Fourier Institute Summer School 2021
on Curvature Constriants and Spaces of Metrics
Intrinsic Flat and Gromov-Hausdorff Convergence
CUNYGC and Lehman College
Abstract: We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and theorems that may be applied to prove these open questions including older techniques developed with Lakzian, with Huang and Lee, and with Portegies. I will also present key new results of Allen and Perales. Students and postdocs interested in working on these problems will be formed into teams. For a complete list of papers about intrinsic flat convergence see: https://sites.google.com/site/intrinsicflatconvergence/
Course Notes: arXiv preprint: Convergence and Scalar Curvature
Students who wish to work on any of the problems suggested in this series of lectures may contact me (sormanic at gmail).
So far the following team is meeting on Friday mornings:
Edward Bryden
Mauricio Che-Moguel
Jason Ledwidge is working separately on a related project.