Orbitwise countings in H(2) and quasimodular forms

We prove formulae for the countings by orbit of square-tiled surfaces of genus two with one singularity. These formulae were conjectured by Hubert & Leli\`{e}vre. We show that these countings admit quasimodular forms as generating functions.Comment: 22 pages, 6 figure

Prime arithmetic Teichmuller discs in H(2)

It is well-known that Teichmuller discs that pass through "integer points'' of the moduli space of abelian differentials are very special: they are closed complex geodesics. However, the structure of these special Teichmuller discs is mostly unexplored: their number, genus, area, cusps, etc. We prove that in genus two all translation surfaces in H(2) tiled by a prime number n > 3 of squares fall into exactly two Teichmuller discs, only one of them with elliptic points, and that the genus of these discs has a cubic growth rate in n.Comment: Accepted for publication in Israel Journal of Mathematics. A previous version circulated with the title "Square-tiled surfaces in H(2)''. Changes from v1: improved redaction, fixed typos, added reference

Enjeux interprétatifs de la féminité dans l’écriture de Souleymane Cissé

Dans tout le cinéma de Cissé se retrouvent deux thèmes : l'Afrique et la femme. Si bien qu'on pourrait considérer que s'y développent des thèses panafricaines ou féministes. Mais à eux seuls ces cadres idéologiques ne permettent pas de saisir la relation qu'entretiennent, selon le Malien, l'Afrique et la femme avec la féminité. Dans un premier temps, cette relation sera abordée à travers la description concrète que fait le cinéaste de la condition des femmes africaines; dans un second temps, elle sera identifiée au passage à un discours plus abstrait du cinéaste sur la condition féminine de l'Afrique. On comprendra ce passage dans la mesure où on aura d'abord considéré l'écriture cinématographique de Cissé sur la féminité comme porteuse d'un sens métaphorique.The recurrence of two themes (Africa and women) in Cissé's cinema as a whole would tend to suggest that his body of work develops pan-African as well as feminist theses. Yet these ideological frameworks alone do not suffice to understand the relationship which, according to the Malian director, Africa and women have with femininity. This relationship will first be examined through the concrete description by the filmmaker of the condition of African women; it will then be identified with Cissé's movement towards a more abstract discourse on the condition of women in Africa

Histoire, mémoire, et légitimation politique dans les cinémas africains

L’objectif de cet article est de rappeler l’importance du ‘rapport à la mémoire’ dans les médias cinématographiques et audiovisuels d’Afrique subsaharienne par opposition aux usages souvent idéologiques qui ont pu être fait d’un ‘rapport à l’histoire’. Dans un premier temps, il s’agit de revenir sur des tentatives de représentations de l’histoire telles qu’elles ont pu apparaître chez des réalisateurs comme Ousmane Sembène, Med Hondo ou Haile Gerima, en considérant ces représentations dans le cadre de discours de légitimation politique. Dans un second temps, cet article veut situer ces discours de légitimation politique au sein de la littérature critique et théorique qui a pu apparaître à propos des cinémas africains depuis les années 70; il s’agit alors de déterminer les limites qui, dans un cadre théorétique englobant un questionnement d’ordre ‘méthodologique-épistémologique’ aussi bien qu’esthétique, doivent être nécessairement assignées à ces discours de légitimation politique. Finalement, dans un troisième temps, il s’agit de revenir sur un certain nombre de films africains réalisés à partir des années 90 dans lesquels un ‘rapport à la mémoire’ est engagé. En conclusion, on considère que, dans les discours sur ces médias, le danger a toujours été plutôt du côté de la légitimation politique de tel ou tel rapport à l’histoire que du côté d’une relation symbolique et esthétique à la mémoire.This article aims to recall the significance of the ‘relationship to memory’ in cinematic and audio-visual media in Sub-Saharan Africa in contrast to the often ideological uses which have been made of a ‘relationship to history’. The article begins by reconsidering attempts to represent history by directors such as Ousmane Sembène, Med Hondo and Haile Gerima, by analysing these representations within the framework of political discourse of legitimization. Then, this article attempts to situate this discourse within the critical and theoretical literature which have appeared in relation to African cinema since the 1970s; thus the question is to determine limitations which must necessarily be assigned to this discourse of political legitimization, within a theoretical framework which includes a ‘methodological-epistemological’ point of view as well as an aesthetical one. The article then reconsiders some African films made since the 1990s in which a ‘relationship to memory’ was involved. The article concludes that, in discourse about African media, the danger has always been more on the side of the political legitimization of a certain relationship to history the symbolical and aesthetical relationship to memory

Noncongruence subgroups in H(2)

Accepted for publication in International Mathematics Research Notices.International audienceWe study the congruence problem for subgroups of the modular group that appear as Veech groups of square-tiled surfaces in the minimal stratum of abelian differentials of genus two

Statistical hyperbolicity in groups

In this paper, we introduce a geometric statistic called the "sprawl" of a group with respect to a generating set, based on the average distance in the word metric between pairs of words of equal length. The sprawl quantifies a certain obstruction to hyperbolicity. Group presentations with maximum sprawl (i.e., without this obstruction) are called statistically hyperbolic. We first relate sprawl to curvature and show that nonelementary hyperbolic groups are statistically hyperbolic, then give some results for products, for Diestel-Leader graphs and lamplighter groups. In free abelian groups, the word metrics asymptotically approach norms induced by convex polytopes, causing the study of sprawl to reduce to a problem in convex geometry. We present an algorithm that computes sprawl exactly for any generating set, thus quantifying the failure of various presentations of Z^d to be hyperbolic. This leads to a conjecture about the extreme values, with a connection to the classic Mahler conjecture.Comment: 14 pages, 5 figures. This is split off from the paper "The geometry of spheres in free abelian groups.