X$ is a rank 2 Riemannian symmetric space, a 2-dimensional…

Let a and b be non-zero rational numbers that are multiplicatively independent. We study the natural density of the set of primes p for which the subgroup of the multiplicative group of the finite field with p elements generated by (a\mod…

Let $\Gamma$ be a distance-regular graph with classical parameters $(D, b, \alpha, \beta)$ satisfying $b\geq 2$ and $D\geq 3$. Let $r=1+b+b^2+\cdots+b^{D-1}$. In 1999, K. Metsch showed that there exists a positive constant $C(\alpha,b)$…

Let $\{Z_t, t\geq 0\}$ be a strictly stable process on $\R$ with index $\alpha\in (0,2]$. We prove that for every $p > \alpha$, there exists $\gamma = \gamma (\alpha, p)$ and $\k = \k (\alpha, p)\in (0, +\infty)$ such that…

A group G is said to have the Magnus property if the following holds: whenever two elements x,y have the same normal closure, then x is conjugate to y or its inverse. We prove: Let p be an odd prime, and let G,H be residually finite-p…

In the random hypergraph H=H(n,p;3) each possible triple appears independently with probability p. A loose Hamilton cycle can be described as a sequence of edges {x_i,y_i,x_{i+1}\} for i=1,2,...,n/2. We prove that there exists an absolute…

Fix $c\in (0,1)$ and let $\Gamma$ be a $\lfloor c n\rfloor$-regular digraph on $n$ vertices drawn uniformly at random. We prove that when $n$ is large, the (non-symmetric) adjacency matrix $M$ of $\Gamma$ is invertible with high…

Suppose that $\Gamma=(V,E)$ is a graph with vertices $V$, edges $E$, a free group action on the vertices $\mathbb{Z}^d \curvearrowright V$ with finitely many orbits, and a linear operator $D$ on the Hilbert space $l^2(V)$ such that $D$…

Given a unital $C(X)$-algebra $A$ discrete group $\Gamma$ and an action $\alpha: \Gamma\to \text{aut}(A)$ which leaves $C(X)$ invariant and such that $C(X)\rtimes_{\alpha,r} \Gamma$ is simple, and a $2$-cocycle $\omega$, we obtain a…

Let $\Gamma$ be a discrete group with property $(T)$ of Kazhdan. We prove that any Riemannian isometric action of $\Gamma$ on a compact manifold $X$ is locally rigid. We also prove a more general foliated version of this result. The…

Type B 3-fold supersymmetry is a necessary and sufficient condition for a quantum Hamiltonian to admit three linearly independent local solutions in closed form. We show that any such a system is invariant under GL(3,C) homogeneous linear…

Let R be a finitely generated commutative ring with 1, let A be an indecomposable 2-spherical generalized Cartan matrix of size at least 2 and M=M(A) the largest absolute value of a non-diagonal entry of A. We prove that there exists an…

We show that for any claw-free graph $G$ and any graph $H$, $\gamma(G\square H)\geq \frac{2}{3}\gamma(G)\gamma(H)$, where $\gamma(G)$ is the domination number of $G$.

Let $\Gamma$ be a discrete group. Following Linnell and Schick one can define a continuous ring $c(\Gamma)$ associated with $\Gamma$. They proved that if the Atiyah Conjecture holds for a torsion-free group $\Gamma$, then $c(\Gamma)$ is a…

This is a survey of two papers joint with A. Borisov and a paper joint with I. Spakulova. It is based on my lectures at the conference "Groups St. Andrews 2009", Bath (August 2009). We prove that almost all 1-related groups with at least 3…

We prove a variation of Thompson's Theorem. Namely, if the first column of the character table of a finite group $G$ contains only two distinct values not divisible by a given prime number $p>3$, then $O^{pp'pp'}(G)=1$. This is done by…