Mucosal associated invariant T-cells (MAIT) are a phylogenetically conserved subset of alpha/beta T-cells with natural killer-like (NK) activity. MAIT are defined by the expression of an invariant T-cell receptor alpha (TCRα) chain; in mice and humans this chain uses the orthologous mVα19/hVα7.2-Jα33 genes respectively. Available evidence indicates that MAIT are restricted by MR1, a highly conserved MHC class I-related molecule, and that their development is dependent on B lymphocytes. They appear to constitute part of the innate immune response, but their precise functional role is poorly understood. This study aimed to characterise MAIT and MR1 in ruminants, and to further the knowledge and understanding of these unique cells. Using PCR primers based on partial database sequences, orthologous full-length TCRα chains were identified in circulating bovine and ovine T cells. The germline elements of the respective α chains were identified and their overall frequency of expression within the bovine TCRα repertoire determined. Experiments using the orthologous TCRα chain as a marker for MAIT cells to examine expression in bovine and ovine blood and various tissues showed that spleen and mesenteric lymph nodes contained the highest frequency of MAIT cells. Use of the same technique to study levels of this marker in cattle of different ages revealed very low numbers of MAIT cells in neonatal animals, followed by a marked increase in the first 3 weeks of life. Analyses of MAIT TCRα expression in different T cell subsets showed that, unlike mice and humans in which MAIT cells are predominantly within the CD4-/CD8- T-cell population, MAIT cells in bovine blood are predominantly CD8+. Full-length cDNAs were isolated for bovine and sheep MR1 and their sequences were found to display marked cross-species conservation. Using a specific PCR, MR1 was shown to be expressed in peripheral blood and by different lineages of Theileria-transformed cells. Alternatively-spliced transcripts of MR1 were detected in both cattle and sheep and several of these retained an intact open-reading frame. Constructs of bovine MR1 and an MR1/MHC chimera were prepared in a eukaryotic expression vector but these failed to give detectable cell surface expression following transfection into Cos-7, despite positive intracellular expression.

We study dynamical systems in the complex plane under the effect of constant noise. We show for a wide class of polynomial equations that the ergodic property is valid in the associated stochastic perturbation if and only if the noise added is in the direction transversal to all unstable trajectories of the deterministic system. This has the interpretation that noise in the "right" direction prevents the process from being unstable: a fundamental, but not well-understood, geometric principle which seems to underlie many other similar equations. The result is proven by using Lyapunov functions and geometric control theory.

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This thesis is on moduli spaces of complexes of sheaves and diagrams of such moduli spaces. The objects in these diagrams are constructed as geometric invariant theory quotients and the points in these quotients correspond to certain equivalence classes of complexes. The morphisms in these diagrams are constructed by taking direct sums with acyclic complexes. We then study the colimit of such a diagram and in particular are interested in studying the images of quasi-isomorphic complexes in the colimit. As part of this thesis we construct categorical quotients of a group action on unstable strata appearing in a stratification associated to a complex projective scheme with a reductive group action linearised by an ample line bundle. We study this stratification for a closed subscheme of a quot scheme parametrising quotient sheaves over a complex projective scheme and relate the Harder-Narasimhan types of unstable sheaves with the unstable strata in the associated stratification. We also study the stratification of a parameter space for complexes with respect to a linearisation determined by certain stability parameters and show that a similar result holds in this case. The objects in these diagrams are indexed by different Harder-Narasimhan types for complexes and are quotients of parameter schemes for complexes of this fixed Harder-Narasimhan type. This quotient is given by a choice of linearisation of the action and so the diagrams depend on these choices. We conjecture that these choices can be made so that for any quasi-isomorphism between complexes representing points in this diagram both complexes are identified in the colimit of this diagram.

