Date: Wednesday, January 04, 2017
Location: 4096 East Hall (4:10 PM to 5:30 PM)
Title: Polynomial functors and algebraic Ktheory
Abstract: The Grothendieck group K_0 of a commutative ring is wellknown to be a \lambdaring: although the exterior powers are nonadditive, they induce maps on K_0 satisfying various universal identities. The \lambdaoperations are known to give homomorphisms on higher Kgroups.
In joint work in progress with Barwick, Glasman, and Nikolaus, we give a general framework for such operations. Namely, we show that the Ktheory space is naturally functorial for polynomial functors, and describe a universal property of the extended Ktheory functor. This extends an earlier algebraic result of Dold for K_0. In this picture, the \lambdaoperations are precisely those given by the "strict polynomial functors" of FriedlanderSuslin.
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Speaker: Akhil Mathew
Institution: Harvard University
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