Ancient solutions of curvature flows with cylindrical backward limits

Near their singularities, the solutions of curvature flows are modeled by ancient solutions; special solutions defined for all sufficiently negative t. Even though it currently seems hopeless to try to classify all ancient solutions, it is generally believed that in many important cases and at least generically there aren't too many of them. In this talk we will review some examples and classification results of ancient solutions with a focus on the structure of their backward limits, and discuss a joint work with Zilu Ma and Natasa Sesum for the case of "wing-like" solutions of 4 dimensional Ricci flow.

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