Created by Gauss to take account of the curvature of the Earth in surveys of large areas in Germany, differential geometry with its notion of curvature was extended to spaces of arbitrary dimension by Riemann, and found significant application in dimension 4 in Einstein’s general relativity. It has also developed many connections with complex analysis, algebraic geometry, PDE, and other areas of mathematics. Members of our department study curvature and the Ricci tensor, geometry of symmetric spaces and compact 2-step nilmanifolds, rough metric tensors, Gromov-Hausdorff convergence, and connections with PDE.