An introduction to orthogonal and unitary homotopy calculi

01/02/2019, 14:00 - 15:00 in MAP/0G/018

Taggart, Niall (Queen’s University Belfast)

Abstract:

Orthogonal calculus was developed in the 1990s as a tool to study functors from the category of real vector spaces to the category of (based) topological spaces. One inputs a functor F, and the calculus outputs a tower of polynomial approximations of F similar to Taylor’s Theorem in the smooth calculus setting. Moreover, the difference between successive polynomial approximations is a topological space built from the derivatives of the inputted functor which is easy to understand. In recent years unitary calculus has developed as a natural analogue to study functors from the category of complex vector spaces to the category of (based) topological spaces.

In this talk, I plan to introduce and motivate the calculi by discussing examples from a geometric viewpoint.