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Graduate Seminar
Paul McKenney Carnegie Melllon University Title: The Banach Tarski Paradox Abstract: The Banach Tarski "paradox" is a theorem which states that the unit ball in R^3 (ie Euclidean space) can be partitioned into finitely many pieces which can be rearranged using rotations and translations to form two disjoint copies of the same unit ball. The standard proof makes heavy use of the axiom of choice, and after going through this proof Ill discuss why this is necessary. However, many people in the field of geometric group theory believe that the Banach Tarski paradox is more an expression of the paradoxical nature of the free group on two generators; Ill try to explain their point of view, and in the process prove some theorems about amenable groups. Date: Tuesday, October 19, 2010 Time: 5:30 pm Location: Wean Hall 8220 Submitted by: Daniel Spector 