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Mathematics Colloquium


Date:  Tuesday, November 06, 2007

Title:  Large scale index theory

Abstract:  The Atiyah Singer index theorem relates analysis and topology through the crucial notion of the Fredholm index of an elliptic operator (this is basically linear algebra: the difference between how much existence and how much uniqueness there is for solutions of a given equation). In this talk I will explain how forming the index can be viewed as a process of coarsening forgetting small scale structure. This leads to new versions of the index theorem on spaces that lack the compactness property necessary for the usual elliptic/Fredholm theory. The talk will be accessible to graduate students.

Speaker:  John Roe
Institution:  Penn State University


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