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November 2017

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## Thomas Beck (MIT), Analysis & PDE Seminar

Title: Ground state eigenfunctions on convex domains of high eccentricity Abstract: In this talk, I will discuss the ground state eigenfunction of a class of Schrödinger operators on a convex planar domain. We will see how to construct two length scales and an orientation of the domain defined in terms of eigenvalues of associated differential operators. These length scales will determine the shape of the intermediate level sets of the eigenfunction, and as an application allow us to deduce properties…

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