First of all, please, note the new Zoom address for the next talk only (we'll return to our regular Zoom address after that):
https://arizona.zoom.us/j/88142390041
No password
The next talk at our seminar by Robert McCann, Toronto "Optimal transportation between unequal dimensions" is this coming Tuesday, February 22, 2022 at 12PM EST (8pm in Moscow, 6pm in Europe, 12noon in Toronto, 10am in Tucson, 9am in LA).
Abstract: In the last few decades, the theory of optimal transportation has blossomed into a powerful tool for exploring applications both within and outside mathematics. Its impact is felt in such far flung areas as geometry, analysis, dynamics, partial differential equations, economics, machine learning, weather prediction, and computer vision. The basic problem is to transport one probability density onto other, while minimizing a given cost c(x,y) per unit transported. In the vast majority of applications, the probability densities live on spaces with the same (finite) dimension. After briefly surveying a few highlights from this theory, we focus our attention on what can be said when the densities instead live on spaces with two different (yet finite) dimensions. Although the answer can still be characterized as the solution to a fully nonlinear differential equation, it now becomes badly nonlocal in general. Remarkably however, one can identify conditions under which the equation becomes local, elliptic, and amenable to further analysis.
--
FROM 37.61.213.*