College of Liberal Arts and Sciences

# Department of Mathematics

## PDE and Differential Geometry Seminar

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Title: A uniqueness theorem for asymptotically cylindrical shrinking Ricci solitons
Speaker: Brett Kotschwar (Arizona State University)
Time: Monday, October 23, 2017 at 2:30 pm
Place: MONT 214Abstract: Shrinking Ricci solitons are generalized fixed points of the Ricci flow equation and models for the geometry of solutions to the flow in the neighborhood of a developing singularity. It is conjectured that every four-dimensional complete noncompact shrinking soliton is smoothly asymptotic to either a cone or a standard cylinder at infinity . I will discuss recent joint work with Lu Wang related to this conjecture in which we prove that a shrinking Ricci soliton which is asymptotic to infinite order along some end to one of the standard cylinders $S^k\times {\mathbb{R}}^{n-k}$ for $k\geq 2$ must actually be isometric to the cylinder on that end.

Organizer: Lihan Wang