Transforming personal experience and emotions through education to cultural diversity: an interplay between unicity and genericity

When subjects studied at school are close to societal discourses and to the students' social identities, when they have high emotional resonance, is it possible to enable the students to distance themselves from their emotions and personal experience, and to conceptualise them? Examining the relation between emotion and learning through the lens of socio-cultural psychology, the aim of our study was to shed light on "secondarisation" processes, that is, processes that transform personal experience and emotions into conceptualised forms of thinking. We analysed 85 video-recorded lessons in education for cultural diversity involving 12 teachers (of primary and secondary schools). Having identified episodes in which emotions were put into words or personal experience was reported, we analysed the use of pronouns (taken as indicators of secondarisation processes) and found a recurrent pattern: "the unicity-genericity routine". We illustrate the functioning of this routine with various excerpts taken from lessons in education for diversity taught in the classes of two teachers in primary school. The results show that the interplay between unicity and genericity works as a discursive resource for the development of secondarisation processes.

Genericity of Nondegeneracy for Light Rays in Stationary Spacetimes

Given a Lorentzian manifold (M, g), an event p and an observer U in M, then p and U are light conjugate if there exists a lightlike geodesic gamma : [0, 1] -> M joining p and U whose endpoints are conjugate along gamma. Using functional analytical techniques, we prove that if one fixes p and U in a differentiable manifold M, then the set of stationary Lorentzian metrics in M for which p and U are not light conjugate is generic in a strong sense. The result is obtained by reduction to a Finsler geodesic problem via a second order Fermat principle for light rays, and using a transversality argument in an infinite dimensional Banach manifold setup.

Genericity of Nondegenerate Critical Points and Morse Geodesic Functionals

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical techniques, we prove an abstract genericity result that employs the infinite dimensional Sard-Smale theorem, along the lines of an analogous result of B. White [29]. Applications are given by proving the genericity of metrics without degenerate geodesics between fixed endpoints in general (non compact) semi-Riemannian manifolds, in orthogonally split semi-Riemannian manifolds and in globally hyperbolic Lorentzian manifolds. We discuss the genericity property also in stationary Lorentzian manifolds.

GENERICITY OF NONDEGENERATE GEODESICS WITH GENERAL BOUNDARY CONDITIONS

Let M be a possibly noncompact manifold. We prove, generically in the C(k)-topology (2 <= k <= infinity), that semi-Riemannian metrics of a given index on M do not possess any degenerate geodesics satisfying suitable boundary conditions. This extends a result of L. Biliotti, M. A. Javaloyes and P. Piccione [6] for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P subset of M x M that satisfies an admissibility condition. Such condition holds, for example, when P is transversal to the diagonal Delta subset of M x M. Further aspects of these boundary conditions are discussed and general conditions under which metrics without degenerate geodesics are C(k)-generic are given.

Locally recurrent functions, density topologies and algebraic genericity

We study the algebraic and topological genericity of certain subsets of locally recurrent functions, obtaining (among other results) algebrability and spaceability within these classes.

Locally recurrent functions, density topologies and algebraic genericity

We study the algebraic and topological genericity of certain subsets of locally recurrent functions, obtaining (among other results) algebrability and spaceability within these classes.

Deterministic Genericity and the Computation of homological Invariants

The main goal of this thesis is to discuss the determination of homological invariants of polynomial ideals. Thereby we consider different coordinate systems and analyze their meaning for the computation of certain invariants. In particular, we provide an algorithm that transforms any ideal into strongly stable position if char k = 0. With a slight modification, this algorithm can also be used to achieve a stable or quasi-stable position. If our field has positive characteristic, the Borel-fixed position is the maximum we can obtain with our method. Further, we present some applications of Pommaret bases, where we focus on how to directly read off invariants from this basis. In the second half of this dissertation we take a closer look at another homological invariant, namely the (absolute) reduction number. It is a known fact that one immediately receives the reduction number from the basis of the generic initial ideal. However, we show that it is not possible to formulate an algorithm – based on analyzing only the leading ideal – that transforms an ideal into a position, which allows us to directly receive this invariant from the leading ideal. So in general we can not read off the reduction number of a Pommaret basis. This result motivates a deeper investigation of which properties a coordinate system must possess so that we can determine the reduction number easily, i.e. by analyzing the leading ideal. This approach leads to the introduction of some generalized versions of the mentioned stable positions, such as the weakly D-stable or weakly D-minimal stable position. The latter represents a coordinate system that allows to determine the reduction number without any further computations. Finally, we introduce the notion of β-maximal position, which provides lots of interesting algebraic properties. In particular, this position is in combination with weakly D-stable sufficient for the weakly D-minimal stable position and so possesses a connection to the reduction number.

