Abstract

Many manifolds of interest are equipped with a geometrical structure specified by a distinguished closed form. We will motivate the usefulness of considering pairs of differential forms that are linked together by a map of the distinguished form. We will show how this lead to new notions of Morse theory and flat connections, and also novel Yang-Mills type functionals. This talk is based on joint works with David Clausen, Xiang Tang, and Jiawei Zhou.