Cascade Topology Seminar
Prof. Kristine Bauer
612 Campus Place N.W.
University of Calgary
2500 University Drive N.W.
Calgary, AB Canada T2N 1N4
Title: Calculus and Applications: Andre - Quillen Homology
Abstract: Andr\'e-Quillen homology for commutative rings was described by Quillen as the "correct" homology for these rings. We consider the Andr\'e-Quillen homology of a commutative k-algebra R which is augmented over a ring A. Kantorovitz-McCarthy and Schwede independently showed that the Andr\'e-Quillen homology is related to derivative of the augmentation ideal functor from commutative augmented A-algebras to A-modules. In doing so, they used a version of functor calculus due to Johnson-McCarthy which was intended to be more "algebraic" or "discrete" than Goodwillie's original calculus of functors. The theory at the time would only apply to functors from categories which had a basepoint. This kind of calculus was deficient in its need for a basepoint: Goodwillie's original theory did not require a basepoint, and to recover Andr\'e-Quillen homology as an example of calculus a basepoint needed to be added. More recently, Johnson-McCarthy and I have extended the algebraic version of calculus to functors which do not require a basepoint. In this talk, we'll examine potential examples of this type of "unbased" calculus, including the potential of Andr\'e-Quillen homology to be one of these examples.
This work is related to a project by a group of young women topologists led by myself, Maria Basterra and Brenda Johnson at the upcoming WIT (Women in Topology) workshop at the Banff International Research Station. This is a workshop designed to encourage women in homotopy theory to continue in the field. Unlike many other meetings designed to encourage women in mathematics, the goal of this workshop is that every participant will be a joint author on a peer-reviewed article at the end of the workshop.