On cellularization for simplicial presheaves and motivic homotopy theory.

We construct cellular homotopy theories for categories of simplicial presheaves on small Grothendieck sites and discuss applications to the motivic homotopy category of Morel and Voevodsky

Étale homotopy types of moduli stacks of polarised abelian schemes

We determine the Artin–Mazur étale homotopy types of moduli stacks of polarised abelian schemes using transcendental methods and derive some arithmetic properties of the étale fundamental groups of these moduli stacks. Finally we analyse the Torelli morphism between the moduli stacks of algebraic curves and principally polarised abelian schemes from an étale homotopy point of view

Secondary Theories for Simplicial Manifolds and Classifying Spaces

Abstract. We define secondary theories and characteristic classes for simplicial smooth manifolds generalizing Karoubi’s multiplicative Ktheory and multiplicative cohomology groups for smooth manifolds. As a special case we get versions of the groups of differential characters of Cheeger and Simons for simplicial smooth manifolds. Special examples include classifying spaces of Lie groups and Lie groupoids

Atiyah sequences, connections and characteristic forms for principal bundles over groupoids and stacks

We construct connections and characteristic forms for principal bundles over groupoids and stacks in the differentiable, holomorphic and algebraic category using Atiyah exact sequences associated with transversal tangential distributions. Nous construisons les connexions et formes caractéristiques pour les fibrés principaux sur les groupoïdes et les champs dans la catégorie différentiable, holomorphe et algébrique à l’aide des suites d’Atiyah associées aux distributions transversales tangentielles

Geometry of moduli stacks of (k, l)-stable vector bundles over algebraic curves

We study the geometry of the moduli stack of vector bundles of fixed rank and degree over an algebraic curve by introducing a filtration made of open substacks build from (k,l)-stable vector bundles. The concept of (k,l)-stability was introduced by Narasimhan and Ramanan to study the geometry of the coarse moduli space of stable bundles. We will exhibit the stacky picture and analyse the geometric and cohomological properties of the moduli stacks of (k,l)-stable vector bundles. For particular pairs (k,l) of integers we also show that these moduli stacks admit coarse moduli spaces and we discuss their interplay

Equivariant cohomology of differentiable stacks

We construct and analyse models of equivariant cohomology for differentiable stacks with Lie group actions extending classical results for smooth manifolds due to Borel, Cartan and Getzler. We also derive various spectral sequences for the equivariant cohomology of a differentiable stack generalising among others Bott’s spectral sequence which converges to the cohomology of the classifying space of a Lie group

The Lusternik-Schnirelmann Category for a Differentiable Stack

We introduce the notion of Lusternik-Schnirelmann category for differentiable stacks and establish its relation with the groupoid Lusternik-Schnirelmann category for Lie groupoids. This extends the notion of Lusternik-Schnirelmann category for smooth manifolds and orbifolds

Seroconversion with progress of disease.

<p>CD28 abs measured in one female patient during a period of more than 10 years in association with the course of the disease.</p

Detailed data of melanoma patients.

<p>SSM = superficial spreading melanoma, NMM = nodular malignant melanoma, LMM = Lentigo maligna melanoma, ALM = acrolentiginous melanoma, AMM = amelanotic melanoma, UCM = unclassified melanoma, others = melanoma of the mucosa or uvea.</p

Competition assay using a mouse CD28 monoclonal antibody and purified human CD28 autoantibodies.

<p>Jurkat cells were incubated with mixtures of mouse monoclonal CD28 antibodies with increasing amounts of purified human autoantibodies (CD28 or G250). Competition was detected for human CD28 autoantibodies while human G250 autoantibodies had no effect. Cell viability was measured by EZ4U assay.</p