Uploaded August 2026 | Updated September 2026, 2 weeks ago
Singularity Models in 3D Ricci Flow
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Since its introduction by Richard Hamilton in 1982, the Ricci flow has become a fundamental tool in geometry and topology. From the point of view of PDE, the Ricci flow is a system of nonlinear parabolic equations. It can be viewed as the heat equation analogue of the Einstein equations in general relativity. The central problem is to understand singularity formation. In other words, what does the geometry look like at points where the curvature is large? In a spectacular breakthrough in 2002, Perelman achieved a qualitative understanding of singularity formation in dimension 3; this is sufficient for topological conclusions. In this lecture, we will discuss more recent developments which have led to a complete classification of singularity models in dimension 3.
Singularity Models in 3D Ricci Flow
~
Since its introduction by Richard Hamilton in 1982, the Ricci flow has become a fundamental tool in geometry and topology. From the point of view of PDE, the Ricci flow is a system of nonlinear parabolic equations. It can be viewed as the heat equation analogue of the Einstein equations in general relativity. The central problem is to understand singularity formation. In other words, what does the geometry look like at points where the curvature is large? In a spectacular breakthrough in 2002, Perelman achieved a qualitative understanding of singularity formation in dimension 3; this is sufficient for topological conclusions. In this lecture, we will discuss more recent developments which have led to a complete classification of singularity models in dimension 3.
