Household Allocations and Endogenous Information

This paper tests for the endogeneity of one of the main elements separating different models of intrahousehold allocations, namely the household information set. Based on unusually rich data, I find that split migrant couples in the Nairobi slums invest considerable resources into information acquisition through visits, sibling and child monitoring, budget submissions, and marital search. I also find potentially substantial welfare losses when information acquisition becomes costly, not only through reduced remittances but more importantly as families opt for family migration into the slums. That households invest in information when there are welfare gains complements a large and growing literature that seeks to explain intrahousehold allocations through more complex modes of decision-making.Survey Methods, Household production and Intrahousehold Allocation, Marriage, Family Structure, Migration

On the Regularization of the Kepler Problem

We show that for the Kepler problem the canonical Ligon-Schaaf regularization map can be understood in a straightforward manner as an adaptation of the Moser regularization. In turn this explains the hidden symmetry in a geometric way.Comment: 12 page

Superexpanders from group actions on compact manifolds

It is known that the expanders arising as increasing sequences of level sets of warped cones, as introduced by the second-named author, do not coarsely embed into a Banach space as soon as the corresponding warped cone does not coarsely embed into this Banach space. Combining this with non-embeddability results for warped cones by Nowak and Sawicki, which relate the non-embeddability of a warped cone to a spectral gap property of the underlying action, we provide new examples of expanders that do not coarsely embed into any Banach space with nontrivial type. Moreover, we prove that these expanders are not coarsely equivalent to a Lafforgue expander. In particular, we provide infinitely many coarsely distinct superexpanders that are not Lafforgue expanders. In addition, we prove a quasi-isometric rigidity result for warped cones.Comment: 16 pages, to appear in Geometriae Dedicat

Simple Lie groups without the Approximation Property

For a locally compact group G, let A(G) denote its Fourier algebra, and let M_0A(G) denote the space of completely bounded Fourier multipliers on G. The group G is said to have the Approximation Property (AP) if the constant function 1 can be approximated by a net in A(G) in the weak-* topology on the space M_0A(G). Recently, Lafforgue and de la Salle proved that SL(3,R) does not have the AP, implying the first example of an exact discrete group without it, namely SL(3,Z). In this paper we prove that Sp(2,R) does not have the AP. It follows that all connected simple Lie groups with finite center and real rank greater than or equal to two do not have the AP. This naturally gives rise to many examples of exact discrete groups without the AP.Comment: Version 4, 29 pages. Minor correction

A semidefinite programming hierarchy for packing problems in discrete geometry

Packing problems in discrete geometry can be modeled as finding independent sets in infinite graphs where one is interested in independent sets which are as large as possible. For finite graphs one popular way to compute upper bounds for the maximal size of an independent set is to use Lasserre's semidefinite programming hierarchy. We generalize this approach to infinite graphs. For this we introduce topological packing graphs as an abstraction for infinite graphs coming from packing problems in discrete geometry. We show that our hierarchy converges to the independence number.Comment: (v2) 25 pages, revision based on suggestions by referee, accepted in Mathematical Programming Series B special issue on polynomial optimizatio

A quartet in E : investigating collaborative learning and tutoring as knowledge creation processes

This paper is a short report of a continuing international study that is investigating networked collaborative learning among an advanced community of learners engaged in a master’s programme in e-learning. The study is undertaking empirical work using content analysis (CA), critical event recall (CER) and social network analysis (SNA). The first two methods are employed in the work reported in this paper. We are particularly interested in knowledge creation among the participants as they engage in action research for their master’s work. At the same time, another underlying aim of the main study is to develop methodology, enrich theory and explore the ways in which praxis (theory informed tutoring and learning on the programme) and theory interact as we try to understand the complex processes of tutoring and learning. The paper reports some of the current findings of this work and discusses future prospects

Simple Lie groups without the Approximation Property II

We prove that the universal covering group $\widetilde{\mathrm{Sp}}(2,\mathbb{R})$ of $\mathrm{Sp}(2,\mathbb{R})$ does not have the Approximation Property (AP). Together with the fact that $\mathrm{SL}(3,\mathbb{R})$ does not have the AP, which was proved by Lafforgue and de la Salle, and the fact that $\mathrm{Sp}(2,\mathbb{R})$ does not have the AP, which was proved by the authors of this article, this finishes the description of the AP for connected simple Lie groups. Indeed, it follows that a connected simple Lie group has the AP if and only if its real rank is zero or one. By an adaptation of the methods we use to study the AP, we obtain results on approximation properties for noncommutative $L^p$-spaces associated with lattices in $\widetilde{\mathrm{Sp}}(2,\mathbb{R})$. Combining this with earlier results of Lafforgue and de la Salle and results of the second named author of this article, this gives rise to results on approximation properties of noncommutative $L^p$-spaces associated with lattices in any connected simple Lie group.Comment: Final version. Continuation of the work in 1201.1250 and 1208.593

Using pattern languages to mediate theory–praxis conversations in design for networked learning

Educational design for networked learning is becoming more complex but also more inclusive, with teachers and learners playing more active roles in the design of tasks and of the learning environment. This paper connects emerging research on the use of design patterns and pattern languages with a conception of educational design as a conversation between theory and praxis. We illustrate the argument by drawing on recent empirical research and literature reviews from the field of networked learning

A complete characterization of connected Lie groups with the Approximation Property

We give a complete characterization of connected Lie groups with the Approximation Property for groups (AP). To this end, we introduce a strengthening of property (T), that we call property (T*), which is a natural obstruction to the AP. In order to define property (T*), we first prove that for every locally compact group G, there exists a unique left invariant mean on the space of completely bounded Fourier multipliers of G. A locally compact group G is said to have property (T*) if this mean is a weak* continuous functional. After proving that the groups SL(3,R), Sp(2,R), and the universal covering of Sp(2,R) have property (T*), we address the question which connected Lie groups have the AP. A technical problem that arises when considering this question from the point of view of the AP is that the semisimple part of the global Levi decomposition of a connected Lie group need not be closed. Because of an important permanence property of property (T*), this problem vanishes. It follows that a connected Lie group has the AP if and only if all simple factors in the semisimple part of its Levi decomposition have real rank 0 or 1. Finally, we are able to establish property (T*) for all connected simple higher rank Lie groups with finite center.Comment: 18 pages, more details were included in Sections 5 and 6 and some additional minor changes were mad