Danny Gillam will give the talk on Tuesday, September 13 at 4:15 in Math 622. This lecture will be open to all.
Abstract: We'll discuss (without proof) several problems of the form: Given two sets A, B \subseteq R^n (satisfying various properties), is it possible to partition them into subsets which are pairwise isometric (or pairwise isometric via certain types of isometry). For example, the Banach-Tarski paradox answers such a question. Clearly these questions are related to questions of the form: Is there a (certain kind of) measure on (various subsets of) R^n which is invariant under (certain kinds of) isometry?
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