报告摘要：
Fixing $\epsilon > 0$, a complete Riemannian $n$-manifold $M$ is called $\epsilon$-collapsed, if every unit ball in $M$ has a volume <$\epsilon$. 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, which has found several applications.
In this talk, we will survey a development in the last decade in investigating collapsed manifolds of Ricci curvature bounded below and universal covering of every unit ball in $M$ is not collapsed.
报告人简介：
Xiaochun Rong received his undergraduate and master's degrees from Capital Normal University (1977–84), and a Ph.D. from State University of New York at Stony Brook in 1990. Rong was a Ritt assistant professor at Columbia University (1990–94), and an assistant professor at University of Chicago (1994–96). Since 1996, he has been a faculty at Rutgers University, and a distinguished professor since 2008. Professor Rong's research fields are in Differential Geometry and Metric Riemannian Geometry, where he has published 55 papers; 25 were in the following journals: Adv. Math., Amer. J. Math., Ann. of Math., Duke Math., GAFA, Invent. Math., J. Diff. Geom. Rong received a Sloan Research Fellowship (1996–98), was a 45-minute speaker at 2002 International Congress of Mathematicians, and became a fellow of the American Mathematical Society in 2017.
