permitted kernel functions, cosmology therewith

I spent a while at the group meeting of applied mathematician Leslie Greengard (NYU, Simons Foundation), telling the group how cosmology is done, and then how it might be done if we had some awesome math foo. In part we got on to how you could make a non-parametric kernel function for a Gaussian Process for the matter density field at late times, given that you need to stay non-negative definite. Oh wait, I mean positive semi-definite. Oh the things you learn! Anyway, it turns out that this is not really a solved problem and possibly a project was born. Hope so! I would love to recreate our discovery of the baryon acoustic feature with proper inference. At the group meeting, Foreman-Mackey and I had an "aha moment" about Ambikasaran et al's method for solving and taking the determinants of kernel matrices (Siva Ambikasaran (NYU) was in attendance), and then spent the post-group-meeting lunch in part quizzing Mike O'Neil (NYU) about how to structure our code to work fast in the three-dimensional case (the cosmology case).

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