Every point in Teichmüller space is a hyperbolic metric on a given Riemann surface, therefore, a Weil-Petersson geodesic in Teichmüller space can be viewed as a 3-manifold. We investigate the sectional curvatures of this 3-manifold, with a natural metric. We obtain explicit formulas for the curvature tensors of this metric, and show that the “average”s of them are zero, and hence the geometry o...

We say a lattice Λ is rigid if it its isometry group acts irreducibly on its ambient Euclidean space. We say Λ is Mordell-Weil if there exists an abelian variety A over a number field K such that A(K)/A(K)tor, regarded as a lattice by means of its height pairing, contains at least one copy of Λ. We prove that every rigid lattice is Mordell-Weil. In particular, we show that the Leech lattice can...

For each natural number N , let R(N) denote the number of representations of N as a sum of two primes. Hardy and Littlewood proposed a plausible asymptotic formula for R(2N) and showed, under the assumption of the Riemann Hypothesis for Dirichlet Lfunctions, that the formula holds “on average” in a certain sense. From this they deduced (under ERH) that all but O (x1/2+ ) of the even natural num...

This paper introduces a general method for relating characteristic classes to singularities of a bundle map. The method is based on the notion of geometric atomicity. This is a property of bundle maps α : E → F which universally guarantees the existence of certain limits arising in the theory of singular connections. Under this hypothesis, each characteristic form 8 of E or F satisfies an equat...

In this paper it is proved that the volumes of the moduli spaces of polarized Calabi-Yau manifolds with respect to Weil-Petersson metrics are rational numbers. Mumford introduce the notion of a good metric on vector bundle over a quasi-projective variety in [10]. He proved that the Chern forms of good metrics define classes of cohomology with integer coefficients on the compactified quasi-proje...

On June 23, 1993, Andrew Wiles unveiled his strategy for proving the Shimura-Taniyama-Weil conjecture for semistable elliptic curves defined over the field Q of rational numbers. Thanks to the work of Gerhard Frey, JeanPierre Serre and Kenneth Ribet, this was known to imply Fermat’s Last Theorem. Six years later, Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor have finally ann...

We extend a result of Spearman which provides a sufficient condition for elliptic curves of the form y2 = x3 − px, with p a prime, to have Mordell-Weil rank 2. As in Spearman’s work, the condition given here involves the existence of integer points on these curves.

Given a surface of higher genus, we will look at the Weil-Petersson completion of the Teichmüller space of the surface, and will study the isometric action of the mapping class group on it. The main observation is that the geometric characteristics of the setting bear strong similarities to the ones in semi-simple Lie group actions on noncompact symmetric spaces.

MATHIEU DECLERCK and JUDIT KORMOS Bilingualism: Language and Cognition / Volume 15 / Issue 04 / October 2012, pp 782 ­ 796 DOI: 10.1017/S1366728911000629, Published online: 04 January 2012 Link to this article: http://journals.cambridge.org/abstract_S1366728911000629 How to cite this article: MATHIEU DECLERCK and JUDIT KORMOS (2012). The effect of dual task demands and proficiency on second lan...

To provide an overview of leptospirosis in Queensland, the World Health Organization/Food and Agriculture Organization Collaborating Centre for Reference and Research on Leptospirosis undertook a study of notifications of the disease from 1985 to 1996. The review encompassed information drawn from notifications to Queensland Health and questionnaires sent to doctors. Notifications were highest ...