The Fate of SUSY Flat Directions and their Role in Reheating

We consider the role of supersymmetric flat directions in reheating the Universe after inflation. One or more flat directions can develop large vevs during inflation, which can potentially affect reheating by slowing down scattering processes among inflaton decay products or by coming to dominate the energy density of the Universe. Both effects occur only if flat directions are sufficiently long-lived. The computation of their perturbative decay rate, and a simple estimate of their nonperturbative decay have led to the conclusion that this is indeed the case. In contrast, we show that flat directions can decay quickly through nonperturbative channels in realistic models. The mass matrix for MSSM excitations around flat directions has nondiagonal entries, which vary with the phase of the (complex) flat directions. The quasi-periodic motion of the flat directions results in a strong parametric resonance, leading to the rapid depletion of the flat direction within its first few rotations. This may preclude any significant role for the flat directions in reheating the Universe after inflation in models in which the inflaton decays perturbatively.Comment: 30 pages, 6 .ps figures. Final published versio

About Gordan's algorithm for binary forms

In this paper, we present a modern version of Gordan's algorithm on binary forms. Symbolic method is reinterpreted in terms of $\mathsf{SL}_2(\mathbb{C})$--equivariant homomorphisms defined upon Cayley operator and polarization operator. A graphical approach is thus developed to obtain Gordan's ideal, a central key to get covariant bases of binary forms. To illustrate the power of this method, we obtain for the first time a minimal covariant basis for \Sn{6}\oplus\Sn{4} and \Sn{6}\oplus\Sn{4}\oplus \Sn{2}

Working Memory in Writing: Empirical Evidence From the Dual-Task Technique

The dual-task paradigm recently played a major role in understanding the role of working memory in writing. By reviewing recent findings in this field of research, this article highlights how the use of the dual-task technique allowed studying processing and short-term storage functions of working memory involved in writing. With respect to processing functions of working memory (namely, attentional and executive functions), studies investigated resources allocation, step-by-step management and parallel coordination of the writing processes. With respect to short-term storage in working memory, experiments mainly attempted to test Kellogg's (1996) proposals on the relationship between the writing processes and the slave systems of working memory. It is concluded that the dual-task technique revealed fruitful in understanding the relationship between writing and working memory

Prospective Elementary School Teachers’ Ways of Making Sense of Mathematical Problem Posing

The study tackled prospective teachers’ sense-making of mathematical problem posing and the impact of posing different contextual problems on their learning. Focus was on the generation of new problems and reformulation of given problems. Participants were 40 prospective elementary teachers. The findings provide insights into possible ways these teachers could make sense of problem posing of contextual mathematical problems and the learning afforded by posing diverse problems. Highlighted are five perspectives and nine categories of problem posing tasks to support development of proficiency in problem-posing knowledge for teaching