Closed geodesics in Alexandrov spaces of curvature bounded from above

In this paper, we show a local energy convexity of $W^{1,2}$ maps into $CAT(K)$ spaces. This energy convexity allows us to extend Colding and Minicozzi's width-sweepout construction to produce closed geodesics in any closed Alexandrov space of curvature bounded from above, which also provides a generalized version of the Birkhoff-Lyusternik theorem on the existence of non-trivial closed geodesics in the Alexandrov setting.Comment: Final version, 22 pages, 2 figures, to appear in the Journal of Geometric Analysi

Measurable versions of the LS category on laminations

We give two new versions of the LS category for the set-up of measurable laminations defined by Berm\'udez. Both of these versions must be considered as "tangential categories". The first one, simply called (LS) category, is the direct analogue for measurable laminations of the tangential category of (topological) laminations introduced by Colman Vale and Mac\'ias Virg\'os. For the measurable lamination that underlies any lamination, our measurable tangential category is a lower bound of the tangential category. The second version, called the measured category, depends on the choice of a transverse invariant measure. We show that both of these "tangential categories" satisfy appropriate versions of some well known properties of the classical category: the homotopy invariance, a dimensional upper bound, a cohomological lower bound (cup length), and an upper bound given by the critical points of a smooth function.Comment: 22 page

Reflections on designing a Biology/Humanities interdisciplinary module

This paper uses the reflections of a recent workshop on biology and the humanities subject areas to consider the potential for designing a first year interdisciplinary module that brings together teachers and learners in the Biosciences with their counterparts in English and History. It considers three building blocks of module design: aims and objectives; teaching and learning strategies; and assessment; and provides a commentary on the discussion of interdisciplinarity in the broader literature. The authors argue that interdisciplinary teaching and learning must be transformative, but not in the way many previous advocates of interdisciplinarity have assumed. Rather than transcending disciplines, the authors contend that the aim should be to enhance disciplinary understanding. Learners should emerge from the interdisciplinary module not having lost their identity as biologists, but having enhanced it. They should have become ‘better’ biologists in the sense of having developed a broader, critical understanding of the precepts of their discipline, as a first step to an understanding of biology inflected with a literary and historical awareness