John Meier
Lafayette College

From Poincare to Perelman: An Introduction to Classifying Manifolds

Abstract: Here's a question: What's the shape of space? If that one seems too hard, you might tackle: What possible shapes could our universe take? These are grand questions but it appears that they might not be completely intractable. In fact, following on ideas of some famous mathematicians (Bill Thurston and Richard Hamilton), Grisha Perelman has recently announced a solution to the second problem. In addition to glory and honor, if his work holds up under close examination, Perelman will get a million dollars from the Clay Mathematics Institute. I will try to give some idea of the principal mathematical objects under discussion (3-manifolds), some of the historical development of the subject, and perhaps a hint at Perelman's approach.