Approximate solutions for optimization problems become of interest if the ‘true’ optimum cannot be found: this may happen for the simple reason that an optimum does not exist or because of the ‘bounded rationality’ (or bounded accuracy) of the optimizer. This paper characterizes several approximate solutions by means of consistency and additional requirements. In particular we consider invarian...

Topological rigidity is an analogue of the Baum-Connes conjecture, and is motivated by Mostow rigidity and Margulis superrigidity. I will discuss some of the places where this heuristic reasoning fails, and the rigidity shows some cracks – that are rather different than the places where strong forms of the Baum-Connes conjecture fails.

We perform the Batalin-Vilkovisky quantization of Yang–Mills theory on a 2-point space, discussing the formulation of Connes–Lott as well as Connes’ real spectral triple approach. Despite of the model’s apparent simplicity the gauge structure reveals infinite reducibility and the gauge fixing is afflicted with the Gribov problem. 1

We construct a KK-theory for Banach algebras, equivariant with respect to the action of a groupoid. We prove the Baum–Connes conjecture with commutative coefficients for hyperbolic groups and for the Poincaré groupoids of foliations with a compact base and a longitudinal Riemannian metrics with negative sectional curvature. Mots clés : théorie de Kasparov ; conjecture de Baum–Connes ; algèbres ...

We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way...