La zone marginale de la rate apparaît comme un lieu stratégique de détection des antigènes et agents pathogènes véhiculés par le sang. Ces propriétés sont principalement liées à la présence de cellules appartenant au système immunitaire inné parmi lesquelles se trouvent des nombreuses cellules présentatrices d’antigènes (APC), comme les macrophages, les lymphocytes B de la zone marginale (MZB) ou encore les cellules dendritiques (DC). Ces cellules représentent une première ligne de défense contre les pathogènes véhiculés par le sang et sont importantes pour l’initiation des réponses immunes. Il a fortement était suggéré la localisation dans la zone marginale d’une autre population appartenant au système immunitaire inné : les lymphocytes T Natural Killer invariants ou iNKT. Ces lymphocytes T non conventionnels sont caractérisés par l’expression de marqueurs de cellules NK et de lymphocytes T conventionnels notamment le TCR. Contrairement aux lymphocytes T conventionnels, les iNKT reconnaissent des antigènes (Ag) lipidiques (d’origine exogène ou endogène) présentés par l’intermédiaire de la molécule CD1d exprimée à la surface des APC, notamment les DC. En réponse à ces lipides, et notamment l’α-galactosylceramide (α-GalCer), les cellules iNKT ont la capacité unique de sécréter rapidement de grandes quantités de cytokines immunomodulatrices comme l’IFN-γ et/ou l’IL-4 qui, en retour, permettent l’activation d’autres populations immunes telles que les DC, les cellules NK, les lymphocytes B et lymphocytes T conventionnels. Les DC, en tant qu’APC professionnelles, sont de puissantes cellules activatrices des lymphocytes T conventionnels mais également des iNKT. Cependant, bien que souvent souligné dans la littérature, le rôle des autres APC dans l’activation des lymphocytes T conventionnels mais surtout des iNKT restait relativement obscur lorsque ce travail de thèse a débuté. Parmi les APC, les MZB représentaient des cibles idéales puisqu’elles ont la particularité d’exprimer fortement les molécules de présentation telle que les molécules du CMH de classe II, la molécule CD1d mais aussi les molécules de co-stimulation. Nous avons donc débuté notre travail par l’étude du rôle des MZB dans l’activation des lymphocytes conventionnels et des iNKT. Nous montrons que les MZB sensibilisés avec un peptide de l’ovalbumine sont capables d’activer les lymphocytes T CD4+, dont la réponse est orientée vers un profil Th1 après l’activation des MZB par le CpG-ODN (agoniste du TLR-9). Ainsi, les MZB se comportent comme de véritables APC. Nous avons ensuite étudié l’activation des iNKT en réponse à lα’-GalCer. De façon surprenante, bien que les MZB expriment fortement la molécule CD1d, elles sont incapables d’activer in vitro les iNKT primaires en réponse l’α-GalCer libre. Elles sont cependant capables de présenter l’α-GalCer aux iNKT suggérant qu’il manque aux MZB des facteurs (solubles ou non) pour induire l’activation des iNKT. De façon intéressante, l’ajout de DC non sensibilisées restaure la production d’IFN-γ et d’IL-4 par les iNKT co-cultivés en présence de MZB sensibilisés avec l’α-GalCer. Nous montrons que les DC participent à cette activation via un mécanisme de présentation croisée mais également via l’apport de facteurs nécessaires aux MZB pour induire l’activation des iNKT. Il existe une réelle coopération entre ces deux types d’APC pour une activation optimale des iNKT. Finalement, nous montrons que les MZB sensibilisés avec l’α-GalCer induisent l’activation des lymphocytes iNKT et NK in vivo. Nous nous sommes ensuite concentrés sur les DC qui comme indiqué ci-dessus, sont des APC professionnelles. Cependant, dans la rate, les DC représentent une population très hétérogène dont le rôle de chaque sous-population notamment dans l’activation des iNKT était également très peu connu lorsque ce travail a débuté. / The spleen, with its highly specialized lymphoid compartments, plays a central role in clearing blood-borne pathogens. Innate immune cells, that are mainly present in the marginal zone of the spleen, are strategically located to respond to blood-borne microorganisms and viruses. Among innate cells, macrophages and marginal zone B (MZB) cells represent the first line of defense against blood-borne pathogens and with dendritic cells (DC) are important for initiation of the immune response. Along with these populations of antigen-presenting cells (APC), it was also suggested that invariant Natural Killer T (iNKT), a population of innate-like T lymphocytes, were also located in the marginal zone of the spleen. Unlike conventional T lymphocytes, iNKT cells recognize exogenous and self (glyco)lipid antigens (Ag) presented by the non-classical class I Ag presenting molecule CD1d expressed on APC, in particular DC. Upon lipid recognition, in particular in response to the non-mammalian glycolipid, α-galactosylceramide (α-GalCer), iNKT cells have the unique capacity to rapidly produce large amounts of immunoregulatory cytokines, including IFN-γ and IL-4, which lead to downstream activation of other immune populations (DC, NK cells, B cells and conventional T cells). Through this property, iNKT cells influence the strength and quality of the ensuing immune response. Dendritic cells, as professional APC, are potent activators of conventional T lymphocytes and iNKT cells. When we started our PhD, the role of APC other than DC in the priming of T lymphocytes including iNKT cells remained unclear. Among them, MZB cells represented good candidates since they express high levels of MHC class II and CD1d molecules and their ability to activate and orientate conventional and innate-like T lymphocytes, such as iNKT cells, were elusive. We show that MZB cells, when loaded OVA peptide promote the release of IFN-γ and IL-4 by antigen specific CD4+ T lymphocytes and their stimulation with CpG-ODN biases them toward more Th1 inducers. Surprisingly, although able to activate iNKT hybridomas, MZB cells sensitized with free α-GalCer do not directly activate ex vivo sorted iNKT cells unless DC are added to the culture system. Dendritic cells help MZB cells to promote iNKT cell activation in part through α-GalCer cross-presentation and also through DC-expressed co-factors. Interestingly, MZB cells amplify the DC-mediated activation of iNKT cells and depletion of MZB cells from total splenocytes strongly reduces iNKT cell activation in response to α-GalCer. Thus, DC and MZB cells provide help to each other to optimize iNKT cell stimulation. Finally, in vivo transfer of α-GalCer-loaded MZB cells potently activates iNKT and NK cells. Thus, we show for the first time a role of MZB cell in iNKT cell activation in response to free α-GalCer, an important finding to better understand the modalities of iNKT cell activation. As mentioned above, DC are professional APC and thus are strong activators of conventional and unconventional T lymphocytes. However, DC in the spleen represent an heterogeneous cell population and when we started our study, the role of DC subsets in T lymphocyte priming was still unclear. Among DC subsets, we concentrated on the major splenic DC subset located in the marginal zone, the CD8α- DC. This DC subset was further subdivided in CD4+ and CD4- subtypes. We provide evidences that CD4+ and CD4- DC are equally efficient at priming CD4+ T lymphocytes when loaded with OVA peptide and whole OVA, leading to a mixed Th1/Th2 response, and also CD8+ T lymphocytes when pulsed with OVA peptide (but not whole OVA).

