The infranil fiber bundle is a typical structure appeared in the collapsing geometry with bounded sectional curvature. In this talk, I will discuss a topological condition on the first Betti numbers that guarantees a torus fiber bundle structure (a special type of infranil fiber bundle) for collapsing manifolds with only Ricci curvature bounded below. A major technique applied here is smoothing by Ricci flows. This is a joint work with Bing Wang.

Bio: Shaosai Huang is currently working as a postdoc in the University of Wisconsin - Madison, USA. He earned his doctorate from Stony Brook University in 2018, under the supervision of Xiuxiong Chen. Shaosai studies the convergence and degeneration of Riemannian manifolds with approporiate conditions on the Ricci curvature.