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Tuesday, March 17, 2015

**Abstract:** Analytic functors from based spaces to spectra can be classified via modules over the Koszul duals of the E_n-operads. The goal of this talk is to outline this classification and then to consider how Waldhausen's algebraic K-theory functor A(X) fits into it. In particular we will show that the derivatives of A(X) have the structure of a module over the Koszul dual of E_3. This is joint work with Greg Arone. If there is time, I will describe work in progress with Andrew Blumberg to describe the structure on the derivatives of algebraic K-theory as a functor of associative or commutative ring spectra.