## Algebraic K-Theory Seminar

Akhil Mathew

Harvard

Polynomial functors and algebraic K-theory

**Abstract:**The Grothendieck group K_0 of a commutative ring is well-known to be a \lambda-ring: although the exterior powers are non-additive, they induce maps on K_0 satisfying various universal identities. The \lambda-operations yield homomorphisms on higher K-groups. In joint work in progress with Barwick, Glasman, and Nikolaus, we give a general framework for such operations. Namely, we show that the K-theory space is naturally functorial for polynomial functors, and describe a universal property of the extended K-theory functor. This extends an earlier algebraic result of Dold for K_0. In this picture, the \lambda-operations come from the "strict polynomial functors" of Friedlander-Suslin.

Wednesday January 11, 2017 at 1:00 PM in SEO 1227