Distinguished Lecture ——Collapsed manifolds of local Ricci bounded covering geometry

Speaker: Xiaochun Rong

Venue: Lecture Hall 210, Haina Complex Building 2, Zijingang Campus

Abstract: Fixing E> 0, a complete Riemannian n-manifold M is called E-collapsed, if every unit ball in M has a volume <E. In Riemannian geometry, interplays between a collapsing geometry and topology has been an important component, 

and complexities in topology of a collapsed M is linked to a bound on curvature. Around 1980-2000, collapsed

manifolds of bounded sectional curvature was intensively studied by Cheeger-Fukaya-Gromov and many others, 

which has found several applications. In this talk, we will survey a development in the last decade in investigating collapsed manifolds of Ricci curvatureb ounded below and universal covering of every unit ball in M is not collapsed.