42 citations · 103 across the 15 of their papers we have counts for
19 papers
Separation profiles of free products
David Hume
We deduce from a theorem of Dvorak--Norin that the separation and treewidth profiles of graphs are asymptotically equivalent, resolving a question of Huang--Hume--Kelly--Lam. As an…
Asymptotic dimension for covers with controlled growth
David Hume, John M. Mackay, Romain Tessera
We prove various obstructions to the existence of regular maps (or coarse embeddings) between commonly studied spaces. For instance, there is no regular map (or coarse embedding) $…
Thick embeddings of graphs into symmetric spaces via coarse geometry
Benjamin Barrett, David Hume, Larry Guth +1
We prove estimates for the optimal volume of thick embeddings of finite graphs into symmetric spaces, generalising results of Kolmogorov-Barzdin and Gromov-Guth for embeddings into…
Poincaré profiles of Lie groups and a coarse geometric dichotomy
David Hume, John M. Mackay, Romain Tessera
Poincaré profiles are a family of analytically defined coarse invariants, which can be used as obstructions to the existence of coarse embeddings between metric spaces. In this pap…
Dirichlet-Poincaré profiles of graphs and groups
David Hume
We define Poincaré profiles of Dirichlet type for graphs of bounded degree, in analogy with the Poincaré profiles (of Neumann type) defined in [HMT19]. The obvious first definition…
Poorly connected groups
David Hume, John M. Mackay
We investigate groups whose Cayley graphs have poor\-ly connected subgraphs. We prove that a finitely generated group has bounded separation in the sense of Benjamini--Schramm--Tim…