Geometric Regularity of Singularity Models of the Kähler-Ricci Flow

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Max Hallgren, Rutgers University
Fine Hall 314

One way to understand singularities of Ricci Flow is to zoom in near a singularity and study the subsequential limits, called singularity models. In this talk, we will discuss new results on the structure of singularity models in the setting of complex projective manifolds, building on recent estimates developed by W. Jian, J. Song, and G. Tian. We will see a new differential Harnack inequality for the heat equation coupled to the Kähler-Ricci Flow and how such an estimate may be applied to prove distance distortion estimates. We will also discuss the consequences of these estimates for singularity models of projective Kähler-Ricci Flows, including their continuity in time and a more precise description of their infinitesimal structure.