In order to participate, you should connect to the Zoom conference a few minutes prior to the start of the seminar via the following link: https://zoom.us/j/98737796263?pwd=K3didCtqcUh0N3JJbHVxc09hMGZMZz09 or manually in the Zoom app using the conference ID 987 3779 6263 and the password 277571.In 1878 C. Jordan proved that every finite subgroup G of GLn(C) contains a normal abelian subgroup whose index in G is bounded by a constant that depends only on n, but not on G. Informally speaking, one can interpret this result as boundedness of complexity of finite subgroups of GLn(C), if one assumes that finite abelian groups are easy to understand, and complexity is defined by the structure of a quotient by a normal abelian subgroup. In 2007, J.-P. Serre realized that a similar property holds for finite subgroups of the birational automorphism group of the projective plane, although this group is infinite-dimensional, and its other properties are very different from those of algebraic groups. I will discuss the geometric situations wh ere one meets this kind of boundedness for finite subgroups of automorphism and birational automorphism groups of algebraic and complex varieties.
