MSCS Graduate Student Seminar

Fall 2000

October 27 and November 3

SPEAKER: Peter Shalen
TITLE: Topology in three dimensions I & II
ABSTRACT: The traditional objects of study in differential geometry are curves, surfaces, and their generalizations to arbitrary dimenions, known as manifolds. It has been recognized since the time of Gauss that the topological invariants of a manifold impose restrictions on its geometry. This is one of the reasons why the study of the topology of manifolds has attracted the attention of so many mathematicians for the last 100 years. While progress on the topological theory of manifolds in all dimensions has been remarkable, the theory turns out to be especially rich in dimension 3 because of its uniquely close interaction with the geometric theory. I will try to communicate something of the flavor of the subject.