Algebraic Geometry in an applied setting?

Well, as Grassmannians parameterize vector subspaces of a vector space, they are pretty much in control of any sort of linear thing, like tensors, so at the least, I don't think it's surprising that they come up. As far as sources on the Grassmannians, I wrote a series of posts on the cohomology of Grassmannians at Rigorous Trivialities, and for a more thorough exposition on some of the same stuff, you can check out the last section of Fulton's "Young Tableux." As far as more analytic properties of Grassmannians, I don't have good references, and most of the time algebraic geometers seem to be interested in cohomology (of various sorts) of flag varieties and of using them to make other moduli spaces. Hope this helps.