The topic of this thesis is the moduli theory of (parabolic) sheaves on stable curves. Using geometric invariant theory (GIT), universal moduli spaces of semistable parabolic sheaves on stable marked curves are constructed: `universal' indicates that these are moduli spaces of pairs where the underlying marked curve may vary as well as the parabolic sheaf (as in the Pandharipande moduli space for pairs of stable curves and torsion-free sheaves without augmentations). As an intermediate step in this construction, we construct moduli spaces of semistable parabolic sheaves on flat families of arbitrary projective schemes (of any dimension or singularity type): this is the technical core of this thesis. These moduli spaces are projective, since they are constructed as GIT quotients of projective parameter spaces. The stability condition for parabolic sheaves depends on a choice of polarisation and is derived from the Hilbert-Mumford criterion. It is not quite the same as traditional stability with respect to parabolic Hilbert polynomials, but it is closely related to it, and the resulting moduli spaces are always compactifications of moduli of slope-stable parabolic sheaves. The construction works over algebraically closed fields of arbitrary characteristic.

The gauge-invariant formulation of quantum mechanics is compared to the conventional approach for the case of a one-dimensional charged harmonic oscillator in an electromagnetic field in the electric dipole approximation. The probability of finding the oscillator in the ground state or excited states as a function of time is calculated, and the two approaches give different results. On the basis of gauge invariance, the gauge-invariant formulation of quantum mechanics gives the correct probability, while the conventional approach is incorrect for this problem. Therefore, expansion coefficients or a wave function cannot always be interpreted as probability amplitudes. For a physical interpretation as probability amplitudes the expansion coefficients must be gauge invariant.

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Topology studies the geometric properties of spaces that are preserved by continuous deformations. Manifolds are the main examples of topological spaces, with the local properties of Euclidean space in an arbitrary dimension n. They are the higher dimensional analogs of curves and surfaces. For example a circle is a one-dimensional manifold. Balloons and doughnuts are examples of two-dimensional manifolds. A balloon cannot be deformed continuously into a doughnut, so we see that there are essential topological differences between them. An "invariant" of a topological space is a number or an algebraic structure such that topologically equivalent spaces have the same invariant. For example the essential topological difference between the balloon and the doughnut is calculated by the "Euler characteristic", which is 2 for a balloon and 0 for a doughnut. In this thesis I investigate the relation between three different but related invariants of manifolds with dimension divisible by 4: the signature, the Brown-Kervaire invariant and the Arf invariant. The signature invariant takes values in the set (...;-3;-2;-1; 0; 1; 2; 3; ...) of integers. In this thesis we focus on the signature invariant modulo 8, that is its remainder after division by 8. The Brown-Kervaire invariant takes values in the set (0; 1; 2; 3; 4; 5; 6; 7). The Arf invariant takes values in the set (0; 1). The main result of the thesis uses the Brown-Kervaire invariant to prove that for a manifold with signature divisible by 4, the divisibility by 8 is decided by the Arf invariant. The thesis is entirely concerned with pure mathematics. However it is possible that it may have applications in mathematical physics, where the signature modulo 8 plays a significant role.