There is seldom much interesting for ML person in this paper. (disclaimer: I haven't made much sense of its goal either. This reminds me of a saying “Write for lay audience, so maybe specialists will understand; Write for specialists, then noone will”)

It's just Bern Strumfels running his research program, which is somewhat obscure even for algebraic geometrers. He is an expert on algorithms of algebraic geometry and their applications e.g. to optimization, and whatnot. There was a thematic school on that, videos should be buried somewhere here, http://www.ima.umn.edu/2006-2007/. This may be interesting line of research—for a mathematician—or ML person willing to learn stacks of pure mathematics leading to fluency with at least the book by Cox, Little and O'Shea just to make sense of labels on buttons.