Let G1 = (V1, E1) and G2 = (V2, E2) be two edge-coloured graphs (without multiple edges or loops). A homomorphism is a mapping Ï† : V1 7âˆ’â†’ V2 for which, for every pair of adjacent vertices u and v ofâ€¦ (More)

We present a new approach and improvements to the recent results of Gabai, Meyerhoff and Milley concerning tubes and short geodesics in hyperbolic 3-manifolds. We establish the following two facts:â€¦ (More)

A cylinder of radius r in hyperbolic space is the closed set of points within distance r of a given geodesic. We define the density of a packing of cylinders of radius r in n dimensions and proveâ€¦ (More)

We find necessary conditions for a digraph H to admit a homomorphism from every oriented planar graph of girth at least n, and use these to prove the existence of a planar graph of girth 6 andâ€¦ (More)

We discuss our recent solution to Siegelâ€™s 1943 problem concerning the smallest co-volume lattices of hyperbolic 3-space. Over the last few decades the theory of Kleinian groupsâ€”discrete groups ofâ€¦ (More)

the 21-Century Gastarbeiter Jessamyn Blau Sciences-Po Paris To Western observers, burning cars have become the symbol of the European failure to integrate what tends to be a predominantly Muslimâ€¦ (More)