Shintani Cocycles on \GL_{n}

The aim of this paper is to define an n-1-cocycle $\sigma$ on \GL_{n}(\Q) with values in a certain space \hD of distributions on \A_f^{n}\setminus\{0\}. Here \A_f denotes the ring of finite ad\`{e}les of \Q, and the distributions take values in the Laurent series \C((z_{1},...,z_{n})). This cocycle can be used to evaluate special values of Artin L-functions on number fields at negative integers. The construction generalizes that of Solomon in the case n=2.Comment: 14 pages. To appear in LMS Bulleti

Construction of eigenvarieties in small cohomological dimensions for semi-simple, simply connected groups

We study low order terms of Emerton's spectral sequence for simply connected, simple groups. As a result, for real rank 1 groups, we show that Emerton's method for constructing eigenvarieties is successful in cohomological dimension 1. For real rank 2 groups, we show that a slight modification of Emerton's method allows one to construct eigenvarieties in cohomological dimension 2

Nonperturbative Techniques for QED Bound States

Advantages of using a low-energy effective theory to study bound state properties are briefly discussed, and a nonperturbative implementation of such an effective theory is described within the context of nonrelativistic quantum mechanics. The hydrogen atom, in the approximation of a structureless, infinite-mass nucleus, but with the leading relativistic and radiative corrections included, is used to demonstrate the construction and solution of the effective theory. The resulting Hamiltonian incorporates a finite ultraviolet cutoff and can be solved nonperturbatively. An appendix lists explicit formulae for the various matrix elements necessary to diagonalize the Hamiltonian using gaussian basis sets.Comment: 11 pages. Talk presented at the MRST conference, U. of Rochester, 8-9 May 2000, to appear in the proceeding

Teaching te reo Māori as a second language in primary schools: two case studies.

The provision of second language education in New Zealand primary schools has been, until recently, a rare addition to programmes. Its wider implementation in New Zealand primary schools has always been limited by low numbers of fluent bilingual teachers, and a perception that in a predominantly English speaking country such as New Zealand there is no need to teach additional languages in primary schools. The New Zealand Curriculum (Ministry of Education, 2007) provides the first opportunity to formally include second language education in primary schools, and to establish the learning of second languages as a worthwhile pursuit in New Zealand. However, the success of such a policy change will depend on the ability of the Ministry of Education and course providers to upskill teachers in their ability to speak additional languages and teach them. This article reports on the outcomes of a Ministry-funded project designed to strengthen the second language teaching approaches of upper primary school teachers who teach te reo Maori. It provides case studies of two of the teachers who completed this course, and finds that while there are clear benefits to be derived from such teacher professional development courses, these courses need to focus on long-term objectives and be channelled to those teachers and students who stand to benefit the most from professional development courses