A Practical Tour of Computational Optimal Transport

In the late 1700s, the French mathematician Gaspard  Monge, began the mathematical field of optimal transport by considering the question: What is the most efficient way to transport dirt when constructing a road or fort? This simple question has spawned the field of optimal transport, which was generalized by Kantorovich in the early 1900s and has exploded in recent decades with the invention of efficient computational techniques for solving many optimal transport problems.  Uses of optimal transport can now be found in the training of deep neural networks, the low dimensional embedding of high dimensional datasets, velocimetry, quantization, and many other fields. This talk will provide a cursory overview of optimal transport. Applications in image analysis and inverse problems, especially those arising in sea ice modeling, will be used to motivate several optimal transport problems and the computational techniques used to solve them.