Exact 2-point function in Hermitian matrix model

J. Harer and D. Zagier have found a strikingly simple generating function for exact (all-genera) 1-point correlators in the Gaussian Hermitian matrix model. In this paper we generalize their result to 2-point correlators, using Toda integrability of the model. Remarkably, this exact 2-point correlation function turns out to be an elementary function - arctangent. Relation to the standard 2-point resolvents is pointed out. Some attempts of generalization to 3-point and higher functions are described.Comment: 31 pages, 1 figur

Language teaching in 3D virtual worlds with machinima: Reflecting on an online machinima teacher training course

This article is based on findings arising from a large, two-year EU project entitled “Creating Machinima to Enhance Online Language Learning and Teaching” (CAMELOT), which was the first to investigate the potential of machinima, a form of virtual filmmaking that uses screen captures to record activity in immersive 3D environments, for language teaching. The article examines interaction in two particular phases of the project: facilitator-novice teacher interaction in an online teacher training course which took place in Second Life and teachers' field-testing of machinima which arose from it. Examining qualitative data from interviews and screen recordings following two iterations of a 6-week online teacher training course which was designed to train novice teachers how to produce machinima and the evaluation of the field-testing, the article highlights the pitfalls teachers encountered and reinforces the argument that creating opportunities for pedagogical purposes in virtual worlds implies that teachers need to change their perspectives to take advantage of the affordances offered