Spring 2018

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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.