Sunday April 25th, 2021 | |
| Contact Name: | Simon Donaldson, SCGP, Stony Brook University, and Imperial College, London |
| Details: | |
| Hitchin formulated the equations for $G_{2}$ holonomy in seven dimensions and Calabi-Yau structures in six dimensions in terms of variational problems for closed 3-forms. We will discuss versions of these ideas for manifolds with boundary. In the second case this leads to a mapping problem for maps from a five dimensional manifold to ${\bf C}^{3}$ which is related to CR geometry, contact geometry and four-dimensional Riemannian geometry and has a dimension reduction to the classical Minkowski problem for convex surfaces in 3-space. http://www.math.stonybrook.edu/geomfest/ | |