Oct 31

Title: Four-dimensional complete gradient shrinking Ricci solitons with half positive isotropic curvature

Speaker: Junming Xie (Rutgers-New Brunswick)

Abstract:  In this talk, we will discuss the geometry of 4-dimensional complete gradient shrinking Ricci solitons with half positive isotropic curvature (half PIC) or half nonnegative isotropic curvature. We prove a certain form of curvature estimates for such Ricci shrinkers, including a quadratic curvature lower bound estimate for noncompact ones with half PIC. As a consequence, we classify 4-dimensional complete gradient shrinking Ricci solitons with half nonnegative isotropic curvature, except the half PIC case. We also treat the half PIC case under an additional assumption on the Ricci tensor. This talk is based on the joint work with Huai-Dong Cao.