Title: The algebraic De Rham complex and calculus
Speaker: Kristine Bauer (University of Calgary)
Abstract: Differentiation is one of the most familiar processes in mathematics and it is pervasive. In algebra, the Kahler differentials are the adaptation of differential forms for commutative rings. In fact, for polynomial rings forming the Kahler differentials corresponds exactly to taking the derivative of polynomial functions. The Kahler differentials are essential to the construction of the de Rham complex, which contains rich information about a commutative ring or algebra. To what extent should these homological tools be considered as analogues or consequences of differentiation? In this talk we present two possible approaches to this question. The first approach uses Goodwillie’s functor calculus, which is very strongly analogous to the Taylor series of a function, but for functors. The second approach uses Blute, Cockett and Seely’s differential categories. Both of these approaches can be used to explain how the interpretation of the Kahler differentials as derivatives is more than mere analogy. In this talk, I will explain these two generalizations of differentiation and to what extent they are related.
Seminar URL: https://www.asc.ohio-state.edu/fontes.17/homotopy_seminar/
