Abstract: 

The interplay between curvature and topology is always one of the central topics in Riemannian geometry. For open (noncompact and complete) manifolds with nonnegative Ricci curvature, it is known that the fundamental groups could be torsion-free nilpotent. This is distinct from open manifolds with nonnegative sectional curvature, whose fundamental groups are virtually abelian. This talk will cover how the virtual nilpotency/abelianness of the fundamental group is related to the equivariant asymptotic geometry.

Bio: 

Jiayin Pan is currently an assistant professor of mathematics at University of California, Santa Cruz. He obtained his Ph.D. degree in 2018 from Rutgers University, New Brunswick, advised by Xiaochun Rong. He works in Riemannian geometry; more precisely, the interplay between Ricci curvature and topology, (equivariant) Gromov-Hausdorff convergence, and Ricci limit spaces.

Video：http://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=Nonnegative_Ricci_curvature_nilpotency_and_asymptotic_geometry.html