What kind of mathematical background is needed to understand the demo?

If I want to get you, the reader, up to speed on my research interests, I'll need to start a little ways back. We'll need to talk about a few things surrounding optimal transport (OT), including

• The optimal transport problem: what it is, why it's interesting.
• Kantorovich's solution: a formulation of that makes transport tractable to solve, and remains a key piece of the puzzle for most modern applications of OT (although not in the graph context!)
• The Wasserstein metric: a metric on the space of (appropriately "nice") probability measures that arises out of solutions to the Kantorovich problem
• The Benamou-Brenier formula: a fluid dynamics interpretation of the transport problem, which allows us to think about moving mass around from a PDE point of view
• Barycentric coding models: a way of using OT to do signal processing jobs where classical tools don't fit the bill
• Transport problems on graphs: a situation that breaks some key assumptions about the transport problem in Euclidean space, and the setting of (the most interesting part of) my dissertation work.

I'll try to tackle these ideas one at a time, although several may require a few posts. More to come!