Department Colloquium: Young-Heon Kim

Probability measures are key objects in many scientific and engineering areas that deal with randomness, distributions, data sets, etc. When coupled with optimization, many interesting questions naturally arise. In this talk, I will explain a few of such questions from the point of view of optimal transport theory, which gives a natural and robust framework for studying probability measures. These involve among others, matching probability measures in an optimal way following certain rules (e.g martingale), as well as finding geometric averages between probability measures.