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Monday, April 13, 2015

**Abstract:** Let G be a group and H a subgroup. Frobenius showed in 1898 how to "enlarge" a representation of H to a representation of G. His method, now called induction, rapidly became a useful tool in algebra and analysis and was adapted by others in various ways. For instance, in 1965 Bott made a systematic study of induction methods based on elliptic differential operators in the context of compact Lie groups, which led to generalizations of the Weyl character formula. I will review and update Bott's work and discuss some applications to K-theory. This is a report on joint work with Greg Landweber.