A Ghost at ω1\omega_1

In the final chain of the countable powerset functor, we show that the set at index $\omega_1$, regarded as a transition system, is not strongly extensional because it contains a "ghost" element that has no successor even though its component at each successor index is inhabited. The method, adapted from a construction of Forti and Honsell, also gives ghosts at larger ordinals in the final chain of other subfunctors of the powerset functor. This leads to a precise description of which sets in these final chains are strongly extensional

Teamwork on the field and at work

One way that people learn teamwork, informal mentoring, and other workplace skills is through participating in sports. Yet, many women of my generation did not get a chance to develop these talents since they had fewer opportunities to participate in organized athletics when they were young. I came to understand the importance of sports from my own experience: My passion—all the rest is a hobby—is coaching girls’ soccer, something I have done for the last 15 years.Sports for women ; Mentoring

Do academic laboratories correspond to scientific communities? Evidence from a large European university.

Although acknowledged as central in the economic literature, the issue of intra academic collaboration has been, insofar, relatively overlooked. This paper fills this gap by stressing the importance of communities in academic research. By analysing the publication behavior of researchers from a large European scientific university, we argue that in certain cases, the community level constitutes a relevant level for analysing the collaborative nature of scientific investigation. Indeed, the reality of research collaborations doesn’t always fit the institutional division of academic work provided by laboratories.Economics of Science, Knowledge Intensive Communities, Academic Collaborations, Social Network Analysis.

Generic singularities of nilpotent orbit closures

According to a well-known theorem of Brieskorn and Slodowy, the intersection of the nilpotent cone of a simple Lie algebra with a transverse slice to the subregular nilpotent orbit is a simple surface singularity. At the opposite extremity of the nilpotent cone, the closure of the minimal nilpotent orbit is also an isolated symplectic singularity, called a minimal singularity. For classical Lie algebras, Kraft and Procesi showed that these two types of singularities suffice to describe all generic singularities of nilpotent orbit closures: specifically, any such singularity is either a simple surface singularity, a minimal singularity, or a union of two simple surface singularities of type $A_{2k-1}$. In the present paper, we complete the picture by determining the generic singularities of all nilpotent orbit closures in exceptional Lie algebras (up to normalization in a few cases). We summarize the results in some graphs at the end of the paper. In most cases, we also obtain simple surface singularities or minimal singularities, though often with more complicated branching than occurs in the classical types. There are, however, six singularities which do not occur in the classical types. Three of these are unibranch non-normal singularities: an $SL_2(\mathbb C)$-variety whose normalization is ${\mathbb A}^2$, an $Sp_4(\mathbb C)$-variety whose normalization is ${\mathbb A}^4$, and a two-dimensional variety whose normalization is the simple surface singularity $A_3$. In addition, there are three 4-dimensional isolated singularities each appearing once. We also study an intrinsic symmetry action on the singularities, in analogy with Slodowy's work for the regular nilpotent orbit.Comment: 56 pages (5 figures). Minor corrections. Accepted in Advances in Mat