Poorly connected groups

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\'ar if and only if it is virtually free. We then prove a gap theorem for connectivity of finitely presented groups, and prove that there is no comparable theorem for all finitely generated groups. Finally, we formulate a connectivity version of the conjecture that every group of type $F$ with no Baumslag-Solitar subgroup is hyperbolic, and prove it for groups with at most quadratic Dehn function.Comment: 14 pages. Changes to v2: Proof of the Theorem 1.2 shortened, Theorem 1.4 added completing the no-gap result outlined in v

Panel on the Maintenance of Life in Uremia

Panel on the Maintenance of Life in Uremia held at the Second Annual Kidney Symposium, Virginia Chapter of the National Kidney Disease Foundation, Richmond, October 16, 1964. Moderated by David M. Hume

Characterizations of Morse quasi-geodesics via superlinear divergence and sublinear contraction

We introduce and begin a systematic study of sublinearly contracting projections. We give two characterizations of Morse quasi-geodesics in an arbitrary geodesic metric space. One is that they are sublinearly contracting; the other is that they have completely superlinear divergence. We give a further characterization of sublinearly contracting projections in terms of projections of geodesic segments.Comment: 24 pages, 5 figures. v2: 22 pages, 5 figures. Correction in proof of Thm 7.1. Proof of Prop 4.2 revised for improved clarity. Other minor changes per referee comments. To appear in Documenta Mathematic

Poincar\'e profiles of groups and spaces

We introduce a spectrum of monotone coarse invariants for metric measure spaces called Poincar\'{e} profiles. The two extremes of this spectrum determine the growth of the space, and the separation profile as defined by Benjamini--Schramm--Tim\'{a}r. In this paper we focus on properties of the Poincar\'{e} profiles of groups with polynomial growth, and of hyperbolic spaces, where we deduce a connection between these profiles and conformal dimension. As applications, we use these invariants to show the non-existence of coarse embeddings in a variety of examples.Comment: 55 pages. To appear in Revista Matem\'atica Iberoamerican

Uma espécie de história da minha vida

Tradução para o português de "Uma espécie de história de minha vida" (A kind of history of my life), ou Carta a um médico (A Letter to a Physician), uma carta escrita por Hume (1711-1776), endereçada em março ou abril de 1734 a um médico não identificado (segundo Norton provavelmente John Arbuthnot ou George Cheyne), na qual Hume pede alguns conselhos para continuar com o seu trabalho filosófico. O título atual é extraído do primeiro parágrafo.A carta foi escrita em 1734, um pouco antes de Hume viajar para Bristol, onde, “forçado a fazer uma rápida incursão em uma vida mais ativa”, conforme relata em sua autobiografia Minha vida, buscou empregar-se no comércio. A importância dessa carta reside no seu caráter autobiográfico e nos comentários que Hume faz sobre seu projeto filosófico. A carta foi publicada originalmente em Life and correspondence of David Hume, John Hill Burton(Ed.), Edinburgh 1846, v. 1, p. 30-39; ela foi reproduzida em The Letters of David Hume. Grey, J. Y. T. (ed.) Oxford: Clarendon Press, 1932, 2v; v.1, n.3, p. 12-18, e pode ser encontrada também em The Cambridge companion to Hume, David Fate Norton, Jacqueline Taylor (ed.) 2 ed. Cambridge University Press, 2009, p. 515-522. Para essa tradução consultamos o texto original conforme apresentado nas duas últimas edições aqui mencionadas

Reclaiming Virtue Ethics for Economics

Virtue ethics is an important strand of moral philosophy which normative economists have largely neglected. It underpins influential critiques of the market (as a domain in which instrumental motivation corrodes virtue) and of economics (as justifying such motivation). We explain and respond to this critique. Using the methods of virtue ethics and with reference to the writings of major economists, we propose an understanding of the ‘telos’ (purpose) of markets as cooperation for mutual benefit, and identify traits that thereby count as virtues for market participants. We conclude that the market need not be seen as a virtue-free zone