Jordan groups

The notion of abstract Jordan group introduced in 2010 has been inspired by the classical Jordan theorem of 1878 and Serre's theorem of 2008. It appeared to be fruitful in the context of such classical directions of algebraic geometry and differential topology as studies of finite subgroups of groups of biregular or birational automorphisms of algebraic varieties and groups of diffeomorphisms of topological smooth manifolds. This concept brings in these studies a "social" aspect of qualitative properties of all such subgroups together. The last two years are marked by increasing activity in this direction.