Orthogonal calculus is a version of functor calculus that sits at the interface between geometry and homotopy theory; the calculus takes as input functors defined on Euclidean spaces and outputs a Taylor tower of functors reminiscent of a Taylor series of functions from differential calculus. The interplay between the geometric nature of the functors and the homotopical constructions produces a calculus in which computations are incredibly complex. These complexities ultimately result in orthogonal calculus being an underexplored variant of functor calculus.
On the other hand, homological localizations are ubiquitous in homotopy theory. They are employed to split ‘integral’ information into ‘prime’ pieces, typically simplifying both computation and theory.
In this talk, I will describe a ‘local’ version of orthogonal calculus for homological localizations, and survey several immediate applications.
This talk relates to this arXiv paper.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
