Functor Calculus, Cartesian Differential Categories, and Operads (22rit268)


(University of Calgary)

Brenda Johnson (Union College)

Sarah Yeakel (University of California, Riverside)


The Banff International Research Station will host the "Functor Calculus, Cartesian Differential Categories, and Operads" workshop in Banff from June 26 to July 3, 2022.

A basic goal of algebraic topology is to find algebraic invariants that classify topological spaces up to various notions of equivalence. Computing such invariants can be extremely difficult, yet can lead to spectacular outcomes. Some of the most acclaimed results in algebraic topology and K-theory in recent years, including Hill, Hopkins and Ravenel’s solution to the Kervaire Invariant One problem and Voevodsky’s use of motivic homotopy theory in resolving longstanding conjectures in K-theory, are founded on such computations.

Broadly speaking, we seek to further these comparisons by
1. finding analogues of theorems from homotopy calculus in abelian calculus,
2. identifying how such theorems area result of the differential category structure in abelian calculus, and
3. generalizing this relationship to create and compare results in various versions of functor calculus.

In the long term, we expect the flow of information to yield a new framework for dealing with unreduced functors in homotopy calculus, a topic with few results and important applications.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).