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Abstract: The study of tempered representations of Lie groups can be thought of as a generalization of classical Fourier theory. The purpose of this talk will be to illustrate that fact with elementary examples and to explain how the machinery of operator algebras can be used to study the topology of the tempered dual, considered as a "noncommutative space". Time permitting, we will discuss recent applications in representation theory of our approach to the Connes-Kasparov isomorphism. The talk will be accessible to a general mathematical audience.

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Gexin Yu

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