Mathematics Department Colloquium
Spring 2005

Date: Thursday, March 17
Time: 4:00 p.m.
Location: 215 Thomas Building
Name: A.B. Sossinsky
Affiliation: Independent University of Moscow
Title: Could the Poincaré conjecture be false?

Abstract: Despite rumors that the Poincaré conjecture has been solved (by Grisha Perelman), an approach to DISPROVING the conjecture will be described. The approach is NOT an attempt to devise a specific counterexample, but is based on an unexpected relationship between algorithmically undecidable problems in group theory and three-dimensional topology; this relationship will be explained. It will also be explained that recent work of S. Matveev shows that counterexamples, if they exist, are too complicated to be found "by hand", and the chances of finding a counterexample by computer will also be discussed.