Abstract: Because I will be giving an intentionally vague talk, This will be an intentionally vague abstract. I'll talk about some places where algebraic geometry appears in geometric analysis. This will probably include Grothendieck's theorem on vector bundles over P^1 and an application to a sphere theorem for manifolds with positive isotropic curvature. Additional topics could include how complex hypersurfaces of C^n are area minimizing as codimension 2 real "submanifolds," and puzzling consequences. I will not assume knowledge of differential geometry.