William Browder served as President of the American Mathematical Society during 1990-1991. This videotape contains his Retiring Presidential Address--which combined short remarks about his presidency with a mathematical lecture--preceded by an informal interview in which he discusses a range of topics, including public awareness of mathematics and his interest in music. The lecture discusses the action of finite groups on manifolds, exploring the question of how large a finite group can effectively act on a given manifold (here, "effectively" means that there is no subgroup that fixes everything). A related question is, what kind of spaces have the given manifold as a covering space? Beginning with the historical roots of these questions, Browder concentrates on familiar examples such as the sphere, the \(n\)-sphere, or a product of spheres of different dimensions. The lecture is accessible to mathematics majors with background in algebraic topology. The interview segment provides a fine complement to the lecture.

Reviews

"The reviewer recommends enthusiastically this tape to the mathematical community, in particular those interested in algebraic topology and its applications to transformation groups."

-- Zentralblatt MATH