A better proof of the Goldman-Parker conjecture

The Goldman-Parker Conjecture classifies the complex hyperbolic C-reflection ideal triangle groups up to discreteness. We proved the Goldman-Parker Conjecture in [Ann. of Math. 153 (2001) 533--598] using a rigorous computer-assisted proof. In this paper we give a new and improved proof of the Goldman-Parker Conjecture. While the proof relies on the computer for extensive guidance, the proof itself is traditional.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper35.abs.htm

A note related to the CS decomposition and the BK inequality for discrete determinantal processes

We prove that for a discrete determinantal process the BK inequality occurs for increasing events generated by simple points. We give also some elementary, but nonetheless appealing relationship, between a discrete determinantal process and the well-known CS decomposition.Comment: To appear in Journal of Applied Probabilit

Fresh Water and Smarter Growth: Restoring Healthy Land-water Connections

The paper describes water resources in the United States, discusses the principles of the land-water connection, outlines the current regulatory framework, and explains the impact of climate change. It also introduces the concept of low impact development while providing examples, and highlights how funders are having an impact on sustainable water management. With bibliographical references

Riggs on strong justification

In 'The Weakness of Strong Justification' Wayne Riggs claims that the requirement that justified beliefs be truth conducive (likely to be true) is not always compatible with the requirement that they be epistemically responsible (arrived at in an epistemically responsible manner)1. He supports this claim by criticising Alvin Goldman's view that if a belief is strongly justified, it is also epistemically responsible. In light of this, Riggs recommends that we develop two independent conceptions of justification, one that insists upon the requirement that beliefs be truth conducive and another that insists that they be epistemically responsible. It will then, on his view, be possible to properly evaluate beliefs with regard to each conception of justification. Riggs, however, is mistaken in supposing that the two epistemic requirements are independent. If a belief is responsibly arrived at, it is therefore likely to be true. He is thus also mistaken in supposing that the two epistemic requirements are incompatible. This mistake arises because Riggs assumes that justification is possible or, at least, that it involves standards that are akin to our own. Moreover, once this assumption is made explicit, we can see why a notion of justification that connects epistemic practice with likely truth is significant

Self-similar minimizers of a branched transport functional

We solve here completely an irrigation problem from a Dirac mass to the Lebesgue measure. The functional we consider is a two dimensional analog of a functional previously derived in the study of branched patterns in type-I superconductors. The minimizer we obtain is a self-similar tree.Comment: Indiana University Mathematics Journal, Indiana University Mathematics Journal, In pres

Physical Degrees of Freedom for Gauge Fields and the Issue of Spin

The conflict between the physical degrees of freedom of gauge bosons and the Lorentz group irreps naturally used to describe their couplings to matter fields are illustrated and discussed, and applied to issues of linear and angular momentum.Comment: 10pp., no figures, to appear in PACSpin2011 (Cairns, 20-24 June, 2011) conf. proc. (AIP