Length spectra and degeneration of flat metrics

In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectrally rigid, that is, when the length vector determines a metric among the class of flat metrics. Secondly, we give an embedding into the space of geodesic currents and use this to get a boundary for the space of flat metrics. The geometric interpretation is that flat metrics degenerate to "mixed structures" on the surface: part flat metric and part measured foliation.Comment: 36 page

Statistical hyperbolicity in groups

In this paper, we introduce a geometric statistic called the "sprawl" of a group with respect to a generating set, based on the average distance in the word metric between pairs of words of equal length. The sprawl quantifies a certain obstruction to hyperbolicity. Group presentations with maximum sprawl (i.e., without this obstruction) are called statistically hyperbolic. We first relate sprawl to curvature and show that nonelementary hyperbolic groups are statistically hyperbolic, then give some results for products, for Diestel-Leader graphs and lamplighter groups. In free abelian groups, the word metrics asymptotically approach norms induced by convex polytopes, causing the study of sprawl to reduce to a problem in convex geometry. We present an algorithm that computes sprawl exactly for any generating set, thus quantifying the failure of various presentations of Z^d to be hyperbolic. This leads to a conjecture about the extreme values, with a connection to the classic Mahler conjecture.Comment: 14 pages, 5 figures. This is split off from the paper "The geometry of spheres in free abelian groups.

Harnessing the power of the 'Massive': an innovative approach to participation, digital citizenship and open learning on-line.

In January 2015, the London School of Economics and Political Science (UK) launched an innovative civic engagement project, which aimed to crowd source the United Kingdom Constitution. One of the key intentions of the project was to leverage and magnify the power of the community and the ‘massive’ in order to empower participants to engage in debate, identify solutions and come to a common agreement about the need for and the content of a UK Constitution. Involving over 1500 participants and generating tens of thousands of on-line interactions that increased as opposed to decreased over the 14 week duration of the ‘course’, Crowd Sourcing the UK Constitution challenged some of the dominant paradigms of Massive Open On-line Learning. We will present the findings arising from a critical evaluation of the project and pose a number of questions that emerged from both our engagement with the project and from the participants themselves centred on enhancing the effectiveness of a pedagogical design to harness the power of the massive, a large community of engaged participants working together in order to solve a problem, effect change or develop capacity

Prospectus, February 10, 2010

UNDERSTANDING THE UNIVERSE: PARKLAND HOSTS THE WORLD OF SCIENCE LECTURE; Rising costs, less help from home hurts kids; Chuck Shepherd’s News of the Weird; \u27Til Death Do Us Part; Save energy, reap rewards?; Americans’ distrust of government has deep roots; Great and nutritional breakfast ideas for students on the go; Under Pressure: lower stress to get higher grades; Suspected culprit in Texas woman’s debilitating disorder: denture cream; Prospectus Pick: Doctor Who; A Super day for the Big Ten too; Forget you, Cupid!https://spark.parkland.edu/prospectus_2010/1003/thumbnail.jp