Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo
"An exercise in Riemannian geometry (or how to make a Riemannian geometric omelet without breaking any eggs)"
I will describe a particular class of Riemannian metrics on the total space of a vector bundle, depending only on one natural coordinate $r$, and which are thus of cohomogeneity one. Such metrics arise frequently in the study of special holonomy, By carefully thinking before diving in, one can extract many useful formulas for such metrics without needing to explicitly compute all of the Christoffel symbols and the curvature. For example, these include the rough Laplacian of a function or of a vector field which are invariant under the symmetry group. If time permits, I will explain why I care about such formulas, as they are ingredients in the study of cohomogeneity one solitons for the isometric flow of $\mathrm{G}_2$-structures.
MC 5403