Inverse Problems for multiple invariant curves

Planar polynomial vector fields which admit invariant algebraic curves, Darboux integrating factors or Darboux first integrals are of special interest. In the present paper we solve the inverse problem for invariant algebraic curves with a given multiplicity and for integrating factors, under generic assumptions regarding the (multiple) invariant algebraic curves involved. In particular we prove, in this generic scenario, that the existence of a Darboux integrating factor implies Darboux integrability. Furthermore we construct examples where the genericity assumption does not hold and indicate that the situation is different for these.

Universalité, variables complexes et réarrangement

Nous allons exposer dans ce mémoire divers résultats sur l’universalité en analyse complexe. Nous énoncerons d’abord des résultats généraux sur les séries universelles, puis sur un type d’universalité dû à Fournier et Nestoridis qui établit un lien nouveau entre l’universalité et la non-normalité d’une famille de fonctions. Par la suite, nous introduirons un type différent de séries universelles obtenues en réarrangeant les termes de séries arbitraires. Nous prouverons dans ce mémoire la généricité algébrique de ce type de séries universelles pour tout espace de Banach et la généricité topologique dans les espaces de dimension finie. Aussi, nous démontrerons que pour toute série universelle par réarrangement il existe un réarrangement de ses termes pour lequel cette série devient universelle au sens usuel.

Une littérature sous tension : poétique du fragmentaire dans l'oeuvre de Pierre Michon

Ce mémoire porte sur la poétique du fragmentaire dans trois ouvrages de Pierre Michon, soit "Trois auteurs", "Maîtres et serviteurs" et "Corps du roi". Plus qu’une préoccupation d’ordre formel, le fragmentaire y apparaît avant tout comme un champ de tensions, qui se manifeste à la fois sur le plan narratif, discursif et énonciatif. Une approche essentiellement poétique, à la jonction de la linguistique, de la rhétorique et de la narratologie, permet de réfléchir au fragmentaire dans ses effets, mais aussi dans ses affects. La recherche s’articule autour de trois grands axes : la généricité, la discontinuité et la représentation. Dans un premier temps, le fragmentaire est abordé par le prisme de la généricité, qui se traduit, dans l’œuvre de Michon, par une oscillation constante entre le biographique et le romanesque. La tension entre continuité et discontinuité est ensuite étudiée : marquée par les répétitions et variations, elle se manifeste à la fois sur le plan formel (le recueil) et stylistique (la syntaxe, les figures de style). Cette tension est également à comprendre sur le plan temporel, par une prédilection pour l’instant plutôt que pour la durée. Finalement, ce mémoire interroge la répercussion du fragmentaire sur la notion de représentation, qui subit alors un infléchissement : le récit n’est plus envisagé comme représentation, mais comme figuration, cette notion étant à comprendre à la fois comme posture énonciative et dans son rapport à l’image. La figuration est étudiée à partir des scènes romanesques essaimées dans les récits du corpus.

On the semi-Riemannian bumpy metric theorem

We prove the semi-Riemannian bumpy metric theorem using equivariant variational genericity. The theorem states that, on a given compact manifold M, the set of semi-Riemannian metrics that admit only nondegenerate closed geodesics is generic relatively to the C(k)-topology, k=2, ..., infinity, in the set of metrics of a given index on M. A higher-order genericity Riemannian result of Klingenberg and Takens is extended to semi-Riemannian geometry.

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Superfícies de impasse e bifurcações de sistemas forçados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Generidade e politicidade no último Lukács

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)