# Analysis Seminar

Wasserstein Distance, Fourier Series and Applications

Stefan Steinerberger, Yale University

Friday, January 18th, 2019

1:00 PM - 2:00 PM

Hylan 1106A

1:00 PM - 2:00 PM

Hylan 1106A

Wasserstein Distance (sometimes called Earth Mover Distance) is a natural measure of distance between two probability distributions. We connect it to Fourier Series which then naturally allows for a connection to Analytic Number Theory. We use it to prove that the quadratic residues in a Finite Field are slightly more regular than what the Polya-Vinogradov estimate suggests (in a suitable sense). We then connect it to geometry and use it to prove a Structure Theorem for the zero set of solutions of partial differential equations. There are many open problems and we sketch some of them.

Event contact: hazel dot mcknight at rochester dot edu

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