Periodic orbits of integrable birational maps on the plane: blending dynamics and algebraic geometry, the Lyness' case

Contingut del Pòster presentat al congrés New Trends in Dynamical Systems

Algebraic decay of velocity fluctuations near a wall

Computer simulations of the dynamics of a colloidal particle suspended in a fluid confined by an interface show that the asymptotic decay of the velocity correlation functions is algebraic. The exponents of the long-time tails depend on the direction of motion of the particle relative to the surface, as well as on the specific nature of the boundary conditions. In particular, we find that for the angular velocity correlation function, the decay in the presence of a slip surface is faster than the one corresponding to a stick one. An intuitive picture is introduced to explain the various long-time tails, and the simulations are compared with theoretical expressions where available.

Wiki-supported collaborative learning in primary education. How a dialogic space is created for thinking together

This paper explores how wikis may be used to support primary education students’ collaborative interaction and how such an interaction process can be characterised. The overall aim of this study is to analyse the collaborative processes of students working together in a wiki environment, in order to see how primary students can actively create a shared context for learning in the wiki. Educational literature has already reported that wikis may support collaborative knowledge-construction processes, but in our study we claim that a dialogic perspective is needed to accomplish this. Students must develop an intersubjective orientation towards each others’ perspectives, to co-construct knowledge about a topic. For this purpose, our project utilised a ‘Thinking Together’ approach to help students develop an intersubjective orientation towards one another and to support the creation of a ‘dialogic space’ to co-construct new understanding in a wiki science project. The students’ asynchronous interaction process in a primary classroom -- which led to the creation of a science text in the wiki -- was analysed and characterised, using a dialogic approach to the study of CSCL practices. Our results illustrate how the Thinking Together approach became embedded within the wiki environment and in the students’ collaborative processes. We argue that a dialogic approach for examining interaction can be used to help design more effective pedagogic approaches related to the use of wikis in education and to equip learners with the competences they need to participate in the global knowledge-construction era.

Creative thinking

Portal web d'intercanvi d'idees creatives, confeccionat en tecnología JEE i Liferay com a gestor de continguts i gestor de portlets.

$E_{1}$-Formality of complex algebraic varieties

Let $X$ be a smooth complex algebraic variety. Morgan showed that the rational homotopy type of $X$ is a formal consequence of the differential graded algebra defined by the first term $E_{1}(X,W)$ of its weight spectral sequence. In the present work, we generalize this result to arbitrary nilpotent complex algebraic varieties (possibly singular and/or non-compact) and to algebraic morphisms between them. In particular, our results generalize the formality theorem of Deligne, Griffiths, Morgan and Sullivan for morphisms of compact Kähler varieties, filling a gap in Morgan"s theory concerning functoriality over the rationals. As an application, we study the Hopf invariant of certain algebraic morphisms using intersection theory.