Should we solve Plateau's problem again?

After a short description of various classical solutions of Plateau's problem, we discuss other ways to model soap films, and some of the related questions that are left open. A little more attention is payed to a more specific model, with deformations and sliding boundary conditions.Comment: Lecture for the conference in Honor of E. Stein, 201

Conformal holonomy, symmetric spaces, and skew symmetric torsion

We consider the question: can the isotropy representation of an irreducible pseudo-Riemannian symmetric space be realized as a conformal holonomy group? Using recent results of Cap, Gover and Hammerl, we study the representations of SO(2,1), PSU(2,1) and PSp(2,1) as isotropy groups of irreducible symmetric spaces of signature (3,2), (4,4) and (6,8), respectively, describing the geometry induced by a conformal holonomy reduction to the corresponding subgroups. In the case of SO(2,1) we show that conformal manifolds with such a holonomy reduction are always locally conformally flat and hence this group cannot be a conformal holonomy group. This result completes the classification of irreducible conformal holonomy groups in Lorentzian signature. In the case of PSU(2,1), we show that conformal manifolds of signature (3,3) with this holonomy reduction carry, on an open dense subset, a canonical nearly para-Kaehler metric with positive Einstein constant. For PSp(2,1) we also show that there is an open dense subset endowed with a canonical Einstein metric in the conformal class. As a result, after restricting to an open dense subset the conformal holonomy must be a proper subgroup of PSU(2,1) or of PSp(2,1), respectively. Finally, using a recent result of Graham and Willse we prove the following general non-existence result: for a real-analytic, odd-dimensional conformal manifold, the conformal holonomy group can never be given by the isotropy representation of an irreducible pseudo-Riemannian symmetric space unless the isotropy is SO(p+1,q+1).Comment: 39 pages, comments welcome. In version 2 the statement of Theorem 2 is corrected, see also Remark 4 on page 24. In version 3, the technical Lemma 6 in the appendix is changed, typos are corrected and acknowledgements adde

An analysis of persistent non-player characters in the first-person gaming genre 1998-2007: a case for the fusion of mechanics and diegetics

This paper describes the results of an analysis of persistent non-player characters (PNPCs) in the first-person gaming genre 1998-2007. Assessing the role, function, gameplay significance and representational characteristics of these critical important gameplay objects from over 34 major releases provides an important set of baseline data within which to situate further research. This kind of extensive, genre-wide analysis is under-represented in game studies, yet it represents a hugely important process in forming clear and robust illustrations of the medium to support understanding. Thus, I offer a fragment of this illustration, demonstrating that many of the cultural and diegetic qualities of PNPCs are a product of a self-assembling set of archetypes formed from gameplay requirements