Colloquium Math Dept ULB : Pierre-Emmanuel Caprace (UCLouvain) : ``Non-discrete simple locally-compact groups’’.

Friday 14 Oct 2016, 14:00 → 15:00 Europe/Brussels

9th Floor, NO Building (Salle des Professeurs)

Through the history of their developments, locally compact groups provide a beautiful illustration of the unity of mathematics. Initiated at the turn of the 20th century under the impetus of Hilbert’s fifth problem, their investigation led to the creation of topological algebra, laid the foundations of abstract harmonic analysis, and revealed the relevance of measure and integration, as well as ergodic theory, to classical number theory. In this talk I will focus on simple groups. Prominent examples to keep in mind are the simple Lie groups over the reals and the simple algebraic groups over p-adic fields. Many more examples are known and happen to enjoy various rich geometric features with a strong flavour of non-positive curvature. The goal of the talk is to explain how the class of non-discrete simple locally compact groups as a whole recently became an independent subject of study, one of whose main challenges is to provide a theoretical framework that would account for the geometric features of those groups in a unified way.