Title:  Spectral Partitions for One-Dimensional Schrödinger Operators

Speaker: Anmol Lorenz, Memorial University

Abstract: Spectral partition problems study how a space should be divided when each part is assigned a spectral quantity. In this talk, I will focus on partitions of intervals and circles, where each cell carries the first Dirichlet eigenvalue of a one-dimensional Schrödinger operator. Starting from the elementary case of the Dirichlet Laplacian on an interval, I will explain how non constant potentials change the geometry of the problem. I will then discuss how different partition energies lead to different balance conditions between neighbouring cells, and how these conditions can produce more than one critical partition. The final example will be a large-amplitude cosine potential exhibiting this multiplicity.

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Location: HH3017

Date and Time: Friday, Jul. 10 at 01:00 PM - 01:50 PM (NDT)

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