The London Mathematical Society funds a number of networks in pure mathematics, enabling regular meetings of research mathematicians to allow them to collaborate on areas of shared interest.

Groups are core to algebra, and their study now covers a wide range of techniques. Modern advances in group theory utilise categories to study properties for finite and infinite groups alike. Results obtained using categories such as fusion systems have allowed significant progress in the local-global study of finite groups, while Mackey functors and Bredon cohomology have been a major feature of the functorial study of groups, leading to major advances also in neighbouring areas such as algebraic topology, representation theory and K-theory in particular.

The four nodes of the network are Lancaster, Royal Holloway, University of London, Lincoln and Cambridge and the corresponding organisers are Nadia Mazza (Lancaster University), Brita Nucinkis (Royal Holloway, University of London), Anitha Thillaisundaram (Lincoln) and Rachel Camina (Cambridge).

The next meeting, entitled "Cohomology of functor categories for topological groups" will be held in December 2017, at Royal Holloway, University of London and will focus on new developments in the cohomology of totally disconnected topological groups as well as profinite and pro-p groups.