Wasserstein Distance as a Tool in Analysis

Applied Math And Analysis Seminar

Stefan Steinerberger (Yale University)

Wednesday, April 24, 2019 -
12:00pm to 1:00pm
Location: 
Physics 119

Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.

Last updated: 2019/04/23 - 6:13am