Title: Simplicial Functor Calculus
Speaker: Rhiannon Griffiths
Abstract: Functor calculus is a categorification of differential calculus. In Goodwillie's original series of papers smooth functions are replaced by homotopy functors between categories of spaces and spectra. His results have since been generalised to the broader context of simplicial homotopy theory. In the recent Johnson-McCarthy discrete calculus, a homotopy functor is approximated by a universal degree n-functor, analogous to the degree n-approximation of a smooth function. We define degree n-approximations for simplicial functors, together with corresponding degree n-model structures on simplicial functor categories This is joint work with Lauren Bandklayder, Julie Bergner, Brenda Johnson and Rekha Santhanam.