Fourier-S21


Fourier Institute Summer School 2021

on Curvature Constriants and Spaces of Metrics


Intrinsic Flat and Gromov-Hausdorff Convergence

Christina Sormani

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


Lecture 1 Slides


Lecture 2 Slides


Lectures 3&4 Slides


Video Playlist on Youtube


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

Lizhi Chen

Andrea Drago

Jason Ledwidge is working separately on a related project.