We present a notion of convergence for sequences of finite graphs {Gn} that can be seen as a generalization of the Benjamini-Schramm convergence notion for bounded degree graphs, regarding the distribution of r-neighbourhoods of the vertices, and the left-convergence notion for dense graphs, regarding, given any finite graph F , the limit of the probabilities that a random map from V (F ) to V ...

The canonical trace on the reduced C∗-algebra of a discrete group gives rise to a homomorphism from the K-theory of this C∗-algebra to the real numbers. This paper addresses the range of this homomorphism. For torsion free groups, the Baum-Connes conjecture and Atiyah’s L-index theorem implies that the range consists of the integers. If the group is not torsion free, Baum and Connes conjecture ...

Given two graphs G = (VG, EG) and H = (VH , EH), a homomorphism from G to H is a function f : VG → VH such that for every uv ∈ EG, f(u)f(v) ∈ EH . A homomorphism from G to H is referred to as an H-colouring of G and the vertices of H are regarded as colours. The graph H is called the target of the homomorphism. These definitions extend to directed graphs by requiring that the mapping must prese...

We prove a conjecture of Medvedev and Scanlon [MS14] in the case of regular morphisms of semiabelian varieties. That is, if G is a semiabelian variety defined over an algebraically closed field K of characteristic 0, and φ : G → G is a dominant regular self-map of G which is not necessarily a group homomorphism, we prove that one of the following holds: either there exists a non-constant ration...

We consider four different models of process interactions that unify and generalise models introduced and studied by Angluin et al. [AAD04] and models introduced and studied by Mazurkiewicz [Maz04a,Maz04b]. We encode these models by labelled (hyper)graphs and relabelling rules on this labelled (hyper)graphs called negotiations. Then for these models, we give complete characterisations of labell...

A connected reductive algebraic group G is said to be an l-adic algebraic monodromy group for ΓQ if there is a continuous homomorphism Gal(Q/Q)→ G(Ql) with Zariski-dense image. In this paper, we give a classification of connected l-adic algebraic monodromy groups for Gal(Q/Q), in particular producing the first such examples for SLn,Sp2n,Spinn and E sc 6 . To do this, we start with a mod-l repre...

‎let $m$ be a non-zero finitely generated module over a commutative noetherian local ring $(r,mathfrak{m})$ with $dim_r(m)=t$‎. ‎let $i$ be an ideal of $r$ with $grade(i,m)=c$‎. ‎in this article we will investigate several natural homomorphisms of local cohomology modules‎. ‎the main purpose of this article is to investigate when the natural homomorphisms $gamma‎: ‎tor^{r}_c(k,h^c_i(m))to kotim...