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Publications (24)
This guide has been created to support you in your role as a senior manager or policymaker in HE. Your past decisions may have directly impacted autistic students or graduates, perhaps without you even knowing it. Here you will find key information, tips and guidelines, based on the experiences of other senior managers and autistic people.
Purpose
This research aims to examine effective support strategies for facilitating employment of autistic students and graduates by answering the following research question: What constitutes effective employment support for autistic students and graduates?
Design/methodology/approach
Data were collected using the method of empathy-based stori...
Loin des clichés sur l’université-tour d’ivoire, les liens universités-entreprises sont déjà nombreux et continuent de se développer. Si les relations entre l’Université et les entreprises sont importantes, nous devons envisager les conditions dans lesquelles celles-ci peuvent être harmonieuses, et donc équilibrées et respectueuses des missions de...
We give a cohomological formula for the index of a fully elliptic
pseudodifferential operator on a manifold with boundary. As in the classic case
of Atiyah-Singer, we use an embedding into an euclidean space to express the
index as the integral of a cohomology class depending in this case on a
noncommutative symbol, the integral being over a $C^\in...
We compute the K-theory of the comparison C *-algebra associated to a manifold with corners. These comparison algebras are an example of the abstract pseudodifferential algebras introduced by Connes and Moscovici [16]. Our calculation is obtained by showing that the comparison algebra associated to a manifold with corners is a homomorphic image of...
We compute the $K$-theory of comparison $C^*$-algebra associated to a manifold with corners. These comparison algebras are an example of the abstract pseudodifferential algebras introduced by Connes and Moscovici \cite{M3}. Our calculation is obtained by showing that the comparison algebras are a homomorphic image of a groupoid $C^*$-algebra. We th...
Can Boutet de Monvel’s algebra on a compact manifold with boundary be obtained as the algebra Ψ 0 (G) of pseudodifferential operators on some Lie groupoid G? If it could, the kernel G of the principal symbol homomorphism would be isomorphic to the groupoid C ∗-algebra C ∗ (G). While the answer to the above question remains open, we exhibit in this...
In his book (II.5), Connes gives a proof of the Atiyah-Singer index theorem for closed manifolds by using deformation groupoids and appropiate actions of these on R^N. Following these ideas, we prove an index theorem for manifolds with boundary. Comment: 6 pages. Preprint submitted to the Academie des Sciences
This survey of the work of the author with several collaborators presents the way groupoids appear and can be used in index theory. We define the general tools, and apply them to the case of manifolds with corners, ending with a topological index theorem.
Can Boutet de Monvel's algebra on a compact manifold with boundary be obtained as the algebra $\Psi^0(G)$ of pseudodifferential operators on some Lie groupoid $G$? If it could, the kernel ${\mathcal G}$ of the principal symbol homomorphism would be isomorphic to the groupoid {$C^*$-algebra} $C^*(G)$. While the answer to the above question remains o...
We define an analytic index and prove a topological index theorem for a non-compact manifold M 0 with poly-cylindrical ends. Our topological index theorem depends only on the principal symbol, and establishes the equality of the topological and analytical index in the group K 0(C *(M)), where C *(M) is a canonical C *-algebra associated to the cano...
We construct and study several algebras of pseudodifferential operators that are closed under holomorphic functional calculus. This leads to a better understanding of the structure of inverses of elliptic pseudodifferential operators on certain non-compact manifolds. It also leads to decay properties for the solutions of these operators. To cite th...
We construct algebras of pseudodifferential operators on a continuous family groupoid G that are closed under holomorphic functional calculus, contain the algebra of all pseudodifferential operators of order 0 on G as a dense subalgebra, and reflect the smooth structure of the groupoid G, when G is smooth. As an application, we get a better underst...
We compute the K-theory, groups of the C*-algebra of the groupoid of a manifold with corners, in which the analytic index takes its values.
We study properties and representations of the convo-lution algebra and the algebra of pseudodifferential operators asso-ciated to a continuous family groupoid. We show that the study of representations of the algebras of pseudodifferential operators of or-der zero completely reduces to the study of the representations of the ideal of regularizing...
We build a longitudinally smooth, differentiable groupoid associated to any manifold with corners. The pseudodifferential calculus on this groupoid coincides with the pseudodifferential calculus of Melrose (also called b b -calculus). We also define an algebra of rapidly decreasing functions on this groupoid; it contains the kernels of the smoothin...
We associate to any manifold with corners (even with non-embedded hyperfaces) a (non-Hausdorff) longitudinally smooth Lie groupoid, on which we define a pseudodifferential calculus. This calculus generalizes the b-calculus of Melrose, defined for manifolds with embedded corners. The groupoid of a manifold with corners is shown to be unique up to eq...
Let G be a Lie groupoid. The pseudodifferential calculus over G defines the analytic index. The tangent groupoid induces a morphism in K-theory; we prove that it coincides with the analytic index. Thus the latter may be defined without considering the pseudodifferential calculus.
Let G be a Lie groupoid. The pseudodifferential calculus over G defines the analytic index. The tangent groupoid induces a morphism in K-theory; we prove that it coincides with the analytic index. Thus the latter may be defined without considering the pseudodifferential calculus.