Ricci flow and Ricci Limit Spaces

Abstract

I survey some of the developments in the theory of Ricci flow and its applications from the past decade. I focus mainly on the understanding of Ricci flows that are permitted to have unbounded curvature in the sense that the curvature can blow up as we wander off to spatial infinity and/or as we decrease time to some singular time. Applications to the study of Ricci limit spaces are surveyed. I emphasise the intuition behind the subject.

Lectures given at the summer school on "Geometric Analysis" at Cetraro in June 2018. To appear in Springer Lecture Notes in Mathematics, CIME subseries. Numbering of theorems etc has changed in v2 in an attempt to match Springer style