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Topology/Geometry Seminar

Ricci solitons in low dimensions---a survey

Ben Chow (UC San Diego)

Location:  Hill 705
Date & time: Tuesday, 30 April 2024 at 4:00PM - 5:00PM

We will survey various works on Ricci solitons, with an emphasis on low dimensions. Ricci solitons are self-similar solutions to the Ricci flow, when we factor in the action of the diffeomorphism group of a manifold on the space of metrics on that manifold. There are three types of Ricci solitons: shrinking, steady, and expanding. The first two are related to the local geometry of solutions to the Ricci flow going into a singularity and the latter to the local geometry coming out of a singularity. In dimensions 2 and 3 there is an almost complete classification of Ricci solitons. In higher dimensions, the picture is much more unclear and thus an interesting direction for future research.

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