Royal Institute of Technology, Stockholm

In the case of Einstein's equations coupled to a non-linear scalar field with a suitable exponential potential, there are solutions for which the expansion is accelerated and of power law type. In the talk I will discuss the future global non-linear stability of such models. The results generalize those of Mark Heinzle and Alan Rendall obtained using different methods.

It became apparent during the last decade that in several questions in classical complex analysis extremal configurations are fractal, making them very difficult to attack: it is not even clear how to construct or describe extremal objects. We will argue that the most promising approach is to consider conformally self-similar random configurations, which should be extremal almost surely.