Ricci Solitons in Dimension 4

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Bennet Chow , UCSD & IAS

In this talk, we will survey progress on Ricci solitons in dimension 4. Ricci solitons, which are self-similar solutions to the Ricci flow, play a central role in singularity analysis for Ricci flow. Singularity analysis is crucial for understanding how to extend Ricci flow past singularities and for potential topological applications. In Bamler’s theory, singularity models are generically shrinking solitons, though steady solitons can also appear as singularity models. Munteanu and Wang have developed a comprehensive theory for studying shrinking and steady solitons in dimension 4. Additionally, we will discuss both recent and older works by Bamler, Chan, Deng, Freedman, Lu, Ma, Shin, Yang, and Zhang.