Speaker: Xiaochun Rong
Abstract. Fixing ϵ > 0, a complete Riemannian n-manifold M is called ϵ-collapsed, if every unit ball in M has a volume < ϵ. 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 report a recent progress in investigating a collapsed manifold M of sectional curvature bounded below and universal covering of every unit ball in M is not collapsed.
Time: 16:00~17:00, Tuesday, Jun. 3, 2025
Location: Room 1610, SIMIS
Brief introduction of speaker: 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 Metric Riemannian Geometry and Geometric Analysis, where he has published 56 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.
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