Final Report Summary - SIMPLELCGPS (Simple locally compact groups: exploring the boundaries of the linear world)
The theory of locally compact groups stretches out between two antipodes: on one hand, connected groups whose structure, according to the solution to Hilbert 5fth problem, is governed by Lie theory and is thus relatively rigid, and on the other hand, discrete groups, which are subject to a spectacular variety of behaviours, going from the most stringent rigidity properties to the most intriguing pathological ones. The goal of this project has been to explore the wide space lying between these two extremes. We establish foundations for a study of non-discrete totally disconnected locally compact groups in terms of their local structure, with a special emphasis on simple groups. A recurrent theme has been to exploit the fruitful and sometimes unexpected relation between discrete and non-discrete groups.