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  • Thanks for your valued comment, Mashbat. I've backgrounds in advanced Riemannian geometry, PDE, and Riemann surfaces, but not exactly geometric analysis, which deals with more analysis than Riemannian geometry. I've switched to computational neuroscience with applications of diff. geo., but I'd be definitely curious to know more about what kind of problems they handle in manifold learning that deal with Riemannian geometry. Commented Mar 5, 2015 at 12:47