Langlands duality for finite-dimensional representations of quantum affine algebras

We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of q-alg/9708006 and 0809.4453. We prove this duality for the Kirillov-Reshetikhin modules and their irreducible tensor products. In the course of the proof we introduce and construct "interpolating (q,t)-characters" depending on two parameters which interpolate between the q-characters of a quantum affine algebra and its Langlands dual.Comment: 40 pages; several results and comments added. Accepted for publication in Letters in Mathematical Physic

Neutrino production coherence and oscillation experiments

Neutrino oscillations are only observable when the neutrino production, propagation and detection coherence conditions are satisfied. In this paper we consider in detail neutrino production coherence, taking \pi\to \mu \nu \ decay as an example. We compare the oscillation probabilities obtained in two different ways: (1) coherent summation of the amplitudes of neutrino production at different points along the trajectory of the parent pion; (2) averaging of the standard oscillation probability over the neutrino production coordinate in the source. We demonstrate that the results of these two different approaches exactly coincide, provided that the parent pion is considered as pointlike and the detection process is perfectly localized. In this case the standard averaging of the oscillation probability over the finite spatial extensions of the neutrino source (and detector) properly takes possible decoherence effects into account. We analyze the reason for this equivalence of the two approaches and demonstrate that for pion wave packets of finite width \sigma_{x\pi} the equivalence is broken. The leading order correction to the oscillation probability due to \sigma_{x\pi}\ne 0 is shown to be \sim [v_g/(v_g-v_\pi)]\sigma_{x\pi}/l_{osc}, where v_g and v_\pi \ are the group velocities of the neutrino and pion wave packets, and l_{osc} is the neutrino oscillation length.Comment: LaTeX, 40 pages, 4 figures. v2: minor typos correcte

Superisolated Surface Singularities

In this survey, we review part of the theory of superisolated surface singularities (SIS) and its applications including some new and recent developments. The class of SIS singularities is, in some sense, the simplest class of germs of normal surface singularities. Namely, their tangent cones are reduced curves and the geometry and topology of the SIS singularities can be deduced from them. Thus this class \emph{contains}, in a canonical way, all the complex projective plane curve theory, which gives a series of nice examples and counterexamples. They were introduced by I. Luengo to show the non-smoothness of the $\mu$-constant stratum and have been used to answer negatively some other interesting open questions. We review them and the new results on normal surface singularities whose link are rational homology spheres. We also discuss some positive results which have been proved for SIS singularities.Comment: Survey article for the Proceedings of the Conference "Singularities and Computer Algebra" on Occasion of Gert-Martin Greuel's 60th Birthday, LMS Lecture Notes (to appear

How effective are conditional cash transfers? Evidence from Colombia

Conditional cash transfer (CCT) programmes are becoming an extremely popular tool for improving the education and health outcomes of poor children in developing countries. An incomplete list of countries in which they are being implemented under the support of the World Bank and other international financial institutions includes Mexico, Honduras, Nicaragua, Brazil, Turkey and Mozambique. While the implementation details vary from country to country, many are modelled on the Mexican PROGRESA. In a typical CCT, mothers from poor backgrounds receive cash conditional on their promoting certain activities on behalf of their children. For their youngest children - usually those below the age of 6 - the conditionality involves visits to preventive healthcare centres in which their growth is monitored. School attendance is the most common stipulation for receipt of cash transfers for older children - usually those between 7 and 17 years old. This targeting of health and education of children is at the essence of the long-term poverty alleviation objective of CCT programmes. Such transfer programmes are also aimed at the short-term reduction of poverty, through the provision of immediate funds to indigent households. In this Briefing Note, we will focus on the programme Familias en Acción (FA), the CCT implemented by the Colombian government from 2001/02. In particular, we will provide estimates of how the programme has influenced key welfare indicators such as school attendance, child nutrition and health status, as well as household consumption. In this respect, we will update the preliminary results that were reported in Attanasio et al. (2003 and 2004)