# CMX Lunch Seminar

*,*Instructor

*,*Applied Mathematics

*,*Columbia University

*,*

Amir is currently an Instructor (starting a termed assistant professorship on July 2020) at the Department of Applied Physics and Applied Mathematics in Columbia University. Before that, he was an Applied Mathematics Ph.D. student in Tel Aviv University's School of Mathematical Sciences, under the supervision of Gadi Fibich and Adi Ditkowski. He obtained his M.Sc. in Mathematics at Tel Aviv University, and his B.Sc. in Mathematics and Physics at the Hebrew University of Jerusalem. He is interested in differential equations, dynamical systems, optics and wave phenomena, uncertainty quantification, and mathematical analysis in general.

In many scientific areas, a deterministic model (e.g., a differential equation) is equipped with parameters. In practice, these parameters might be uncertain or noisy, and so an honest model should account for these uncertainties and provide a statistical description of the quantity of interest. Underlying this computational problem is a fundamental question - If two "similar" functions push-forward the same measure, are the new resulting measures close, and if so, in what sense? In this talk, I will first show how the probability density function (PDF) can be approximated, and present applications to nonlinear optics. We will then discuss the limitations of PDF approximation, and present an alternative Wasserstein-distance formulation of this problem, which through optimal-transport theory yields a simpler theory.