In this thesis, we use the tools of relative homological algebra in triangulated categories to define a sensible notion of support for objects in the bootstrap class of a Kasparov category of C*-algebras over a finite ...

This dissertation investigates representations of Lie groupoids and Lie algebroids and the connection between them. Lie groupoids and Lie algebroids are differential-geometric generalisations of Lie groups and Lie ...

We develop an analogoue of coarse geometry for noncommutative spaces in terms of unitizations of the given C* -algebra. Examples for our theory come from Rieffel deformation of compactifications under strongly continuous ...

This thesis provides an explicit, general trace formula for the Hecke and Casimir eigenvalues of GL(2)-automorphic representations over a global field. In special cases, we obtain Selberg's original trace formula. Computations ...

In this thesis, we propose to use generalized fixed point algebras as an approach to the pseudodifferential calculus on filtered manifolds. A filtered manifold is a manifold \(M\) with a filtration of its tangent ...

We consider a class of Fell bundles over quasi-lattice ordered groups. We show that these are completely determined by the positive fibres and that their cross sectional C*-algebras are relative Cuntz–Pimsner algebras ...

In this thesis, we define a cyclic homology theory for non-archimedean bornological algebras, which we call analytic cyclic homology. Let V be a complete, discrete valuation ring with uniformiser p, residue field k, and ...

We give a new and essentially elementary proof of an important result due to Joseph Bernstein in the theory of smooth representations of a reductive p-adic group G. Main tools for studying these representations are parabolic ...