Time: Tuesday, Nov.6th, 2018, 2:00pm @ MTH3206

Speaker: Stefan Steinerberger (Yale)

Title: Oscillations of Fourier series, Quantitative Sturm-Liouville Theory and Applications

Abstract: The function f(x) = a*sin(12*x) + b*sin(28x) has always between 24 and 56 roots (unless a=b=0). This follows from a classical theorem of Sturm (1836) that has been forgotten and was recently rediscovered by Berard & Helffer. I will tell the (quite fascinating) story behind it, give a simple proof and discuss quantitative refinements, newly emerging connections to elliptic PDEs and the beginning of a Sturm-Liouville theorem in higher dimensions.

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