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Special Colloquium: Einstein metrics and Ricci flow in dimension 4

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Speaker: Tristan Ozuch, MIT
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Location: 2112 MSB
Start time: Tue, Jan 24 2023, 3:10PM

Einstein manifolds and Ricci flow were instrumental tools in answering long standing topological questions in dimension 3. It is now in dimension 4 that most open questions remain, and geometers hope that those same tools will provide some answers. However, Einstein 4-manifolds are still far from being fully understood and many 4-dimensional specific techniques have yet to be applied to Ricci flow. I will motivate Einstein metrics and the Ricci flow approach to topology and discuss what are some of the main difficulties and specificities of dimension 4. I will present my work on the degeneration of Einstein 4-manifolds, some of the questions it answers and the new directions it opens. I will finally discuss new aspects of a 4-dimensional-specific theory of Ricci flow.