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Geometric Analysis and Partial Differential Equations Seminar
May 17, 2013 @ 10:30 am - 11:30 pm
Dr. Glen Wheeler(University of Wollongong)
An introduction to Chen’s conjecture and submanifolds of finite type
Chen’s conjecture is a curiosity which arose in the course of his grand scheme to classify all submanifolds of Euclidean space. While this lofty program is nowhere near completion, work on the conjecture in its original form is almost at an end. In this talk I will take Chen’s original path to his conjecture, which begins with jealousy of the Order from Algerbraic Geometry, goes through an unusual application of spectral resolution of the Laplacian from Functional Analysis, to end up with a beautiful nonlinear system of partial differential equations. After arriving at the conjecture, I will quickly overview progress on it in its original form, including recent solutions (joint work with V.-M. Wheeler and Y. Bernard). My talk is designed to be accessible and elementary, and will not require anything difficult, scary or intimidating to understand.