Objective The theory of locally compact groups stretches out between two antipodes: on one hand, connected groups whose structure, according to the solution to Hilbert fifth 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 research program is to explore the wide space lying between these two extremes.The entire program is built around two major open problems: performing an exhaustive study of compactly generated simple locally compact groups, and finding an algebraic characterization of those locally compact groups which are linear. Although these problems do not seem to be directly approachable given the current state of knowledge, they are nevertheless considered as guidelines suggesting a number of specific questions and conjectures which are envisaged in detail under various perspectives of algebraic, geometric, arithmetic and analytic nature. Each of these specific questions presents independent interest; answers to any of them will moreover provide insight into the guiding problems. Fields of science natural sciencesmathematicspure mathematicsarithmetics Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Call for proposal ERC-2011-StG_20101014 See other projects for this call Funding Scheme ERC-SG - ERC Starting Grant Host institution UNIVERSITE CATHOLIQUE DE LOUVAIN EU contribution € 848 640,00 Address PLACE DE L UNIVERSITE 1 1348 Louvain La Neuve Belgium See on map Region Région wallonne Prov. Brabant Wallon Arr. Nivelles Activity type Higher or Secondary Education Establishments Principal investigator Pierre-Emmanuel Caprace (Dr.) Administrative Contact Anne Bovy (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all UNIVERSITE CATHOLIQUE DE LOUVAIN Belgium EU contribution € 848 640,00 Address PLACE DE L UNIVERSITE 1 1348 Louvain La Neuve See on map Region Région wallonne Prov. Brabant Wallon Arr. Nivelles Activity type Higher or Secondary Education Establishments Principal investigator Pierre-Emmanuel Caprace (Dr.) Administrative Contact Anne Bovy (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data