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

The Impact of Podcasts in Education

This article will be covering the impact of podcasts in education. Multimedia has been apart of education and classroom environments for over 40 years. With the recent rise in podcast creators and consumers, it is natural that this aspect of media would also spread into education. The use of podcasts in education is controversial, one side argues that podcasts have no place in education and are merely a distraction. The same was said about PowerPoint presentations and in-class videos at one point of time, however multimedia in the classroom has become the new norm. This article will provide the argument of how podcasts are beneficial in education in multiple ways. Specifically, podcasts can be used as a teaching resource by teachers, a learning resource by students, and a preparation tool for teacher candidates

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

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

First-Year Library Mentorship Opportunities

The first-year experience at any university library sets the foundation for the future relationship between the new faculty member and the library as a whole. Not only is the librarian being acculturated to the organization, but he or she must decide if the library and university will provide a supportive environment for his or her career goals. In this probationary process, the tenured librarians evaluate their tenure-track colleagues’ professional progression and merit. Many libraries institute a formal first-year mentoring program in order to facilitate the immersion of new faculty members into the organizational culture of the library and university. There are excellent examples of flourishing mentorship programs in libraries, but one can also find examples of informal mentoring that aids in the success of tenure-track faculty. This article discusses the benefits and drawbacks of various forms of library mentorship and how one can make the most of being mentored in diverse university settings

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