Wasserstein Distance between Point Sets and the Lebesgue Measure

Wasserstein Distance between Point Sets and the Lebesgue Measure

Frontiers In Mathematics Seminar

Stefan Steinerberger (Yale University)

Friday, November 22, 2019 -
12:00pm to 1:00pm
Location: 
119 Physics

We describe some recent results regarding the Wasserstein distance between specific sets of points and the Lebesgue measure. This can be understood as a measure of regularity; we describe a Fourier-analytic perspective that allows us to connect to Analytic Number Theory. We revisit the old problem of Numerical Integration of Lipschitz function in the unit cube and refine a 1959 result that was considered sharp. These problems have a funky interpretation: if you are trying to open a coffee shop chain, then you have to start with a few shops at first and then expand. This means the first store should be centrally located; by induction, the first N stores that you open should be well-distributed (with regards to the measure of the coffee-drinking population). Joint work with Louis Brown.

Last updated: 2019/11/18 - 10:29pm