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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 that the Ricci tensor has an eigenvalue with multiplicity 3. This talk is based on the joint work with Huai-Dong Cao.

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Organizers: 林俊吉教授、郭庭榕教授、張樹城教授