Pro-<em>p</em> Extensions of Global Fields and pro-<em>p</em> Groups

Abstract

The meeting \emph{Pro-$p$ Extensions of Global Fields and pro-$p$ Groups} was organised by Nigel Boston (Madison), John Coates (Cambridge) and Fritz Grunewald (D\"{u}sseldorf). As the name of the meeting conveys, a primary aim was to bring together group theorists working in the field of pro-$p$ groups and number theorists interested in pro-$p$ extensions of global fields. The workshop consisted of over $25$ talks, supplemented by informal discussions. Topics included: Galois groups of extensions with restricted ramification, self-similar and automata groups, non-commutative Iwasawa theory, groups acting on rooted trees. This meeting was well attended with over $50$ participants; more than $30$ of these came from countries other than Germany. The range of topics and the diverse backgrounds of the participants led to a stimulating exchange of recent results, challenging problems and general ideas. The organisers and participants thank the \emph{Mathematisches Forschungsinstitut Oberwolfach} for providing the setting for this successful workshop. The following extended abstracts appear in the chronological order of the talks; they were collected and edited by Benjamin Klopsch (D\"{u}sseldorf).