PDE Geometric Analysis seminar

The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.

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 12	Sam Krupa (UT-Austin)	TBD	Lee
February 19	Maja Taskovic (UPenn)	TBD	Kim
March 5	Khai Nguyen (NCSU)	TBD	Tran
March 12	Hongwei Gao (UCLA)	TBD	Tran
March 19	Huy Nguyen (Princeton)	TBD	Lee
April 9	reserved	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.