The Department of Mathematics and Statistics provides excellent undergraduate programs, as well as advanced instruction at the graduate and research levels. Find out more about our degree programs.
October 24, 2016 3:30 PM
Presented by : Kristine Bauer, University of Calgary
Topic : Calculus of functors and the De Rham complex
The calculus of functors, pioneered by Goodwillie in the 1980’s, refers to a way of examining functors which topologists and algebraists often use to distinguish and classify algebraic or topological objects like algebras. The De Rham complex of a commutative algebra over a field, the algebraic analogue of De Rham cohomology of a manifold, is precisely one of these functors. The De Rham complex is closely related to cohomology theories for non-commutative algebras, such as cyclic (co)homology and crystalline cohomology. Goodwillie and Waldhausen observed that the De Rham complex can be thought of as Taylor tower, in the sense of functor calculus, of a certain forgetful functor. Making this observation precise lead my coauthors (Eldred, Johnson and McCarthy) and me to develop a new kind of functor calculus tower. In this talk, I will explain how this new tower works and how it recovers the De Rham complex, and how this suggests another possible model for functors related to non-commutative algebras.