# Difference between revisions of "Spring 2018"

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===Dan Knopf=== | ===Dan Knopf=== | ||

− | Title: Non- | + | Title: Non-Kähler Ricci flow singularities that converge to Kähler-Ricci solitons |

− | Abstract: We describe Riemannian (non- | + | Abstract: We describe Riemannian (non-Kähler) Ricci flow solutions that develop finite-time Type-I singularities whose parabolic dilations converge to a shrinking Kähler–Ricci soliton singularity model. More specifically, the singularity model for these solutions is the “blowdown soliton” discovered by Feldman, Ilmanen, and Knopf in 2003. Our results support the conjecture that the blowdown soliton is stable under Ricci flow. This work also provides the first set of rigorous examples of non-Kähler solutions of Ricci flow that become asymptotically Kähler, in suitable space-time neighborhoods of developing singularities, at rates that break scaling invariance. These results support the conjectured stability of the subspace of Kähler metrics under Ricci flow. |

## Revision as of 16:00, 21 November 2017

## PDE GA Seminar Schedule Spring 2018

date | speaker | title | host(s) |
---|---|---|---|

January 29 | Dan Knopf (UT Austin) | Non-Kähler Ricci flow singularities that converge to Kähler-Ricci solitons | Angenent |

February 5 | Andreas Seeger (UW) | TBD | Kim & Tran |

February 19 | Maja Taskovic (UPenn) | TBD | Kim |

March 5 | Khai Nguyen (NCSU) | TBD | Tran |

April 21-22 (Saturday-Sunday) | Midwest PDE seminar | Angenent, Feldman, Kim, Tran. | |

April 25 (Wednesday) | Hitoshi Ishii (Wasow lecture) | TBD | Tran. |

## Abstracts

### Dan Knopf

Title: Non-Kähler Ricci flow singularities that converge to Kähler-Ricci solitons

Abstract: We describe Riemannian (non-Kähler) Ricci flow solutions that develop finite-time Type-I singularities whose parabolic dilations converge to a shrinking Kähler–Ricci soliton singularity model. More specifically, the singularity model for these solutions is the “blowdown soliton” discovered by Feldman, Ilmanen, and Knopf in 2003. Our results support the conjecture that the blowdown soliton is stable under Ricci flow. This work also provides the first set of rigorous examples of non-Kähler solutions of Ricci flow that become asymptotically Kähler, in suitable space-time neighborhoods of developing singularities, at rates that break scaling invariance. These results support the conjectured stability of the subspace of Kähler metrics under Ricci flow.